2 2

HIGHWAY R E S E A R C H B O A R D

Bulletin 222

Highway Investment

and Financing

ational Academy of Sciences—

National Research Council p u b l i c a t i o n 6 8 2

HIGHWAY RESEARCH BOARD Officers and Members of the Executive Committee

1 9 5 9

HARMER E . DAVIS, Chairman P Y K E JOHNSON, First Vice Chairman W. A. BuGGE, Second Vice Chairman

F R E D BURGGRAF, Director E L M E R M . WARD, Assistant Director

E x e c u t i v e C o m m i t t e e

B E R T R A M D . T A L L A M Y , Federal Highway Administrator, Bureau of Public Roads (ex officio)

A . E . J O H N S O N , Executive Secretary, American Association of State Highway Officials (ex officio)

L O U I S JORDAN, Executive Secretary, Division of Engineering and Industnal Research, National Research Council (ex officio)

C . H . SCHOLER, Applied Mechanics Department, Kansas State College (ex officio, Past Chairman 1958)

R E X M . W H I T T O N , Chief Engineer, Missouri State Highway Department (ex officio, Past Chairman 1957)

R . R . B A R T E L S M E Y E R , Chief Highway Engineer, Ulinois Division of Highways J . E . B U C H A N A N , President, The Asphalt Institute W . A . B U G G E , Director of Highways, Washington State Highway Commission MASON A . B U T C H E R , Director of Public Works, Montgomery County, Md. C. D . C U R T I S S , Special Assistant to the Executive Vice Prcsidoif, American Road

Builders Association H A R M E K E . DAVIS , Director, Institute of Tyn>isi>ort<itio>i and Traffic Etigiticcritig, I'lii-

versity of California D U K E W . DUNBAR, Attorney General of Colorado F R A N C I S V . DU PONT, Consulting Engineer, Washington, D. C. H . S . F A I R B A N K , Consultant, Baltimore, Md. P Y K E J O H N S O N , Consultant, Automotive Safety Fonndation G. DONALD K E N N E D Y , President, Portland Cement AsK,iciatio>i BURTON W . M A R S H , Director, Traffic Engineering and Safety Department, American

Automobile Association G L E N N C . R I C H A R D S , ComwiissioMer, Detroit Department of Public Wiirku W I L B U R S . S M I T H , Wilbur Smith and Associates, New Haven, Conn. K . B . WOODS, Head, School of Civil Engineering, and Director, Joint Highuny Rvsvarch

Project, Purdue University

E d i t o r i a l S taf f

F R E D BURGGRAF E L M E R M . WARD

2101 Constitution Avenue

HERBERT P . ORLAND

Washington 25, D. C.

The opinions and conclusions expressed in this publication are those of the authors and not necessarily those of the Highway Research Board.

A a HIGHWAY RESEARCH BOARD

Bulletin 222

Highway Investment and

Financing

Presented at the 38th ANNUAL MEETING

January 5-9, 1959

^Ij^^i RESEARGH

1959 Washington, D. C.

Department of Economics^ Finance and Administration

CP. St. C l a i r , Cha i rman D i r e c t o r , Highway Cost A l l o c a t i o n Study

Bureau of Publ ic Roads, Washington, D . C.

C O M M I T T E E O N H I G H W A Y T A X A T I O N A N D F I N A N C E

A . K . B r a n h a m , Cha i rman Bureau of Publ ic Roads, Washington, D . C.

C . A . Steele, Secre tary Chief , F i n a n c i a l Research Branch , D i v i s i o n of Highway Economics

O f f i c e of Research, Bureau of Publ ic Roads, Washington, D . C.

Rober t F . Baker , Assoc ia te P r o f e s s o r of C i v i l Eng inee r ing , Ohio State U n i v e r s i t y , Columbus

Gordon D . Campbel l , D i r e c t o r of Techn ica l Services , Canadian Good Roads A s s o c i a t i o n , Ot tawa, Canada

P h i l i p M . Donne l l , E n g i n e e r - D i r e c t o r , Highway Planning Survey D i v i s i o n , Tennessee Depar tment of Highways and Publ ic W o r k s , Nashv i l l e

H . C . Duzan, Highway Cost A l l o c a t i o n Study, D i v i s i o n of F i n a n c i a l and A d m i n i s t r a t i v e Research , Bureau of Publ ic Roads, Washington, D . C.

Yule F i s h e r , Research Counsel , Na t iona l Highway Users Conference, Washington, D . C. James A . Fos t e r , Ass i s t an t Manager , Highway Bureau , Po r t l and Cement A s s o c i a t i o n ,

Chicago P a t r i c k Healy, J r . , Execut ive D i r e c t o r , A m e r i c a n M u n i c i p a l Assoc i a t i on ,

Washington, D . C . Ralph D . Johnson, Ass i s t an t Eng inee r ing Counsel , Na t iona l Highway U s e r s Conference,

Washington, D . C . J . E . Johnston, Highway T r a n s p o r t a t i o n £ i ) e c i a l i s t . Chamber of Commerce of the

Uni ted States, Washington, D . C. R . W . K r u s e r , Deputy A s s ' t C o m m i s s i o n e r f o r A d m i n i s t r a t i o n , O f f i c e of A d m i n i s t r a t i o n ,

Bureau of Pub l ic Roads, Washington, D . C. B e r t r a m H . Landman, Consul t ing Engineer and Economis t , Washington, D . C. James W. M a r t i n , D i r e c t o r , Bureau of Business Research , U n i v e r s i t y of Kentucky,

Lex ing ton Roy T . Messe r , Ass i s t an t Chief , Highway Planning D i v i s i o n , Bureau of Publ ic Roads,

Washington, D . C . M r s . W i l l a W. M y l r o i e , Washington Depar tment of Highways , Highway Planning

Survey, O l y m p i a James C. Nelson , P r o f e s s o r of Economics , State College of Washington, P u l l m a n Glenn N i x o n , New Y o r k Regional E d i t o r , U . S. News and W o r l d Repor t Char les M . Noble , C h e r r y V a l l e y Road, P r i nce ton , New Je r sey W i l f r e d Owen, The Brook ings I n s t i t u t i o n , Washington, D . C. D . F . Pancoast, Eng inee r -Economis t , Ohio Depar tment of Highways , Columbus W i l l i a m D . Ross, Dean, College of C o m m e r c e , Louis iana State U n i v e r s i t y , Baton Rouge Sam M . Rudder , Engineer of Highway Planning, M i s s o u r i State Highway Depar tment ,

J e f f e r s o n C i t y H . S. W i l e y , Planning D i r e c t o r , New Mexico State H ^ h w a y Depar tment , Santa Fe Robley W i n f r e y , Chief , D i v i s i o n of Highway Needs and Economy, Bureau of Publ ic

Roads, Washington, D . C . R i c h a r d M . Z e t t e l , U n i v e r s i t y of C a l i f o r n i a , Eng inee r ing F i e l d Station, B e r k e l e y

C O M M I T T E E O N fflGHWAY COSTS

Robley W i n f r e y , Cha i rman Chief , D i v i s i o n of Highway Needs and Economy

Bureau of Publ ic Roads, Washington, D . C.

M a r i a n Hankerd , Secre tary Execut ive Ass i s t an t , Highways D i v i s i o n ,

Au tomot ive Safety Foundat ion, Washington, D . C.

Dav id M . B a l d w i n , Execut ive Secre tary , Ins t i tu te of T r a f f i c Engineers , Washington, D . C . John B . Benson, J r . , County Engineer , Bradenton, F l o r i d a J . P . Buck ley , Chief Engineer , Au tomot ive Safety Foundat ion, Washington, D . C. C l in t Burnes , A s s t . C o m m i s s i o n e r f o r P r o g r a m m i n g and Planning , Minnesota

Depar tment of Highways , St. Paul Donald O. Covaul t , Depar tment of C i v i l Eng inee r ing , Georg ia Ins t i tu te of Technology,

At lan ta John D . C r u i s e , Ass i s t an t Special Ass ignmen t Engineer , M i c h i g a n State Highway

Depar tment , Lans ing P h i l i p M . Donne l l , E n g i n e e r - D i r e c t o r , Highway Planning Survey D i v i s i o n , Tennessee

Depar tment of Highways and Publ ic W o r k s , Nashv i l l e F r e d B . F a r r e l l , Bureau of Publ ic Roads, Chicago James A . Fos t e r , Ass i s t an t Manager , Highways and M u n i c i p a l Bureau , P o r t l a n d

Cement A s s o c i a t i o n , Chicago C a r l E . F r i t t s , V i c e Pres ident i n Charge of Eng inee r ing , A u t o m o t i v e Safety Foimdat ion ,

Washington, D . C . James O. Granum, Deputy Chief Engineer , A u t o m o t i v e Safety Foundat ion,

Washington, D . C. H . K e i t h G r i f f i t h , Execut ive D i r e c t o r , Na t iona l B i tuminous Concrete A s s o c i a t i o n ,

W a s h i i ^ t o n , D . C . Gordon D . G r o n b e r g , Head, Annua l Cost Section, Bureau of Pub l ic Roads,

Washington, D . C . J . A l Head, Ass i s t an t T r a f f i c Engineer , Oregon State Highway Depar tment , Salem R . G . Hennes, P r o f e s s o r of C i v i l Eng inee r ing , U n i v e r s i t y of Washington, Seattle C u r t i s J . Hooper, 45 Sturges Road, F a i r f i e l d , Connecticut Roy E . Jorgensen, Eng inee r ing Counsel , Na t iona l Highway Use r s Conference ,

W a s h i i ^ t o n , D . C . John J . L a i n g , Supervis ing Highway Engineer , Maintenance Branch , Bureau of Pub l ic

Roads, W a s h i i ^ t o n , D . C . B e r t r a m H . L i n d m a n , Consul t ing Engineer and Economis t , Washington, D . C. Rober t E . L i v i n g s t o n , Planning and Research Engineer , Colorado Depar tment of

Highways , Denver James M . M o n t g o m e r y , T r a n s p o r t a t i o n Economis t , D i v i s i o n of Highway Economics ,

Bureau of Publ ic Roads, Washington, D . C. Theodore F . M o r f , Engineer of Research and Planning , I l l i n o i s D i v i s i o n of Highways ,

l ^ r i n g f i e l d Sam Osofsky , H ^ h w a y Economis t , C a l i f o r n i a Depar tment of Pub l ic W o r k s , Sacramento B o r i s B . P e t r o f f , Head, Sampling Techniques Section, Bureau of Publ ic Roads,

Washington, D . C . F r a n k M . Reynolds , P r i n c i p a l Highway Engineer , C a l i f o r n i a Depar tmen t of Pub l ic

W o r k s , Sacramento L . R . Shureman, Supervis ing Highway Engineer , Bureau of Publ ic Roads,

Washington, D . C . Rober t W i l l i s , E i ^ i n e e r of Highway Planning, State Highway C o m m i s s i o n of Kansas,

Topeka R i c h a r d M . Z e t t e l , U n i v e r s i t y of C a l i f o r n i a , Eng inee r ing F i e l d Station, B e r k e l e y

I'm

Contents F U N D A M E N T A L P R O B L E M S I N R E L A T I N G V E H I C L E S I Z E

T O HIGHWAY C O S T S

Robert F . B a k e r 1

P R I C I N G AND F I N A N C I N G HIGHWAY S E R V I C E S

O. H . Brownlee 27

P R I C E T H E O R Y AND T A X E Q U I T Y IN HIGHWAY F I N A N C E

M . Z . KafogUs 32

U S E O F E C O N O M I C C R I T E R I A F O R HIGHWAY I N V E S T M E N T P L A N N I N G

T i U o E , Kuhn 49

G E N E R A L DISCUSSION

James C . Nelson 75 B e r t r a m H . Lindman 78

Fundamental Problems in Relating Vehicle Size to Highway Costs R O B E R T F . B A K E R , P r o f e s s o r of C i v i l Eng ineer ing , The Ohio State U n i v e r s i t y

Research on the p r o b l e m of d e t e r m i n i n g the r e l a t i onsh ip between highway costs and veh ic le s ize has been i n p r o g r e s s at The Ohio State U n i v e r s i t y f o r m o r e than f o u r yea r s under the sponsorship of f o u r t r u c k i n g f i r m s and the Ohio T r u c k i n g A s s o c i a t i o n . M o s t r ecen t l y , a f i n a l r e p o r t cove red the en t i r e cost ass ignment f o r the condi t ions and expendi tures of the Ohio Depar tment of Highways . The p resen t paper discusses the p r o b l e m s associa ted w i t h the development of cost r e spon ­s i b i l i t y f o r the studies to date .

Spec i f i ca l ly , the paper cove r s the f o l l o w i n g phi losophies that can be u t i l i z e d i n cost ass ignment p r o b l e m s :

1. Use of t h e o r e t i c a l v s e m p i r i c a l r e l a t i ons between v e h i c l e p a r a m e t e r s and cos t i t e m s .

2. T h e o r e t i c a l v s engineer ing solu t ions w h e r e i n s ing l e -va lued r e s u l t s a r e obta ined.

3. D i r e c t o r i n d i r e c t sources of cost r e s p o n s i b i l i t y . 4. D i s t r i b u t i o n of i n d i r e c t costs , c l a s s i c a l l y designated

as engineer ing o r a d m i n i s t r a t i o n .

Several p r a c t i c a l d i f f i c u l t i e s tha t must be ove rcome i n as­sessing cost r e s p o n s i b i l i t y also a r e d iscussed, such as: ( a ) combin ing cap i t a l i m p r o v e m e n t cos ts w i t h annual cos ts f o r maintenance and opera t ions , (b ) combin ing of cost f a c t o r s c o n t r o l l e d by weigh t r e q u i r e m e n t s w i t h those c o n t r o l l e d by f a c t o r s o ther than weight , ( c ) in f luences of t r a f f i c data on the ass ignment of costs to v a r i o u s highway use r groups , and (d) ex t rapo la t ion of e m p i r i c a l data to inc lude veh ic l e s izes g rea t e r than c u r r e n t l y au tho r i zed .

The paper concludes that the genera l shape of the cu rve f o r cost v s v e h i c l e - s i z e i s ava i l ab le . F u r t h e r m o r e , based on a g iven annual expendi ture by a h ighway depar tment , reasonable es t imates of d i f f e r e n t i a l cost can be obta ined. However , t h e o r e t i c a l answers to the cos t - s i ze p r o b l e m w i l l not be ava i lab le u n t i l the es tabl i shment of m o r e r a t i o n a l methods f o r des ign, p a r t i c u l a r l y f o r highway geomet r i e s and the r e l a t e d cost f a c t o r s .

• T H E R E i s no c o m p l e t e l y r a t i o n a l method f o r developing the r e l a t i onsh ip between v e ­h i c l e s ize and the highway costs wh ich a r e r e q u i r e d to p r o v i d e a f a c i l i t y f o r a spec i f i c v e h i c l e . T h e r e f o r e , c u r r e n t so lu t ions w h i c h p r o v i d e such r e l a t ionsh ips a re e m p i r i c a l and r e q u i r e many assumptions and a r b i t r a r y techniques . Whi le fundamenta l concepts can be s tudied and used where app l icab le , l a r g e p o r t i o n s of h ighway expendi tures are c u r r e n t l y p rocessed wi thout d i r e c t r e f e r e n c e to the s ize of the v e h i c l e .

Two types of cons ide ra t ions l ead to the need f o r veh ic l e s i ze and highway cost r e ­la t ions ; namely , (a ) the es tab l i shment of cost r e s p o n s i b i l i t y , and ( b ) the obta in ing of the c h a r a c t e r i s t i c s of the o p t i m u m - s i z e d v e h i c l e f o r the t r a n s p o r t a t i o n s y s t e m . The f a c t that these two p r o b l e m s r e q u i r e the same data as to veh ic l e s ize and highway cos ts does not nece s sa r i l y mean that the approaches to so lu t ion a r e comparab l e . A s a r e s u l t , the phi losophies and techniques wh ich a r e u t i l i z e d w i l l v a r y and w i l l be dependent upon the p r i n c i p a l reason f o r the development of the r e l a t i o n . Highway cos ts as used h e r e i n w i l l r e f e r to those expendi tures by an i n d u s t r y o r gove rnmen ta l agency w h i c h a re r e -

q u i r e d f o r the c o n s t r u c t i o n , maintenance, and opera t ion o f a highway s y s t e m . Speci f ­i c a l l y exc luded a r e the ope ra t ing cos ts expended b y the owner o r ope ra to r of a m o t o r v e h i c l e .

The r e s e a r c h wh ich has been conducted at The Ohio State U n i v e r s i t y has inc luded e f f o r t s t o del ineate the d i f f i c u l t i e s associa ted w i t h both cost r e s p o n s i b i l i t y and o p t i m u m v e h i c l e s i z e . The w o r k has been i n p r o g r e s s f o r m o r e than f o u r yea r s and has r e s u l t e d i n a number of pub l i ca t ions (1^, 2, 3, 4, 5, 6 ) . Sponsorship f o r the inves t iga t ion has c o m e f r o m f o u r i n d i v i d u a l Ohio t r u c k i n g f i r m s , v ^ i c h i n i t i a t e d t he s tudies f o u r y e a r s ago, and, subsequently, f r o m the Ohio T r u c k i n g A s s o c i a t i o n .

The purpose of the f o l l o w i n g paper i s to del ineate the v a r i o u s basic phi losophies w h i c h can be u t i l i z e d i n the highway cos t r e l a t i o n s h i p s . F u r t h e r m o r e , poss ib le po in t s of depar tu re and o r i e n t a t i o n f o r those in t e r e s t ed i n p u r s u i n g such r e s e a r c h have a lso been d i scussed . The scope i s r e s t r i c t e d to the p r o b l e m s concerned w i t h the highway cos t and v e h i c l e s ize r e l a t i o n s h i p s , ^ e c i f i c a l l y excluded a r e t axa t ion t h e o r i e s and the ope ra t ing costs p a i d d i r e c t l y by the highway u s e r . Rather than to a t t empt t o d iscuss a l l of the i n d i v i d u a l cost i t e m s , the f o l l o w i n g r e p o r t r e s t r i c t s i t s e l f to the broader questions w h i c h a r e i n the r e a l m of fundamen ta l phi losophy o r basic engineer ing methodology.

D E F I N I T I O N S

F o r the sake of b r e v i t y , s eve ra l express ions and concepts r e q u i r i n g d e f i n i t i o n w i l l be u t i l i z e d i n the f o l l o w i n g r e p o r t . Frequent r e f e r ences w i l l be made to weight f a c t o r s and non-weigh t f a c t o r s . These two t e r m s a re used to designate v e h i c l e p a r a m e t e r s w h i c h a f f e c t highway cos ts , o r p o r t i o n s of cost i t e m s , wh ich a re in f luenced by weight , a n * b y v a r i a b l e s o ther than weight , r e s p e c t i v e l y . The on ly h ighway cos ts w h i c h a re l a r g e l y i n f luenced by the weight of the v e h i c l e a re s t r u c t u r e s and pavements . A s a m a t t e r of f a c t , s ince these two cos t i t e m s a re a f f e c t e d by f a c t o r s o the r than weight , such as the w i d t h and height of the s t r u c t u r e , on ly a p a r t of the costs i s comple t e ly def ined by weight r e q u i r e m e n t s . Weight e f f ec t s , then, w o u l d include those p o r t i o n s of the s t r u c t u r a l and pavement costs w h i c h a re i n f luenced by the v e h i c l e we igh t . The cos ts may also be r e f e r r e d to as s t r u c t u r a l e f f ec t s , because of the in f luence of s t r u c ­t u r a l capac i ty . Spec i f i c a l l y , the non-weigh t f a c t o r s inc lude the geomet ry of the v e h i c l e , the p e r f o r m a n c e c h a r a c t e r i s t i c s of the v e h i c l e , and the capab i l i t y of the d r i v e r . Since the non-weigh t v a r i a b l e s in f luence costs wh ich a re r e l a t e d to highway geomet ry , the cos ts a r e a lso r e f e r r e d to as geomet r i c e f f e c t s . Pedes t r ians can also be cons idered we igh t and non-we igh t f a c t o r s i n s o f a r as s idewalks and pedes t r i an underpasses o r o v e r ­passes a re concerned . However , d i r e c t pedes t r i an r e s p o n s i b i l i t y i s a neg l ig ib le c o n ­s ide ra t ion i n mos t p r o b l e m s .

The f o l l o w i n g d e f i n i t i o n s have been found qui te u s e f u l f o r the cost ass ignment p r o b ­l e m but a r e not neces sa r i l y v a l i d f o r m o r e genera l usage:

1 . Cons t ruc t ion Costs—direct expendi tures r e l a t e d to cap i t a l i m p r o v e m e n t . 2. Maintenance Costs—direct expendi tures r e l a t ed to p r e s e r v i n g and ma in t a in ing

f a c i l i t i e s w h i c h a re p r o v i d e d by cap i t a l i m p r o v e m e n t . 3. Opera t ion Costs—direct expendi tures r e q u i r e d to expedite the f l o w of t r a f f i c . 4 . A d m i n i s t r a t i o n Cos ts—indi rec t expendi tures i n c u r r e d f o r cons t ruc t i on , m a i n t e n ­

ance, o r opera t ions i n the f o r m of o v e r - a l l d i r e c t i o n and superv i s ion of the sy t em. 5. Eng ine r ing Cos ts—indi rec t expendi tures i n c u r r e d i n the cons t ruc t i on , maintenance,

and opera t ion of the h ighway r e q u i r e d f o r t echn ica l d i r e c t i o n , p lann ing , supe rv i s ion and execut ion of the w o r k p e r f o r m e d .

I n the p reced ing d e f i n i t i o n s , the t e r m d i r e c t expendi ture i m p l i e s tha t the cos ts a r e r e a d i l y t r a c e d to the cost i t e m , whereas i n d i r e c t expendi ture suggests that the n o r m a l account ing sys tem wou ld not p r o v i d e data as to the p r o p e r ass ignment to a spec i f i c cos t i t e m .

The p reced ing cost de l inea t ion does not e l im ina t e p r a c t i c a l p r o b l e m s i n ass igning highway expendi tures . F o r example , t he re i s c e r t a i n to be some quest ion as to whether a cos t should be c lassed as c o n s t r u c t i o n o r maintenance, p a r t i c u l a r l y when the m a i n t e ­nance expendi tures a re qui te l a r g e . A l s o , c e r t a i n costs cou ld l o g i c a l l y be c lassed as

e i the r maintenance o r opera t ions , and a good example i s the rep lacement of a g u a r d ­r a i l . A p r e c i s e de l inea t ion between groups may o r may not be c r i t i c a l . I n mos t i n ­stances, the method of a l l oca t i ng cos t to veh ic les i s independent of the group to wh ich a cost i s ass igned. The dec is ive cons ide ra t ion as to cost g roup ing i s u sua l ly the a v a i l ­a b i l i t y of r e c o r d s .

Cost r e s p o n s i b i l i t y as used h e r e i n r e f e r s to u se r s on ly and to the d i r e c t v a r i a b l e s used to obta in the f i n a l des ign . Th i s d i f f e r s f r o m the m o r e gene ra l d e f i n i t i o n used i n the highway economics f i e l d (13).

The use of benef i t s to a l loca te cos ts i s a recognized p rocedu re , but the benef i t s a r e not i n themse lves v a r i a b l e s tha t a f f e c t the magnitude of highway cost i t e m s .

V A R I A T I O N S I N BASIC PHILOSOPHY

I n i n i t i a t i n g a study of highway cost r e l a t i onsh ip w i t h v e h i c l e s ize the re w i l l be s eve ra l choices as to the basic phi losophies wh ich w i l l be appl ied to the r e s e a r c h . Some of these const i tu te t r u e a l t e rna t i ve s , w h i l e o thers a re r e l a t e d to the purposes f o r wh ich the inves t iga t ion i s es tab l i shed . In the f o l l o w i n g pa ragraphs seve ra l of these quest ions a re d i scussed .

T h e o r e t i c a l Methods v s Des ign Techniques

There a r e two theor i e s under wh ich cos t - s i ze r e l a t i onsh ips can be developed. The f i r s t approach m i g h t be designated as the " t h e o r e t i c a l " i n that a l l express ions r e l a t i n g cos t w i t h v e h i c l e s ize w o u l d be r a t i o n a l . The second approach i n v o l v e s the e s t ab l i sh ­ment of the r e l a t i o n s between cost and s ize on an e m p i r i c a l bas i s , namely one that i s i n c u r r e n t use as a design technique. Complete use of a t h e o r e t i c a l approach i s not a p r a c t i c a l p o s s i b i l i t y because of the many func t ions w h i c h have not been es tabl ished on a r a t i o n a l base. Even i f one cou ld assume that the weigh t a f f e c t s can be evaluated r a t i o n a l l y , the non-weigh t f a c t o r s r ep resen t the comple te r e v e r s a l . The methods f o r d e t e r m i n i n g roadway w i d t h , g rade , c u r v a t u r e , s t r u c t u r e openings, and o the r s i m i l a r geome t r i c f a c t o r s a r e comple t e ly e m p i r i c a l and d i r e c t r e l a t i ons w i t h v e h i c l e s ize a re n o r m a l l y d i f f e r e n t i a t e d only by e x t r e m e s ize v a r i a t i o n s . Even the weight e f f ec t s a r e quest ioned as r e f l e c t e d i n the AASHO tes t s at Ot tawa, I l l i n o i s . I n f a c t , i f a t h e o r e t i c a l answer i s to be obtained, then a l l h ighway r e s e a r c h p r o b l e m s a r e i n v o l v e d .

W h i l e c e r t a i n ad jus tments between t h e o r y and p r a c t i c e cou ld be t o l e r a t e d i n an e f f o r t to obta in as t h e o r e t i c a l an approach as poss ib l e , t he r e i s a m o r e fundamen ta l d i s t i n c t i o n and ph i losophy i n v o l v e d w i t h the choice between the t w o . The impor t ance of the concept of us ing e m p i r i c a l p r a c t i c e s goes beyond the f a c t that the data a r e based upon the best exper ience ava i l ab l e . I f e m p i r i c i s m i s used, ac tual methods employed i n the design p rocedure s cou ld be i n c o r p o r a t e d . Thus , the r e s u l t s wou ld r e f l e c t the methods under wh ich the funds a re be ing expended. The fundamen ta l quest ion becomes, then, whether the cost r e l a t ionsh ips to be developed a r e intended to r e f l e c t a t h e o r e t i c a l l y t r u e c o n ­d i t i o n o r the ac tua l manner i n w h i c h monies a re expended.

Where the p r o b l e m i s one of es tab l i sh ing the o p t i m u m veh ic l e s ize w i t h r e f e r e n c e to costs f o r a l l types of t r a n s p o r t a t i o n , then the t h e o r e t i c a l approach migh t be the m o r e d e s i r a b l e . Where the r e l a t i onsh ips a r e be ing developed f o r the purpose of p r o v i d i n g data f o r ass igning cost r e s p o n s i b i l i t y , the mos t equitable method appears to be r e l a t i o n ­ships based upon c u r r e n t design techniques; that i s , methods under w h i c h funds a re be ing expended.

Degree of A c c u r a c y

A s s ta ted i n the p reced ing pa rag raph , the absence of spec i f i c and i m p l i c i t f u n c t i o n s p reven t s a comple t e ly r a t i o n a l so lu t ion to a cos t - s i ze inves t iga t ion and one mus t as ­sume that any so lu t ion achieved d u r i n g the next f e w y e a r s w i l l r e q u i r e e m p i r i c a l t e ch ­niques o r some m o d i f i c a t i o n to a p u r e l y theo re t i ca l approach . Assoc ia ted w i t h the e m p i r i c i s m w i l l be a quest ion as to the degree of accuracy of the r e s u l t s . The question w i l l be r a i s e d because of (a ) the absence of a r a t i o n a l express ion , and ( b ) the evaluat ion of many v a r i a b l e s which r e q u i r e s t a t i s t i c a l cons ide ra t ions . A s s u m i n g tha t the l e v e l of

accuracy w i l l be a f u n c t i o n , i n p a r t , of the d o l l a r s ava i lab le f o r the s tudy, the re i s s t i l l a p a r t of the accuracy wh ich i s c o n t r o l l e d by the adequacy of the e m p i r i c i s m .

The quest ion to be cons idered i s whether one r e l a t i onsh ip w i l l be obta ined and r e ­f e r r e d to as the so lu t ion , o r whether m u l t i p l e sets of data a re to be developed. M i l t i p l e r e l a t i o n s cou ld take the f o r m of m a x i m u m and m i n i m u m solut ions ( F i g . 2) o r cou ld be s t a t i s t i c a l devia t ions f r o m a s ingle c u r v e . The advantage of a m u l t i p l e set of va lues over a s ing le so lu t ion i s that less a rgument w i l l ex i s t as to the competency of the e x ­t r e m e va lue s . F u r t h e r m o r e , the in f luences of the quest ionable f a c t o r s w i l l have been e s t ima ted .

Some p r o b l e m s , such as one upon which cost r e s p o n s i b i l i t y and, u l t i m a t e l y , t axa t ion i s based, may r e q u i r e tha t a unique r e s u l t be obta ined. A f t e r ob ta in ing m u l t i p l e va lues , judgment may be needed i n o r d e r to reduce the data to a s ing le set .

A v e r y d i f f i c u l t p r o b l e m i s encountered i n a t t empt ing to e s t ima te the t o t a l cost r e ­q u i r e m e n t s , f o r v a r i o u s s i zed veh i c l e s , w h i c h w i l l be needed f o r a m a j o r r o a d n e t w o r k . F o r a l i m i t e d s ize and type of r o a d sys t em, such as a t u r n p i k e , the t o t a l costs f o r v a r i o u s s i zed veh ic l e s can be reasonably p r e c i s e l y d e t e r m i n e d . The t o t a l cost of a m a j o r r o a d sys t em i s compl i ca t ed by the absence of r a t i o n a l methods f o r des ign, and by the wide v a r i a t i o n i n the u n i t costs which ex i s t on a l a r g e geographica l u n i t . Under the e x i s t i n g state of knowledge, es t imates v a r y i n g by 200 to 300 percen t should not be s u r p r i s i n g ( F i g . 2 ) . F u r t h e r m o r e , many d i f f e r e n t answers can be comple t e ly j u s t i f i e d when conducted under the design p r i n c i p l e s of c u r r e n t p r a c t i c e . Unfo r tuna t e ly , a p r e ­c i se type of es t imate should not even be cons ide red w i t h i n the r e a l m of p r a c t i c a l i t y . T o t a l cost r e l a t i onsh ip s should be developed w i t h a f i r m unders tanding of the l i m i t s of accu racy .

Where d i f f e r e n t i a l cos t i s the p r i n c i p a l ob j ec t ive of the study, the r e s u l t s of the inves t iga t ion can be m o r e p r e c i s e l y obta ined than f o r t o t a l cos t . Past s tudies (_2,6) have ind ica ted tha t w h i l e the ac tua l t o t a l cost to be an t ic ipa ted can v a r y o v e r a wide range the d i f f e r e n t i a l cos t s a r e p r ed i c t ab l e w i t h i n much m o r e n a r r o w d o l l a r va lues ( F i g . 2 ) .

In so lv ing the p r o b l e m of cost and s ize r e l a t i onsh ip s , then , i t i s i m p o r t a n t to s tudy the reasons f o r wh ich the r e s e a r c h i s conducted. Since s ing le -va lue data may be d i f f i ­c u l t to j u s t i f y , the double-se t of data i s r ecommended , a t l eas t w i t h i n the f r a m e w o r k of the methodology . Of pa ramoun t impor t ance , however , i s the f a c t that the l i m i t a t i o n s of ex i s t i ng knowledge mus t not be ove r looked , and should be evaluated i f pos s ib l e .

I n d i r e c t v s D i r e c t Sources of Cost Respons ib i l i t y

Cons idera t ion mus t be g iven at the s t a r t of the study as to whether d i r e c t o r i n d i r e c t sources of cost r e s p o n s i b i l i t y a re to be t r e a t e d as m a j o r v a r i a b l e s . F o r the pu rposes of t h i s r e p o r t , the assumpt ion i s made that h ighways a r e so le ly f o r the purpose of the highway u s e r and t h e r e f o r e d i r e c t sources mus t be r e l a t e d to the highway u s e r . D i r e c t sources of cos ts then, r e f e r to the f a c t o r s used i n the design f o r c o n t r o l l i n g the m ^ n i -tude of the s t r u c t u r e o r geome t r i c cond i t ions . Spec i f i c a l l y , the sources of d i r e c t costs a r e the n u m b e r s , we igh t s , and types of v e h i c l e s . D r i v e r a b i l i t y , v e h i c l e p e r f o r m a n c e , and pedes t r i ans a re d i r e c t sources , t h e o r e t i c a l l y , but a r e r a r e l y u t i l i z e d as such i n c u r r e n t des ign c r i t e r i a . I n d i r e c t sources of r e s p o n s i b i l i t y inc lude such th ings as r a i l ­roads , abut t ing p r o p e r t y owners , and p h y s i c a l and n a t u r a l obs tac les . The r a i l r o a d s p roduce a p a r t of the r e q u i r e m e n t s f o r a spec ia l c r o s s i i ^ but the magni tude of the m e m b e r s of the s t r u c t u r e a r e c o n t r o l l e d by the veh ic l e s wh ich w i l l be u t i l i z i n g the c r o s s i n g .

The geology, topography, and c l i m a t e of an a rea a r e t y p i c a l of i n d i r e c t sources of cost r e s p o n s i b i l i t y . They a r e a source of cost i n tha t the d o l l a r s expended a re a f f e c t e d by t h e i r c h a r a c t e r i s t i c s , but a r e i n d i r e c t i n the sense that u l t i m a t e l y v e h i c l e p a r a m e t e r s c o n t r o l the des ign . The p r i n c i p a l in f luence of i n d i r e c t sources i s to inc rease o r de ­c rease the magni tude of the cost d i f f e r e n t i a l . Jn. conduct ing a cos t - s i ze study, a s t a ­t i s t i c a l eva lua t ion of the e f f e c t of geology, topography, and c l i m a t e w i l l be r e q u i r e d . Thus , i f one p a r t of an area i s p a r t i c u l a r l y mountainous and another p a r t i s essen t ia l ly f l a t then the cost d i f f e r e n t i a l ass ignable f o r ea r thwork f o r the combined areas w i l l be some va lue between those p roduced i n the two ex t reme cond i t ions .

D i r e c t cost r e s p o n s i b i l i t y , t h e r e f o r e , associates a l l highway expendi tures w i t h the highway u s e r . I nd i r ec t cos ts on the o the r hand, a f f e c t the magnitude of expendi tures and of cost d i f f e r e n t i a l s , and con t r ibu te t o , but do not " c o n t r o l , " t l i e u l t i m a t e des ign .

There i s no in fe rence intended that i n d i r e c t sources of cos t r e s p o n s i b i l i t y a r e not i m p o r t a n t to highway economic s tudies . F o r such i t e m s as geology, topography, and c l i m a t e the i n d i r e c t sources w i l l become a f a c t o r i n s t a t i s t i c a l evaluat ions f o r a g iven a rea of app l i ca t ion . F o r o ther i n d i r e c t sources , such as r a i l r o a d s , abut t ing p r o p e r t y owner s , and the genera l pub l i c the quest ion i s concerned w i t h economics of the t o t a l socie ty and whether the h ighway user should be r e l i e v e d of any p a r t of the t o t a l cost r e s p o n s i b i l i t y . I n quest ions of taxa t ion t h i s l a s t dec is ion i s c r i t i c a l and associa ted w i t h b r o a d economic ques t ions . In a t t empt ing to de te rmine the o p t i m u m s ize o f veh ic l e the impor t ance of the i n d i r e c t sources may o r may not be p e r t i n e n t . In any event, i n

All T o < « Includtd ( A A - I

Highway Uiers Onl|r Genaral RevcniM Removed

Dotted Lmes Repreeent Moximum ond Minimum Cost Responsibility Bosed Upon I9S3-S4 Conditions n Otiio

Ponel a Pickup Ducks

Form Tnicks

Section - A

Possenger Core

Multi-Unit Trucks

Single Unit Tracks

General Public

Ponel a Pickup Trucks

Form Trucks

Figure 1. Relationship tetween cost responsibility and taxes paid.

o r d e r to develop r a t i o n a l express ions of the r e l a t i o n between highway cost and v e h i c l e s ize , i n d i r e c t sources should not be confused w i t h the d i r e c t sources w h i c h c o n t r o l the design of the v a r i o u s e lements .

Types of Cost to Include

To a c e r t a i n extent, the types of cos ts wh ich should be inc luded i n the r e s e a r c h a r e a f u n c t i o n of the p a r t i c u l a r p r o b l e m . fii mos t cases, the p r o b l e m w i U be addressed to the t o t a l expendi ture r e q u i r e d to cons t ruc t , ma in t a in , and opera te a s y s t e m . A t t e m p t i n g to inc lude a l l poss ib le costs leads to some i n t e r e s t i n g ques t ions . F o r example , the o f f i c i a l s of the state government who dea l w i t h the highway sys tem, such as the g o v e r ­n o r , state t r e a s u r e r , l e g i s l a t o r s , e t c . , undoubtedly should have p a r t of the expendi tures of t h e i r o f f i c e s a t t r i b u t e d to h ighways . F o r m a j o r sys tems these cos ts w i l l be a v e r y s m a l l p a r t of the highway budget, and can be sa fe t ly neglec ted . F o r a t o l l t u r n p i k e the quest ion i s a l i t t l e m o r e confused, since the r e l a t i onsh ip between the t o l l f a c i l i t y and the gove rnmen ta l o f f i c e s may be less c l e a r l y de f ined . I f no charges a r e made, then no ac tua l costs a r i s e , and, t h e r e f o r e , none need be cons ide red .

A n i n t e r e s t i ng cost i s tha t r e q u i r e d f o r conduct ing the business of agencies such as the pub l i c u t i l i t i e s c o m m i s s i o n s . I n some states, the ope ra t ing f u n d s , i n s o f a r as h i g h ­ways a r e concerned, a r e co l l ec t ed d i r e c t l y f r o m t r u c k l i ^ companies i n the f o r m of t axes . The purposes of such c o m m i s s i o n s a re f o r the r egu l a t i on , and thereby , to a degree, the p r o t e c t i o n of the i n d i v i d u a l t r u c k i n g companies and a r e not f o r the ass is tance

6

of highway u s e r s i n g e n e r a l . T h e r e f o r e , such expendi tures w o u l d appear t o be m o r e l o g i c a l l y "opera t ing cos t s " of the u s e r than highway costs as de f ined h e r e i n .

Inc luded i n many highway depar tment l i s t s of expendi tures a r e c e r t a i n i n t e r e s t charges on bonds so ld f o r some phase of highway cons t ruc t ion o r maintenance. The re i s l i t t l e quest ion but tha t these i n t e r e s t costs a re charges accumula ted because of the highway s y s t e m . Sometimes f o r g o t t e n , however , i s the f a c t that the d o l l a r s co l l ec ted on a pay -as -you-go bas is t h e o r e t i c a l l y dep r ive the c i t i z e n s of oppor tun i t i e s to inves t o r to reduce t h e i r own ob l iga t ions . T h e r e f o r e , highway p r o g r a m s -which a r e based upon a pay -as -you-go p r o g r a m should inc lude cons idera t ion of when money i s co l l ec t ed w i t h r e f e r e n c e to when the i m p r o v e m e n t s a r e obta ined o r expended. I f one i s to c o n ­s ide r the t o t a l t r a n s p o r t a t i o n p i c t u r e , i nc lud ing r a i l r o a d , a i r p o r t s , wa t e rways , and p ipe l ines , then the i n t e r e s t cos ts , both on d o l l a r s co l l ec t ed and on bonded indebtedness, should be inc luded as cos t . The i n c l u s i o n o r exc lus ion of i n t e r e s t cos ts w i l l u l t i m a t e l y be decided by the demands of the p r o b l e m . Consistency as to t r e a t m e n t of i n t e r e s t should be encouraged, p a r t i c u l a r l y where i n t e r e s t on bonded indebtedness i s obv ious ly p resen t , but the loss of income to the taxpayer on a pay-as -you-go p lan i s not so o b ­v i o u s .

Types of Taxes to Be Inc luded

Cost r e s p o n s i b i l i t y s tudies w i l l f r e q u e n t l y lead to a c o m p a r i s o n between costs and t axa t ion f o r v a r i o u s h ighway u s e r g roups . Many such s tudies have l e d to c o n f l i c t i n g r e s u l t s , p a r t i c u l a r l y as e f f o r t s a r e made to express taxes p a i d on a u n i t y bas i s . One of the reasons f o r the apparent d i sc repanc ies l i e s i n the types of taxes wh ich a re i n ­c luded . F o r example , i n a p reced ing p a r a g r a p h the taxes co l l ec ted by the pub l i c u t i l i t i e s c o m m i s s i o n s w e r e suggested as l o g i c a l "opera t ing cos t s " and as such cou ld not be t e r m e d taxes p a i d to compare w i t h cost r e s p o n s i b i l i t y . Thus , a p r i n c i p l e i s suggested; namely , that the taxes to be compared w i t h cos t r e s p o n s i b i l i t y should be "h ighway use r t axes" i f highway u s e r s a re cons ide red as the d i r e c t source of a l l h i g h ­way cos t s . A s used he re , "highway u s e r t axes" a r e intended to designate those taxes p a i d by the u s e r and wh ich a re u t i l i z e d f o r highway purposes .

I f the p reced ing p r i n c i p l e i s v a l i d , then taxes pa id by the highway use r wh ich a r e not used f o r highway purposes wou ld not be inc luded . Examples of such taxes w o u l d be F e d e r a l and State income taxes and some exc ise t axes . In c e r t a i n states and l o c a l gov­e rnments p o r t i o n s of the gene ra l f u n d a re used to supplement the highway use r taxes i n o r d e r to have s u f f i c i e n t opera t ing f u n d s . Thus , c e r t a i n p o r t i o n s of genera l taxes may be l o g i c a l l y p r e s u m e d as "highway use" t axes . In such cases, the non-h ighway-use r sources of highway use tax should be c r e d i t e d as the source of p a r t of the monies c o l ­l ec t ed . Resul t s f r o m the Ohio State s tud ies (^ ) a r e inc luded i n F i g . 1 and the in f luence of the taxes inc luded i n the inves t iga t ion i s shown.

Since the i nc lu s ion o r exc lus ion of taxes pa id i s a rgumenta t ive , data under s e v e r a l assumpt ions may be r e q u i r e d . However , the v a l i d i t y of c o m p a r i n g cost r e s p o n s i b i l i t y w i t h taxes p a i d , when the t ax inc luded monies which a re not u t i l i z e d on highways, i s to be quest ioned. The re does appear to be g rea te r consis tency i f on ly highway use taxes a re i nc luded .

P R O B L E M S O F A P P L I C A T I O N

I n the ac tua l development of the r e l a t i onsh ip between highway costs and v e h i c l e s ize many p r a c t i c a l p r o b l e m s a re encountered. Some of the m o r e c r i t i c a l of these quest ions of methodology a r e cove red i n the f o l l o w i n g pa rag raphs . In o r d e r to f a c i l i t a t e the d i s ­cuss ion , the methods used at The Ohio State U n i v e r s i t y have been used by way of i l l u s ­t r a t i o n . The re i s no i n f e r ence intended that the so lu t ions const i tu te the only way no r the best way f o r genera l cond i t ions .

Select ing a Single V e h i c l e Pa rame te r

Mos t cos t - s i ze p r o b l e m s mus t u l t i m a t e l y be expressed as a r e l a t i o n between a s ingle v e h i c l e - p a r a m e t e r and a highway cos t . The se lec t ion of u n i t s f o r cost and s ize

i s a t roub lesome p r o b l e m , p a r t i c u l a r l y f o r the v e h i c l e p a r a m e t e r . Perhaps the s i t ua ­t i o n i s best e x e m p l i f i e d by cons ide r ing pavement and e a r t h w o r k cos t s . Pavement ex ­pendi tures a re obv ious ly m o r e r e l a t e d to axle load than to any o ther veh ic l e p a r a m e t e r , and d imens ions of the v e h i c l e a re not of much impor t ance i n d i f f e r e n t i a l pavement cost ana lys i s . On the o ther hand, e a r t h w o r k expendi tures a re h a r d to r e l a t e to ax le load and cannot be done on a d i r e c t , r a t i o n a l bas is , f o r they a re m o r e l o g i c a l l y associa ted w i t h veh ic l e d imens ions , p e r f o r m a n c e , and the d r i v e r . Whi l e the re i s no es tabl ished

r e q u i r e m e n t that a s ingle p a r a m e t e r be u t i l i z e d , many p r o b l e m s , and p a r t i c u l a r l y the t axa t ion quest ion, must be expressed as a s ingle p a r a m e t e r o r else the so lu t ion w i l l be confused w i t h two veh ic l e p a r a m e t e r s f o r express ing r e l a t i o n s h i p s . W h i l e i t i s reasonable and necessary i n the ea r ly stages to develop independent f u n c t i o n s i n t e r m s of m o r e than one veh ic l e p a r a m e t e r , one should not be s u r p r i s e d to f i n d p r e s ­sures o r reasons to reduce the r e l a t i o n -

n 12 14 16 IS AXLE LXMO IN TONS

Figure 2. Relationship between annual costs and the design axle load.

ship so as to express the highway cos t i n t e r m s of one v e h i c l e v a r i a b l e .

To develop a s ingle v e h i c l e p a r a m e t e r one mus t r e t u r n to the basic f a c t o r s which in f luence expendi tures . A s s u m i n g that on ly d i r e c t sources of cost r e s p o n s i b i l i t y a re to be cons idered , then cost r e s p o n s i ­b i l i t y can be t r a c e d reasonably , to e i the r ( a ) a v e h i c l e weight f a c t o r , o r (b) to a veh ic l e d imens ion o r p e r f o r m a n c e cha rac ­t e r i s t i c . Th i s assumes that the v e r y m i n o r e f f ec t of pedes t r i ans can be neg­l ec t ed . The v e h i c l e weigh t f a c t o r s can convenient ly be reduced to ax le load , i f c e r t a i n cons idera t ions a re t r e a t ed i n t e r m s of ax le spacing. S i m i l a r l y , the e f f ec t s of v e h i c l e d imens ions and p e r f o r m ­ance can be t r a c e d to the way they a f f e c t v a r i o u s phases of highway g e o m e t r y . A l l i t e m s of cost wh ich a r e not a f f ec t ed by weight w i l l then by necess i ty be a f f e c t e d by the v e h i c l e geome t r i c f a c t o r s . To r e ­duce the geome t r i c f a c t o r s to a s ingle v e h i c l e p a r a m e t e r does cause some d i f f i ­c u l t i e s . The best so lu t ion i s achieved by a s t a t i s t i c a l evaluat ion of the t r a f f i c u s ing the h ighways . Another poss ib le technique w o u l d be to use a common design me thod ­o logy , w h e r e i n veh ic l e c h a r a c t e r i s t i c s a re handled so le ly on the bas i s of t r u c k s

NOT 1-WEI 1

GHT F 1

tCTORS

MAXI HUM I ;osT

1

MINIMUM C 3 S T -J

8 10 12 14 AXLE UOAD IN TONS

( 0 )

16 18 20

WEIGHT FACTORS

MAXIMUM COST

M NIMUM COST

from E . E. S. Bulletin No. 168

8 10 12 14 AXLE LOAD IN TONS

(b)

Figure 3. Annual costs versus design axle load for weight and non-weight factors.

8

and passenger c a r s . U t i l i z i n g the l a s t - m e n t i o n e d approach, one can set the m a x i m u m a x l e load f o r passenger c a r s and p i c k - u p t r u c k s and produce a cost d i f f e r e n t i a l f o r heav ie r t r u c k s due to g e o m e t r i c f a c t o r s .

Cons ide r ing f o r a momen t the ac tua l in f luence on a g iven study, one can consider the t h r ee e lements o r g roups of cost ; namely , c a p i t a l i m p r o v e m e n t , maintenance, and ope ra t i on . F o r the f i r s t t w o , the weight and the g e o m e t r i c f a c t o r s can be r e l a t e d to the ac tua l c a p i t a l i m p r o v e m e n t cos t s . Opera t ions , however , a r e r e s t r i c t e d to g e o m e t r i c cons ide ra t ions . F o r a g iven p r o b l e m , then, cost i s d i v i d e d in to weight and geomet r i c r e q u i r e m e n t s w i t h i n the cap i t a l i m p r o v e m e n t and maintenance g roup ings . Having the t o t a l cos t s w h i c h a re a f f e c t e d by the weigh t v a r i a b l e and the t o t a l expendi tures wh ich a r e i n f luenced by g e o m e t r i c cons ide ra t ions , two cos t d i f f e r e n t i a l s can be es tabl i shed. Combin ing the two on a bas i s of a s ing le veh ic le p a r a m e t e r i s accompl i shed f r o m the Ohio State s tudies ( J ) i n F i g . 2 . The bas i s f o r the combined cost i s g iven i n F i g . 3. I t can be seen tha t t he r e i s a cost d i f f e r e n t i a l between axles s m a l l e r and l a r g e r than 2 .5 tons f o r the geome t r i c f a c t o r s but an exponent ia l type of cu rve r e f l e c t s the w e ^ h t i n f l u e n c e . The cu rves of F i g . 2 r e q u i r e a s t a t i s t i c a l evaluat ion of the po in t at wh ich the g e o m e t r i c d i f f e r e n t i a l o c c u r s . F o r some p r o b l e m s , the s i i ^ l e d i f f e r e n t i a l a t 2 .5 tons ( o r s i m i l a r - t y p e value) i s a l l t l i a t m i g h t be r e q u i r e d . However , f o r the case o f es ­t a b l i s h i n g the o p t i m u m s ize of the v e h i c l e s o r f o r p r e d i c t i i ^ the e f f ec t of i nc r ea s ing the s ize of the ax le load , the r e l a t i o n s l i i p suggested by the cost ve r sus ax le load w o u l d be u s e f u l . The re i s no way , based upon design p r a c t i c e , f o r e s t ima t ing the e f fec t of le i^ l thening o r widen ing the v e h i c l e . F i g u r e 3 suggests tha t g e o m e t r i c e f f ec t s a r e independent of the v e h i c l e geomet ry , but such an answer i s a r e f l e c t i o n of design methods r a t h e r than sound ana lys i s of cost d i f f e r e n t i a l .

To s u m m a r i z e , then , a t tempts to r e l a t e a l l h ighway u n i t cos t s to a s ingle veh ic l e p a r a m e t e r m a y produce mi s l ead ing concepts . I t w i l l be des i r ab l e to ind ica te f o r h i g h ­way u n i t cos ts separate r e l a t ionsh ips f o r geomet r i c f a c t o r s and f o r a weight p a r a m e t e r . One add i t iona l reason f o r developing two p a r a m e t e r s i s r e l a t e d to ass igning cost r e ­s p o n s i b i l i t y because use mus t be made of a x l e - m i l e and v e h i c l e - m i l e f o r a l loca t ing cos t s to v a r i o u s u s e r g r o u p s .

Reducing Highway Costs t o a U n i t Bas i s

In so fa r as the h ighway cost v a r i a b l e i s concerned, s e v e r a l methods cou ld be used f o r r educ ing a l l e}q>endltures to a c o m m o n highway u n i t cost p a r a m e t e r . Two c o m m o n l y used f a c t o r s a r e t o t a l cos t and annual cos t p e r m i l e . F o r c e r t a i n k i n d s of p r o b l e m s , the t o t a l cos t ejqiended by a highway depar tment o r b y an agency cou ld be p lo t t ed v e r s u s v e h i c l e s i z e . T o t a l cost i s p a r t i c u l a r l y u s e f u l f o r a t axa t ion p r o b l e m o r f o r a condi t ion where a known amount of funds i s to be a v a i l a b l e . However , vhere the in ten t i s to es ­t a b l i s h the o p t i m u m v e h i c l e s ize i t w i l l be necessary to reduce the highway costs to a u n i t b a s i s .

The handl ing of maintenance and opera t ion costs i s not p a r t i c u l a r l y d i f f i c u l t . Since the ejcpenditures a re made on an annual bas i s and p r e s u m a b l y can be spread over the e n t i r e mi l eage i n the s y s t e m , t o t a l maintenance and t o t a l opera t ions cos ts can be d i ­v i d e d by the number of m i l e s . F o r c ap i t a l i m p r o v e m e n t some reduc t ion i s necessary to ob ta in an annual f i g u r e to combine w i t h maintenance and opera t ions . The r educ t ion of c ap i t a l inves tment to an annual cost poses the n o r m a l quest ion as to the p r o p e r i n t e r ­est r a t e to be u t i l i z e d w i t h a c ap i t a l r e c o v e r y f a c t o r . The se lec t ion of the i n t e r e s t r a t e w i l l undoubtedly p a r a l l e l the p r a c t i c e of a p a r t i c u l a r agency i n i t s n o r m a l economic s tud ies .

Reduct ion of expendi tures f o r m a j o r i m p r o v e m e n t s to annual cost a lso invo lves p r e ­d i c t i ons o r es tab l i shment of design l i f e . There i s qui te a range of va lues c o m m o n l y ass igned ' to v a r i o u s i t e m s of c ap i t a l i m p r o v e m e n t ; f o r example , the des ign l i f e of r i g h t - o f - w a y m a y extend f o r 50 to 75 y e a r s v^e reas f o r pavements the p e r i o d i s r a r e l y m o r e than 20 y e a r s . Fundamenta l p r i n c i p l e s o f engineer ing economics , as used i n i n ­d u s t r i a l p r a c t i c e , suggest tha t the l i f e p e r i o d to be u t i l i z e d f o r a study should be based upon the longest p e r i o d of some component of the cost , p r o v i d e d that the p e r i o d i s c o n ­s i s ten t w i t h the p lanned use of the f a c i l i t y . Components w i t h sho r t e r l i v e s mus t have

9

rep lacement va lues computed . Based on exper iences of the pas t i n the Un i t ed States, i t i s somewhat d i f f i c u l t to envis ion the c u r r e n t r i g h t - o f - w a y and e a r t h w o r k designs being s u f f i c i e n t l y advanced to p e r m i t a design l i f e of 75 y e a r s . F u r t h e r m o r e , the p r o b ­l e m s of obta in ing costs of s eve ra l successive pavements 20 to 40 y e a r s i n the f u t u r e a re obv ious ly i n the r e a l m of c o n j e c t u r e . A s a r e s u l t , i n the s tudies conducted at The Ohio State U n i v e r s i t y , a design l i f e of 20 yea r s was u t i l i z e d f o r a l l e lements of new c o n s t r u c ­t i o n cos t s . T h i s i n e f f ec t assumes tha t w i t h i n 20 y e a r s the roads be ing cons t ruc ted at t h i s t i m e w i l l have o u t l i v e d t h e i r c u r r e n t r i g h t - o f - w a y and e a r t h w o r k des ign . F o r the average state highways, t h i s i s p robab ly t r u e , whereas f o r the in t e r s t a t e s y s t e m i t i s quite l i k e l y that a longer design l i f e w o u l d be p e r m i s s i b l e .

In o r d e r to combine annual cos ts of cap i t a l i m p r o v e m e n t w i t h those f o r annual- type expendi tures , the t o t a l mi leage i n the sys tem mus t be cons ide red . The r a t e of new cons t ruc t ion on an ex i s t i ng sys t em w i l l r a r e l y be g rea t enough to r e b u i l d the sys t em comple te ly w i t h i n the des ign l i f e . T h e r e f o r e , some ad jus tment mus t be made f o r new cons t ruc t ion cos ts to obta in costs f o r cap i t a l i m p r o v e m e n t p e r m i l e . I f a comple t e ly new sys tem i s under s tudy, the cost of new cons t ruc t ion o r cap i t a l i m p r o v e m e n t can be r e a d i l y reduced to an annual basis and combined w i t h an t ic ipa ted maintenance and o p ­era t ions to obta in t o t a l cos t . Such a condi t ion ex i s t s f o r a t o l l t u r n p i k e .

One ad jus tment wh ich can be made f o r an ex i s t i ng sys tem i s accompl i shed by a s s u m ­i n g that the cap i t a l i m p r o v e m e n t f o r a spec i f i ed p e r i o d of t i m e w i l l cons is t of f o u r types of a c t i v i t y ; name ly , new c o n s t r u c t i o n , r e c o n s t r u c t i o n , r e s u r f a c i n g , and su r face t r e a t ­men t . One may also have to assume that c e r t a i n mi leages w i l l r e ce ive no cap i t a l i m ­p r o v e m e n t . B y s t a t i s t i c a l l y evaluat ing and weigh t ing the cos ts f o r the f o u r types of cap i t a l i m p r o v e m e n t , one can get the average cos t of c ap i t a l i m p r o v e m e n t p e r m i l e p e r y e a r . Such a p rocedu re , i n e f f ec t , reduces the cost of c a p i t a l i m p r o v e m e n t f r o m the t y p i c a l va lue f o r new cons t ruc t ion to an expendi ture commensura te w i t h the type of i m ­provement r e ce ived by the sys tem as a who le . Inc lud ing r e s u r f a c i n g and su r f ace t r e a t ­ment as c ap i t a l i m p r o v e m e n t r a t h e r than maintenance i s not p a r t i c u l a r l y c r i t i c a l . I f i t were inc luded as maintenance there w o u l d m e r e l y be a h ighe r number of m i l e s w i t h "no cap i t a l i m p r o v e m e n t , " and the weighted average annual cost of c ap i t a l i m p r o v e m e n t w o u l d be reduced .

Reducing the cost of s t r u c t u r e s to an annual expenditure p e r m i l e obv ious ly r e q u i r e s spec ia l p r o c e d u r e s . V a r i a t i o n s i n s t r u c t u r e cos ts a re f r e q u e n t l y obtained f o r l i nea l f ee t of b r i d g e o r f o r square f ee t of b r i d g e roadway. The conver s ion of such data to annual cost p e r m i l e r e q u i r e s a r educ t ion of the cap i t a l inves tment to an annual bas i s as w e l l as the de t e rmina t i on of how many l i n e a l f e e t o r square f ee t of b r i e v e a re p resen t on a m i l e of h ighway. The f a c t that the type of b r idge s t r u c t u r e w i l l v a r y , thus changing the r e l a t i onsh ip between cos t and s i ze , mus t be handled on a s t a t i s t i c a l , weighted b a s i s . A s s u m i n g tha t one can get a r e a l i s t i c r e l a t i onsh ip between a v e h i c l e p a r a m e t e r and the average cost p e r l i n e a l f o o t of s t r u c t u r e , the p r o b l e m i s to conve r t to a s t r u c t u r e cos t p e r m i l e f o r the s y s t e m .

One reasonable approach wou ld be to obta in the t o t a l number of b r idge f e e t i n the sys t em and by d i v i d i i ^ t h i s va lue by the number of m i l e s , the average number of b r i d g e -fee t p e r m i l e cou ld be obta ined. B y employ ing a f a c t o r to account f o r the r a t e of r e ­p lacement , annual cos ts w o u l d be ava i l ab l e .

A less complex p r o c e d u r e was u t i l i z e d i n the s tudies at The Ohio State U n i v e r s i t y (6). The t o t a l d o l l a r s expended p e r year each of a s i x - y e a r h i s t o r y w e r e averaged i n o r d e r to obta in the avers^e d o l l a r s f o r s t r u c t u r e s p e r y e a r . The t o t a l number of m i l e s of new cons t ruc t i on were also computed on an average annual bas i s and the t o t a l s t r u c ­t u r a l d o l l a r s p e r m i l e of new cons t ruc t i on was obta ined . I t was then assumed tha t the same r a t i o of s t r u c t u r e cost to new cons t ruc t ion mi l eage w o u l d be f o l l o w e d throughout the p e r i o d s tud ied . Such an approach produces the s t r u c t u r a l d o l l a r s p e r m i l e of new highway cons t ruc t ion and no conve r s ion to l i n e a l f e e t i s i n v o l v e d . Since m a x i m u m and m i n i m u m solu t ions were obta ined the accuracy of the es t imate was cons ide red to be reasonable i n l i g h t of o the r assumpt ions r e q u i r e d i n the s tudy.

Considera t ions of Highway Systems

I n many s tudies i n v o l v i n g I n c r e m e n t a l o r d i f f e r e n t i a l cos t s , the highway e:q)endltures

10

a r e separated on a bas i s of highway sys t ems . Sometimes t h i s i s done on the basis of p o l i t i c a l subd iv i s ions , such as f e d e r a l , s tate , county, m u n i c i p a l , e t c . , and i n o the r s i t i s on the bas i s of types of h ighways r e q u i r e d . F o r example , i n Pancoast 's s tudies i n Ohio (7 ) a d i v i s i o n was made on the bas i s of Type A , B , C, and D roads where each of the f o u r types had t y p i c a l c r o s s sect ions f o r pavement and other cost i t e m s . The need f o r such a breakdown can be t r a c e d i n p a r t to aud i t ing and accounting p r o c e d u r e s . The re a r e also r e q u i r e m e n t s f o r such a de l inea t ion because of d i f f e r e n c e s i n des ign, c o n s t r u c ­t i o n , maintenance, and opera t ion p r o c e d u r e s . In many p r o b l e m s , t h e r e i s no need to cons ider the type o f roads . I n f a c t , f o r t h e o r e t i c a l cons idera t ions , the so lu t ion should be achieved u s ing on ly the fundamenta l d i r e c t cost p a r a m e t e r s . However , when cos ts a r e be ing ass igned on the basis of the method u t i l i z e d i n des ign, then road- type becomes a cons ide ra t ion i n s o f a r as the method of design v a r i e s f o r the s eve ra l sys t ems .

Respons ib i l i t y f o r c e r t a i n types of highway costs should not v a r y apprec iab ly w i t h the r o a d sys t em, even u t i l i z i n g the app l i ed approach . F o r example , s t r u c t u r e capaci ty i s n o r m a l l y es tab l i shed f o r a constant type of m a x i m u m load and the f r e q u e n c y of l o a d ­i n g produces m i n o r v a r i a t i o n s . W i t h the except ion of l o w - t r a f f i c secondary h ighways , even pavements a re c u r r e n t l y designed f o r the heaviest ax le load to be expected, but w i t h v a r i a b l e number s of app l i ca t ions . Unfo r tuna te ly , the quant i ta t ive e f f e c t of r e p e t i ­t ions i s not w e l l unders tood . The cos t f a c t o r s c o n t r o l l e d by geome t r i c cons idera t ions do not n o r m a l l y r e q u i r e a de l inea t ion in to highway sys tems since the re i s some i n d i ­ca t ion that the t r a f f i c vo lume i t s e l f ind ica tes the cost d i f f e r e n t i a l { & ) . Thus , the basic v a r i a b l e s of veh ic l e weight and geome t ry p lu s the number of r epe t i t i ons should desc r ibe the v a r i a t i o n adequately, and the use of road sys tems wou ld be r e s t r i c t e d to those cases where d i f f e r e n t p o l i t i c a l subdiv is ions o r design phi losophies produce d i f f e r e n t design s tandards .

One of the m o r e d i f f i c u l t , fundamenta l dec is ions wh ich i s r e q u i r e d i s i n the r e a l m of the l o w - t r a v e l l e d secondary sys tems , p a r t i c u l a r l y f o r the a l loca t ion of cost r e s p o n s i ­b i l i t y f o r the m i n o r t r a v e l e d highways w i t h on ly a n o m i n a l pavement t h i ckness . Such roads a r e capable of c a r r y i n g some heavy ax le loads , p a r t i c u l a r l y d u r i n g c e r t a i n seasons of the y e a r . The loads o r i g i n a t e f r o m p r i v a t e , i n d u s t r i a l , and c o m m e r c i a l sources . The quest ion i s , should a l l veh i c l e s wh ich use the r o a d be respons ib le f o r the costs on a d i f f e r e n t i a l bas is , o r should the l a rges t veh i c l e s be t r e a t ed on an equ iv ­alent bas i s w i t h the l a rges t v e h i c l e f o r wh ich the design i s comple t e ly adequate ? Two answers appear reasonable . One i s to assume that the t heo r i e s and cost ass ignments wh ich a r e appl icab le to the heavy pavements can be appl ied p r o p o r t i o n a l l y to the t h in ones. A second t h e o r y w o u l d be to a r b i t r a r i l y ass ign the cos ts of the l o w - c o s t pavement to the ax le load group w h i c h mos t f r e q u e n t l y uses the h ighway and f o r whom the pave­ment i s comple t e ly adequate. T h i s , i n e f f ec t , wou ld g ive the heav ie r veh ic l e s a " d i f ­f e r e n t i a l - f r e e " r i d e . M o r e p r e c i s e l y , they would be pay ing essent ia l ly the same amount p e r r e p e t i t i o n as would the s m a l l e r v e h i c l e s . I n e f f ec t , the second theory suggests tha t such roads a r e designed f o r the s m a l l e r v e h i c l e s , and a f e w l a r g e r loads can be t o l e r a t e d i n a q u a s i - r e s t r i c t e d manner .

The re a r e sound reasons f o r apply ing e i the r of the two concepts . I n the studies at The Ohio State U n i v e r s i t y , such p r o b l e m s w e r e handled by obta in ing a m i n i m u m and a m a x i m u m re l a t i onsh ip between pavement costs and ax le l oad . I n the cost ass ignment p a r t of the s tudies , the pavement cos ts f o r the th inner pavements were d i s t r i b u t e d i n the same manner as f o r the heav ie r pavements . In a l l f a i r n e s s , since r equ i r emen t s f o r the heav ie r v e h i c l e s a r e not b u i l t in to the road , the re i s some quest ion as to whether the use of d i f f e r e n t i a l cos ts i s a p r o p e r a s sumpt ion .

V e h i c l e - M i l e and A x l e - M i l e A l l o c a t i o n s

The data of F i g s . 2 and 3 r e f e r to the increase i n cost w h i c h i s r e q u i r e d f o r an i n ­crease i n axle l oad . A second p r o b l e m invo lves the a l loca t ion of the cost of a sys tem to a v a r i o u s s ize veh ic l e s o r to u se r g roups . F o r example , i n F i g . 2 the cost to p r o ­v ide a highway capable of c a r r y i n g 9 - ton axles i s suggested. However , a l l veh ic l e s share a p a r t of the r e s p o n s i b i l i t y f o r that cost , and the p r o b l e m i s to de t e rmine what p o r t i o n of a g iven expendi ture can be a t t r i b u t e d to the v a r i o u s - s i z e d ax le s .

11

As stated in the definitions, highway costs are a direct function of axle load, vehicle dimensions and performance (including driver ability), and the number of vehicles. Furthermore, the repetitions of these factors consistently affect all phases of design. In fact, there are practically no costs which are independent of load or vehicle repetition. Thus, there are relatively few dollars which can be allocated solely on the basis of the number of vehicles in the system insofar as direct cost responsibility is concerned. One notable exception is the collection of part of the revenue (motor vehicle registration), In states where a third-structure tax such as axle-mile or a ton-mile is used, even a part of the revenue collection costs are affected by the mileage traveled. In the studies at The Ohio State University i t was assumed that tiie amount of cost which was strictly related to the number of vehicles was negligible and all costs were distributed on the basis of either axle-mile or vehicle-mile.

For those costs which are related to structure capacity (structures and pavements), the distribution was on the basis of axle-miles (Fig. 3b). For those expenditures which were related to geometry or vehicle dimensions (earthwork, right-of-way, drainage, etc.) the allocation was made on the basis of vehicle-miles (Fig. 3a). While there may be justification for assigning costs on a "per vehicle" basis in some highway economic studies, there appears to be no such justification for such an assignment where the question is one of cost responsibility.

A fairly substantial portion of al l highway expenditures can be classed as "uniform" costs. These values represent the expenditures which are independent of vehicle di­mensions.

Pavement and structure costs required for the basic vehicle are typical, as are all costs for axle loads of approximately two tons or less (Fig. 2). The compilation of uniform costs can be separated so as to indicate whether the e:q)enditures are for structural or geometric requirements. While it might be argued that these uniform costs could be allocated on a unit vehicle basis, a fair presumption is that ownership of a vehicle does not constitute reasons for providing extensive mileages of highways; rather, usage of that vehicle. Therefore, axle-miles or vehicle-miles are considered a more reasonable bases for allocation of the uniform costs. Influences of Traffic Data

The type of traffic data which are available affects the accuracy of cost allocation problems. Since highway costs are associated with axle-miles or vehicle-miles, the average ADT (including the number of various types of vehicles), and the average number of axles per vehicle are required for the highway system being studied. Most state highway departments have developed traffic volumes for the various roads in the system. Furthermore, periodic checks have established a reasonable basis for assump­tion as to the numbers and sizes of vehicles. It is probably that the degree of accuracy of the traffic data is commensurate with the accuracy of the other phases of a cost-size investigation.

The contribution of foreign vehicles travelling in the state and the amount of travel of domestic vehicles out of the state is a source of question. Such a problem arises in the application of average miles travelled per year to the numbers of vehicles in order to get axle-miles or vehicle-miles. While a state bureau of motor vehicles can normally give the number and types of registered vehicles, the amount of travel per year which is driven in or out of the state is quite a different matter. It is also difficult to deter­mine the number and average mileage of foreign vehicles. Studies designed to obtain such .data are in progress in some states but no reliable data are yet available. For the studies at The Ohio State University a simplifying assumption was made; namely, that the amount of out of state travel by domestic vehicles was equal and identical in terms of types of vehicle to the amount of in the state travel by foreign vehicles.

While traffic data has a pronounced influence on the allocation of cost responsibility, there is also a significant effect on the crediting of taxes paid to various highway user groups. In attempting to determine how much tax was paid by a given type of user, the total revenue obtained is frequently utilized. Thereafter, average miles per vehicle, average gasoline consumption per mile, and average number of vehicles are used to

12

account for the taxes paid. In the case of third-structure taxes, gross weight, axle-load, or number of axles may also be needed. Having achieved the allocation of taxes to various groups, one may wish to compare the cost responsibility for the same groups. To do so, the same assumptions must be utilized for numbers of vehicle-miles and axle-miles.

In reviewing cost-tax studies, a point of discussion frequently arises with reference to the assumptions that lead to the vehicle-mile and axle-mile values. Smaller or larger mileages are debated in order to improve relationships. A greater number of vehicle-miles assigned to a group wil l indicate a higher percent of the total taxes paid. On the other hand, a greater number of vehicle-miles increases the percent of cost responsi­bility. Special studies were conducted at Ohio State in June, 1958, by Robert Chieruzzi, research associate, to learn more of the rate of change of taxes and cost responsibility with changes in the ratio of vehicle-mile and axle-mile data between the severl high­way-user groups. Contained in the following paragraphs is a summary of the results of that study.

The vehicle miles used in obtaining cost allocation (6) were obtained for the year 1953 in an earlier investigation (JL) by multiplying the number of registered units in each vehicle category by the average annual mileage for the particular vehicle group. The six user-groups selected were passenger cars, panel and pickup trucks, other single-unit trucks, multi-unit trucks, farm trucks, and buses. The registered numbers of units for the passenger car, farm truck, and bus groups were initially obtained directly from the registration records of the Ohio Bureau of Motor Vehicles. Panel and pickup trucks were considered as all registered single-unit trucks with empty weights of 4,000 lb or less. As estimating procedure was necessary to obtain the numbers of

TABLE I

VEHICLE AND AXLE-MILE DATA FOR OHIO IN 1953

Vefatele Group Registered Units CAdiusted)

Average Annual MUeage*

Vehicle-Miles Per Cent of Total

Number of Axles

Axle-Miles Per Cent of Total

1. Passenger Cars 2,772,063 9,235 25,600,001,805 81.1 2 51,200,003,610 76.2

2. Panel and Pickup Truck 140,721 10,127 1,425,081,567 4.5 2 2,850,163,134 4.2

3. Other Single Unit Trucks 121,S44 17,582 2,138,744,808 6.8 2.064 4,414,000,000 6.6

4. Multi-Unit Truck 38,354 42,188 1,618,078,552 S. 1 4.46 7,220,000,000 10.8

5. Farm 72,691 8,044 584,726,404 1.8 2 1,169,452,800 1.7

6. Bus 3,475 47,750 165,931,250 0.7 2 331,862,500 0.5

Total 3,148,948 31,532,564,386 100.0 67,185,482,044

* Assumes that the travel out-of-state by local vehicles is equal and similar to travel in-the-state by foreign vehicles.

units for the "other single-imit" and the multi-unit groups, since such a breakdown was not available. The total truck and tractor registered units with empty weights greater than 4,000 lb was given. The division of these totals into the two groups was based on an estimate reported by Pancoast (1) which involves the fractions of trailer-miles pulled by trucks and by tractor-seml-trailer combinations obtained from studies made in Ohio in 1950 and assumed to be valid for 1953. The average mileages per vehicle for each category were equal to those estimated for 1962 by Pancoast (J) and assumed to be adequate for accelerated conditions existing in 1953. Table 1 summarizes the data for each of the vehicle groups and the vehicle miles are taken verbatim from the tax study (1) .

1 3

A direct method for obtaining the axle-miles was employed. Essentially, it con­sisted of multiplying the assigned vehicle-miles by the average number of axles per vehicle for each group. A total of two axles each was arbitrarily assigned to the pas­senger car, panel and pickup truck, farm truck, and bus groups. Considerably greater difficulty was encountered in computing the number of axles per vehicle for the other two groups. An estimate was obtained for the single-unit trucks with empty weight greater than 4 ,000 lb from the data on the study by Pancoast {J). From the estimated vehicle-miles for two and three axle units, a weighted average number of axles of 2 . 064 was obtained. The calculations are shown below.

Two Axles Three Axles Total Vehicle-miles 1 ,816 ,501 123,690 1 ,940 ,191 Axle-miles 3 ,633 ,102 371,070 4 ,004 ,172

Average number of axles = ^' "^Q' = 2 .064 Hie steps which were required to obtain the axle-estimate fjor the multi-unit groups

were as follows: 1 . The average number of axles for semi-trailers was obtained from data in the

study by Pancoast (t) follows: One Axle Two Axles Total

Vehicle miles 25 ,479 171 ,916 197,395 Axle miles 25 ,479 343 ,832 3 6 9 , 3 1 1

Average number of axles = = 1.871

2. Average number of axles for trailers with empty weights greater than 4 ,000 lb was assumed as equal to two.

3. The bases for combining power units with trailers were the following statements of Pancoast (_7) who traced the data to results obtained from a study in 1950: (a) 45 Vs percent of trailer-miles was pulled by a commercial truck (single-unit greater than 4 ,000 lb); (b) 5 4 % percent of trailer-miles was pulled by a tractor-semi-trailer combination.

Accordingly, the following calculations were made with the use of data from the tax study U ) :

Vehicle-Miles Number of Axle-Miles Axles

1 . Trailers greater than 3 ,000 lb 498,287, 600 2. Trailers pulled by commercial

trucks (45 % percent of Step 1 ) 225 ,800 ,000 4 . 0 0 903 ,200 ,000 3. Trailers pulled by tractor-semi­

trailer (Step 1 - Step 2) 272, 500,000 5 .87 1 ,600 ,000 ,000 4 . Semi-trailers, total (from tax

study) 746 ,444 ,160 5. Semi-trailer combination only

(Step 4 - Step 3) 473 ,944 .160 3 .87 1 ,834 ,163 ,000

6. Total 972 ,244 ,160 4 , 3 3 7 , 3 6 3 , 0 0 0

A K * , 4 , 3 3 7 , 3 6 3 , 0 0 0 . . „ Average number of axles = 9 7 ^ 244 1 6 6 ~

The axle-mile data are summarized in Table 1 . The results of traffic variations can be expressed as percentages of either vehicle-

miles or axle-miles, so that the variation can be in any one of the independent variables of (a) registered units, (b) avers^e annual mileage, and(c) number of axles. For instance, axle-miles ( A ^ ) are obtained by the following equation:

A i n = R - M a - a ( 1 )

14

CHANGES IN COST RESPaNSIBn.ITY WITH TRAFFIC VARIATWNS

Vehicle Variation Vehicle-Mle Axle-Mile Vehicle--Mile Axle-Mile Total Coat Change Group * (%) Dlatributlon Dlatributlon Coat Coat Reaponaibllity (%) Group * (%)

(%) (%> Reaponaibllity Reaponaibllity (%) (%> (%)

Max. Mln. Max. I b n . Max. Mln. Max. Mln.

P 81.1 76.2 43.6 46.5 13.0 22.7 56.6 69.2 (0) (0) C 0 6.8 6.6 5.1 6.8 5.8 9.6 10.9 16.4 (0) (0) B 5.1 10.8 3.8 5.1 9.5 15.8 13.4 20.8 (0) (0) P 82.6 77.9 44.4 47.4 13.3 23.2 57.7 70.6 (+1.1) (+1.4) C +10P 6.3 6.1 4.9 8.7 5.8 9.9 10.7 16.6 (-0. 2) (+0.2) B 4.7 10.0 3.7 5.1 9.5 16.2 13.2 21.3 (-0.2) h-0.5) P 79.5 74.2 42.8 45.6 12.7 22.1 55.4 67.7 (-1.2) (-1.5) C -lOP 7.4 7.1 5.5 7.3 6.1 10.1 11.7 17.4 (+0. 8) (+1.0) B 5.6 11.6 4.2 5.5 10.0 16.4 14.2 22.0 (+0. 8) (+1.2) P 83.8 79.4 45.1 48.1 13.5 23.7 58.6 71.7 (t2.0) (+2.5) C +20P 5.8 5.7 4.7 6.5 5.7 9.8 10.4 16.3 (-0.5) (-0.1) B 4.4 9.3 3.5 4.9 9.3 16.0 12.8 21.0 (-0.6) (+0.2) P 77.5 71.9 41.7 44.5 12.3 21.5 54.0 65.9 (-2. 6) (-3.3) C -20P 8.1 7.8 6.0 7.7 6.3 10.2 12.3 17.9 (H.4) (+1.5) B 6.1 12.7 4.5 5.8 10.3 16.2 14.8 22.4 (+1.4) (+1.1) P 80.6 75.7 43.4 46.2 12.9 22.6 56.3 63.8 (-0. 3) (-0.4) C +10C 7.4 7.2 5.6 7.5 6.4 10.6 12.0 18.1 H-1.1) (+1.7) B 5.1 10.7 3.9 5.1 9.5 15.7 13.3 20.9 (-0. 1) (+0.1) P 81.8 76.7 44.0 46.9 13.1 22.9 57.1 69.8 (+0. S) (+0.6) C -IOC 6.1 5.9 4.8 6.5 5.5 9.3 10.3 15.7 (-0.6) (-0.7) B 5.2 10.8 4.0 5.5 10.0 16.9 14.1 22.4 (+0. 7) (+1.6) P 80.1 75.2 43.1 45.9 12.8 22.4 55.9 68.3 (-0. 7) (-0.9) C +20C 8. 1 7.8 6.1 8.0 6.8 11.2 12.9 19.2 (+2.0) (+2.8) B 5.0 10.6 3.8 5.0 9.2 15.2 13.0 20.2 (-0.4) (-0.6) P 82.3 77.3 44.3 47.2 13.2 23.0 57.5 70.3 (+0.9) (+1.1) C -20C 5.5 5.3 4.3 5.9 5.0 8.5 9.3 14.4 (-1.6) (-2.0) B 5.2 10.9 4.1 5.7 10.3 17.5 14.4 23.2 (+1.0) (+2.4) P 80.8 75.4 43.4 46.3 12.9 22.5 56.3 68.8 (-0.3) (-0.4) C +IOB 6.7 6.5 5.1 6.8 5.7 9.4 10.8 16.3 (-0.1) (-0.1) B 5.6 11.7 4.3 5.7 10.3 17.0 14.5 22.7 (+1.1) (+1.9) P 81.6 77.0 43.9 46.8 13.1 23.0 57.0 69.8 (+0.4) (+0.6) C -lOB 6.8 6.6 5.3 7.2 6.2 10.6 11.5 17.7 (+0.6) <H.3) B 4.7 9.8 3.6 4.9 9.2 15.5 12.8 20.4 (-0.6) (-0.4) P 80.4 74.6 43.2 46.1 12.7 22.3 55.9 68.3 (-0.7) (-0.9) C +20B 8.7 6.4 5.1 6.7 5.5 9.0 10.5 15.6 (-0.4) (-0.8) B 6.1 12.6 4.6 6.1 10.7 17.6 15.3 23.7 (+1.9) (+2.9) P 82.0 77.9 44.1 47.0 13.3 23.2 57.4 70.3 (+0.8) (+1.1) C -20B 6.8 6.7 5.4 7.3 6.6 11.2 11.9 18.6 (+1.0) (+2.2) B 4 .1 8.8 3.3 4.4 8.6 14.7 11.8 19.2 (-1.6) (-1.6)

' P - Paaaenger Cara C - Single Unit Trucka ( Type C ) B - Multi-Unit Trucka ( Type B )

where: R = number of registered units

= average annual mileage per unit a = number of axles per unit

A ten percent change in axle-miles can be obtained by a ten percent change in any one of the three independent variables or as the aggregate of individual changes in all three variables.

For the special study, variations in traffic data were expressed as percentage changes in the vehicle-mile and axle-mile quantities of three vehicle groups, (a) passenger cars, (b) other single-unit trucks, and (c) multi-unit trucks, and were limited to pfus and minus ten and twenty percent. Interpolation and extrapolation are possible for other values. The scheme produced a total of twelve separate variations. The panels and pickups, bus and farm truck groups have a total influence of less than ten percent of total taxes and cost responsibility, and therefore were conbined into a single group.

For each of the twelve variations considered, there are correspondii^ changes in both the vehicle-mile and axle-mile distributions, which produce proportionate changes

TABLE 3

OHIO TAX DATA FOR 1953*

15

Vehicle Group

1. Registration Fees

Registered Units

Registration Fees

Fees per Unit

Passenger Cars Single Unit Trucks Multi-Unit Trucks

2,772,063 121,644 79,592

26,576,913 13,511,092 11,991,923

9.58741 111.07076 150.66744

2. Gas Tax

Vehicle Group

Passenger Cars Single Unit Trucks Multi-Unit Trucks

Vehicle Group

Single Unit Trucks Multi-Unit Trucks

Vehicle Miles

25,600,001,805 2,138,744,808 1,618,078,552

Amount Collected (doUars)

79,258,191 12,514,276 18,330,204

'3. Highway Use Tax

Axle-Mies

4,414,000,000 7,220,000,000

Amount Collected (dollars)

229,000 14,501,000

Unit Tax (dollars per vehicle mile)

0.003096 0.005851 0.011328

Unit Tax (dollars per

axle mile) 0.00005188 0.0020084

* From tax studies (1)

in the assignment of cost responsibility. Shown in Table 2 are the results thus obtained.

For each of the twelve variations in the vehicle-mile and axle-mile quantities, the changes produced in the distribution of tax credit were also computed. Of the various sources of taxes, only the three major sources were considered in the special study— (a) registration, (b) gas, and(c) highway use. Pertinent tax data, shown in Table 3 were obtained from the tax study (_1). The changes in the three taxes which are asso­ciated with the traffic variations are summarized in Table 4.

TABLK 4

SUMMARY OF DATA FOR TRAFFIC VARIATIONS

Vehicle Group Variaticm Registration Gas Tax Highway Use Total Involved (%) Fee (dollars) (dollars) Tax (dollars) Taxes

(dollars)

Passenger Car lOP 2,657,688 7,925,816 _ 10,583,504 20P 5,315,375 15,851,633 - 21,167,008

Single Unit Trucks IOC 12,164 1,297,678 24 1,309,866 (TypeC) 20C 24,328 2,595,356 48 2,619,732

Multi-Unit Trucks lOB 3,835 1,833,022 1,443 1,838,300 (Type B) 20B 7,670 3,666,044 2,886 3,676,599

16

TABLE S

CHANGES IN TAXATION ESTIMATES WITH TRAFFIC VARIATICJNS

Variation Vehicle Tax Scheme Tax Scheme Tax Scheme Tax Scheme (%) Group a ) (2) (3) (4)

(%) (%) a,) <%»

0 P 68.1 58.1 52.9 51.3 C 10.0 12.6 10.8 11.1 B 15.4 21.3 18.2 18.8

Gen. Pub. — — 13.0 11.8 +10P P 68.9 59.8 54.7 53.0

C 9.8 12.1 10.4 10.7 B 15.0 20.5 17.5 18.1

Gen. Pub. — — 10.8 11.4 -lOP P 67.2 56.3 50.9 49.4

C 10.3 13.1 11.3 11.5 B 15.9 22.2 18.9 19.5

Gen. Pub. — — U . 7 12.2 +20P P 69.7 61.3 56.3 54.6

C 9.5 11.6 10.0 10.3 B 14.7 19.7 16.8 17.5

Gen. Pub. — — 10.4 11.0 -20P P 66.3 54.4 48.8 47.5

C 10.6 13.7 11.8 11.9 B 16.3 23.2 19.7 20.3

Gen. Pub. — — 12.2 12.7 •flOC P 67.9 57.8 52.6 51.0

C 10.3 13.0 11.3 11.5 B 15.4 21.2 18.1 18.7

Gen. Pub. — — 11.2 11.7 -IOC P 68.3 58.4 53.1 51.5

C 9.7 12.1 10.4 10.7 B 15.5 21.4 18.3 18.9

Gen. Pub. — — 11.3 11.8 +20C P 67.6 57.5 52.3 50.8

C 10.6 13.4 11.7 11.9 B 15.3 21.1 18.0 18.6

Gen. Pub. — — 11.1 11.7 -20C P 68.5 58.7 53.4 51.7

C 9.4 11.7 10.0 10.3 B 15.5 21.5 18.3 19.0

Gen. Pub. — — 11.3 11.9 +10B P 67.8 57.7 52.5 51.0

C 10.0 12.4 10.8 11.0 B 15.8 21.9 18.7 19.3

Gen. Pub. — — 11.2 11.7 -lOB P 68.4 58.5 53.2 51.6

C 10.1 12.6 10.9 11.1 B 15.0 20.7 17.6 18.3

Gen. Pub. — — 11.3 11.9 +20B P 67.5 57.3 52.1 50.6

C 9.9 12.4 10.7 10.9 B 16.2 22.4 19.3 19.8

Gen. Pub. — — 11.1 11.6 -20B P 68.7 59.0 53.6 51.9

C 10.1 12.7 11.0 11.2 B 14.6 20.2 17.0 17.8

Gen. Pub. ~ — 11.4 11.9

17

By introducing the proper changes in the tax credits for each of the traffic variations, corresponding tax credit distributions were obtained. As stated previously, a signifi­cant factor in the comparisons of cost responsibility with taxes paid is the taxes which are included in the analysis. Each of the following four tax schemes was considered in the specidal study:

TABLE 6

E F F E C T UPON TAXES PAID-COST RESPONSmiLlTY RELATIONSHIPS

Vehicle Group More Favorable*

Tacreaae Decrease

NegUglble Effect

Passenger PI Cars (P) P2

P3 P4 CI Bl

C2, C3, B2. B3.

C4 B4

Other Single- PI , P2, P3, P4 Unit Trucks CI

(C)

Bl B2 B3 B4

C2 C3 C4

Multi-Unit PI Trucks P2

(B)

CI C2 C3 C4

P3 P4

B l B2 B3 B4

Numbers used with letters refer to the four tax assumptions. The column indicates the tax assuii4)tlons that produce more favorable cost-size relations, and whether Qie txaS&e variation for a given vehicle group must be increased or decreased to obtain the better relation.

18

1. Al l taxes were included except the general public's portion. 2. Al l taxes were included except state sales, federal excise and the general

public portion. 3. Al l taxes were included except non-highway use taxes. 4. A l l taxes were included except state sales and federal excise taxes.

Non-highway use taxes were those obtained from highway users but not expended on Ohio highways, while the general public's portion came from the general funds of the state and local governments; that is, not highway user taxes. The results are some­what misleading in that the federal tax laws of 1953 and 1954 are considered. Several types of taxes which were not utilized on highways at that time must now be incorporated into the highway budget. The various tax credit distributions are tabulated in Table 5.

The influences of the traffic variations were expressed on the basis of the variations produced more or less favorable taxes paid-cost responsibility relationships for each

72

70

68

P I I

Passenger C ars

- Cost

Maximu

Respon

m

sibility

P I

C - Cost

Maximu

Respon

m

sibility r ^ •

y y

y

P2

y y

y

P I note: N iefer to issumpi

umbers Tox ion

y / —

C2 —-B2 P3

F note: N iefer to issumpi

umbers Tox ion

- Cost

Minimui

Respon

n /

/ . / /

y

-^^^^^ y

y

C B P4

- Cost

Minimui

Respon libility

• /

/ /

y y

-03 -B3

04 /

/ — a t • y

/ /

'—y -03

-B3 04

/ /

/ / - Taxes Paid

1 1

6 4

62

60

6.

K |2

I " •S 56

I " u

50

4 8

4 6 - 2 0 -10 0 +10 + 20

Traffic VoriatUxi - P«r Cent

Figure 1̂ . Effect of t r a f f i c variation on taxes paid and on cost responsibility passenger cars.

19

of the vehicle groups considered. Summarized in Table 6 and in the following are the trends indicated in the plots of the data shown in Figs. 4, 5, and 6.

Passenger Cars, —(a) Under the Tax Schemes 2, 3, and 4 the effects of variations in both C and B Type traffic data ( Table 3) are negligible, (b) Under Tax Scheme 1 an

I

20-

18

16

i 12

10

c "C" Type Vehii :les

- Cost Maximu Respo

m nsibility > < p

- Cost Maximu Respo

m nsibility ^ — B

Note: r Refer Assum

itumberi to Tox ption CZ

c BZ

I r "

^ l 3

Note: r Refer Assum

itumberi to Tox ption

Minimu

Cost ResDon

in

sibility.

CZ c BZ

I r "

^ l 3

in

sibility.

CZ c BZ

I r "

^ l 3

- 2 0 -10 0 +10 + 2 0 Tra f f i c Variation-Par Cent

Figure 5. Effect of t r a f f i c variation on taxes paid and on cost responsibility-type "C" vehicles.

I

5

26

24

22

20

18

16

14

12

10

"B" Type 1

Vehicles B

BZ

CZ P S - B 4 ^ 8 3 C4 C3

Maximum

Cost Responsibility

CZ P S - B 4 ^ 8 3 C4 C3

1 4ote: N tefer to Xssump

umbers Tax

tion > P4 P3 Bl

- F 4ote: N tefer to Xssump

umbers Tax

tion

Cost

Minimu Respon

m sibility

CI B

PI

Cost

Minimu Respon

m sibility

C P

- 2 0 -10 Tra f f i c

0 +10 + 2 0 Variation - Per Cent

Figure 6. Effect of t r a f f i c variation on taxes paid and on cost responsibility type "B" vehicles.

20

increase in both C and B traffic and a decrease in P vehicle-miles will produce favor­able effects.

Type C Trucks, —(a) Variation in the passenger car vehicle miles wil l have negli­gible effect, regardless of tax schemes, (b) Favorable effects are produced by a de­crease in the C Type vehicle-miles underTax Schemes 1, 3, and 4 and an increase in B Type vehicle-miles under Tax Schemes 1. (c) Under Tax Scheme 2 an increase in the C Type vehicle-miles wil l produce non-favorable effects.

B Type Trucks.—(a) Favorable effects will be produced by an increase in C Type vehicle-miles and a decrease in both P and B Type vehicle-miles under all Tax-Schemes except one which has negligible effect, namely a passenger car variation under Tax Scheme 1.

The analyses for the special study were not complete and represent the results pro­duced by the consideration of only three of the tax sources: (a) registration fees, (b) fuel tax, and (c) highway use. Furthermore, the tax and traffic data were obtained from the tax study (^)and highway cost study {6} and variations were made therefrom. However, the following significant statements are considered reasonable interpretations of the results.

There are two major variations which improve the taxes paid-cost responsibility relationship for the B and C Type vehicles. One condition is produced by a decrease in their respective vehicle and axle miles. This infers that although the tax credits increase with increased vehicle and axle mileage, the cost responsibility increases at a faster rate. Conversely, the cost responsibility diminishes at a faster rate than taxes paid. The other favorable variation is an increase in vehicle and axle mileage in the other group; that is, an increase in B Type vehicle and axle mileage wil l produce im­proved relationships for the C Type group and vice versa. Again, the reason for this situation stems from different rates at which the taxes paid and cost responsibility are affected.

An increase in passenger car vehicle-miles produces favorable effects for all tax schemes except the one which includes most of the taxes which are paid by highway users but are not used on Ohio highways. This indicates that the taxes paid increase at a greater rate than cost responsibility except for the one instance.

Considerations in Establishing a Basic Vehicle The basic vehicle can be defined as that vehicle which can satisfactorily operate on

highways without adding to the minimum highway costs required for the safety and con­venience of the smallest vehicle. The establishment of the basic size of vehicles is critically necessary for problems where differential costs between vehicles is the basis or where allocation of cost responsibility is concerned. On the other hand, if one is attempting to establish the optimal design, considerations of the basic vehicle may not be pertinent. The last statement assumes that the size of the basic vehicles is at least as great as a passenger car. In developing a relationship between highway costs and vehicle size, one can originate with, or extrapolate to, the lowest sized vehicles. At some point near the lowest limit of vehicle size, climatic and non-highway user re­quirements start controlling. It is at this point that the size of the basic vehicle is de­fined. Figure 2 illustrates the point by use of the Ohio studies. As can be seen, if the optimum-sized vehicle has an axle load larger than 2.5 tons, the size of the basic ve­hicle is not a factor.

On the other hand, assignment of cost responsibility requires an estimate of the size of the basic vehicle, since all vehicles share, on some equivalent basis, the costs re­quired for the basic vehicle. The indirect source of cost which affects the size of the basic vehicles more than any other is climate. Another contribution however, is the minimum construction cost which is feasible. To a certain extent, the topography is also a factor in the geometries due to the performance characteristics of the vehicle. Since climate, topography, and construction costs are factors, the size of the basic vehicles wil l vary from one locale to another; that is, the basic vehicle for the State of Maine wi l l be different than that for New Mexico. For area-wide studies, then, the basic vehicle is based upon a statistical evaluation of the conditions in the area.

21

In starting an investigation of the relationship between highway costs and vehicle size it wil l be important to know whether the establishment of a basic vehicle is requir­ed in the problem. Secondly, i t should be understood that the size of the basic vehicle is a function of the region and the area under study must be utilized as a basis rather than the adoption of a value derived for different conditions.

Reconstruction, Resurfacing, and Surface Treatment Allocating cost responsibility for reconstruction, resurfacing, and surface treat­

ment includes certain uniqjue considerations. While the following discussion is limited to pavement costs, the principles would be applicable to other costs which are normally included in reconstruction.

An interesting (Question, pertaining primarily to reconstruction and resurfacing, can be stated as follows: to what size vehicle should costs be assigned for those pave­ment expenditures which attempt to extend the design life? In the strictest sense, there is no problem because the heaviest axle loads which are utilizing the pavement undoubt­edly produce the greatest stress per repetition. Hie confusing element is the fact that climate has contributed to the reduction in structural capacity of the pavement. Un­fortunately, the effect the smaller vehicles would have on the pavement cannot be ration­ally determined. Furthermore, climate alone may start producing damage which wil l require maintenance. It has been argued that since the pavement has gone beyond the design life, all vehicles should share on an equivalent basis for its rehabilitation. For the studies at The Ohio State University, however, the direct responsibility for the pavement disintegration was considered as resting with the heavy trucks. It was also recognized that this assumption produced extreme relationships since the climatic de­terioration of the structure and the activity of the lighter-weight vehicles undoubtedly contribute. Therefore, the method finally adopted was to compute maximum cost dif­ferential by assigning the entire reconstruction and resurfacing pavement costs to the heavy vehicle. For the minimum cost differential i t was assumed that vehicles shared responsibility on the same basis as they would for new construction.

The uncertainties associated with surface treatment are somewhat different. The definitions for surface treatment vary with organizations, but for the following dis­cussion i t wil l be assumed that surface treatments are those additions to the pavement which add no structural capacity. It is also assumed that no serious surface irregular­ities could be levelled by surface treatment, and one can conclude, therefore, that the surface treatment is principally placed for control of climatic influences.

On newly-constructed secondary highways the inclusion of surface treatment may furnish the completion of a long-range, new-construction project. In such cases, sur­face treatment should be considered as new construction and prorated in accordance with the accepted pavement design techniques. The procedure followed for The Ohio State studies consisted of applying the principles of pavement cost allocations for new construction in order to obtain the maximum cost differential. Whereas for a minimum cost differential, the costs were distributed uniformly on a usage basis. In no case were the costs of surface treatment assigned directly to the truck as was done for re­construction and resurfacing.

From the foregoing it wi l l be noted that an engineering decision was made with ref­erence to the assignment of the costs. By more rigorous study of the cost data, it might be possible to assign the expenditure on a more rational basis. However, i t wi l l be (juite an unusual situation where the available cost and design records are sufficient to permit a detailed analysis of the type and extent of reconstruction, resurfacing, and surface treatment.

Engineering and Administration The cost responsibility for engineering and administration has been generally al­

located on one of two basic concepts. One philosophy states that engineering and ad­ministration is a function of the dollar size of the program and should, therefore, be divided proportionally among the various cost items for which the engineering and ad­ministration has been required. Under this theory the dollars for engineering and ad-

22

ministration would be allocated on the same basis as the individual cost items to which they are assigned; that is, dollars of engineering and administration added to the cos*̂ of pavements would be allocated on the same basis as the actual pavement costs.

A second theory for considering engineering and administration deals with the as­sumption that such costs are a function of the numbers of vehicles and miles of highways in the system and not a function of the size of the vehicle; that is, engineering and ad­ministration would be approximately the same even if passenger cars were the largest vehicles using the highway. From a viewpoint of plan preparation or design engineering, one is inclined to accept the second theory. For actual construction, however, the in­creased quantities required for the heavier vehicles undoubtedly add to the cost for field engineering and administration. The fact that engineering fees are based upon a per­centage of the contract costs is used as an argument in favor of the f i r s t theory. How­ever, actual costs of plan preparation and construction supervision would not vary sig­nificantly with the sizes of the vehicle for which the design is accomplished without varying the level of effort to achieve the design.

From a practical point of view, it seems certain that the actual relationship lies somewhere between the two extremes su^ested in the two aforementioned theories. In application, the f i r s t theory leads to the allocation of costs on the same basis as other highway costs which would place a higher cost differential on the larger vehicles. Under the second theory, the engineering and administration would be considered a function of the number of vehicle-miles or of axle-miles, but on a uniform basis, rather than an added increment assigned to the larger vehicles.

Estimating EMfferential Costs

The extensive work required for developing cost-size relations, and the dependency upon design methods for current results discourages many agencies from undertaking detailed analyses. Most of the research at Ohio State was devoted to the basic meth­odology of obtaining cost-size relationships for the individual cost items. Since the studies were for Ohio highway conditions only, the results are not directly applicable to other areas or agencies. However, in lieu of other information, the data are con­sidered to be approximately equivalent, at least qualitatively. Where comparable design criteria are utilized, the shape of the cost-size curve shown in Fig. 2 is con­sidered as representative of results using comparable assumptions. Further enlighten­ment may be provided by Table 7 which summarizes the equations which lead to the combined data.

Assuming that the relations expressed in Fig. 2are acceptable, particularly as to the shape of the curves, differential costs can be estimated directly from total annual cost (or total cost per mile) and the legal load (or design load). The following is the math­ematical expression for total costs:

Cmax = 9-7Wi°-^*^^ (2) in which:

^max ~ Maximum total annual cost per mile in thousands of doUars. Wi = Weight of axle load in tons.

C „ ^ . 4 . 5 W . (3) in which:

Cmin = Minimum total annual cost per mile in thousands of dollars. The equations hold for a range of W of 5 to 20 tons, and for the single value of 2 tons. However, there is an implication that the axle load weights of 10 to 20 tons wil l (a) not involve a change in vehicle dimensions, or (b) not affect the geometric requirements.

For the general solution:

C = CaW^ (4)

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in which: C = annual cost per mile for the axle load, W. Ca = annual cost per mile for the unit axle load. s = constant (equal to the slope of the logarithmic relation).

The unit axle load is defined as the axle load for which is known. If no data are available as to cost for a specific axle load. Equation 4 wil l not be helpful. However, for an existing system, the legal (or design) load can be used in conjunction with the actual expenditures and a solution achieved. Values of s are a function of the design techniques, which for Ohio were defined by:

s = 0.00163C9.5 + 0.1210 (5)

in which: C 9 . 5 = Total annual cost per mile in thousands of dollars for a design axle

load of 9.5 tons. The equation is considered applicable for C9 .5 values between $6,000 and $13, 200. Where the differential costs between two axles is desired:

C2 = C^Wi' s D = Ci

in which: D = Differential costs between requirements for axle loads of Wi and Wa .

T A B L E 7

EQUATIONS USED IN D E V E L O P I N G C O S r - S I Z E R E L A T I O N S

Cost Jtem Equation Remarks

Pavements (P)

P 9.5 New construction, two-lane f u l l d ^ t h

Structures (S)

Cg max = 410 log W + 90

Cg m m = 115 log W + 155

Weighted combination f o r s ix s t ruc tura l types and seven vehicle types

Earthwork (E)

C g j j = 32. 8 log T -63. 6

C „ „ = 0 . 0 0 1 1 o g T + 1 2 . 1

Rura l new construction

Rura l reconstruction

Blght-of-Way (A)

C ^ j , = 4.0 T + 6 . 4

C ^ H = 0. 003 T +3. 8

Rura l new construction

Rura l r e c m s t r notion

Roadside Development

( Q )

CQJJ = 0. 000005 T +5.5

CQJJ = 0.0001 T + 3 . 7

RuraTnew construction

Rura l reconstruction

Drainage <D)

C j j j j = 0. 007 T +2. 8 Rura l new construction no re la t ion found f o r reconstruction

Maintenance (M)

C j j = 4 . 9 1 . 19 + 0.206 T j j Roadbed and surface maintenance and repair - excludes resurfac ing, surface creatment, etc.

Total Cmax = « - ^ W 0 - 1 « 2

C ^ . „ = 4 . 5 W » - 1 3 0 2

Discontinuous over the range 2 to 5 ton axle loads. Assumes no increase i n geometric dimensions of vehicles f o r 10 to 20 tons. Unit axle load is one ton.

(6)

C - Annual cost per m i l e in thousands of do l la rs .

N - New construction

R - Reconstruction

S - Constant

W - Axle load i n tons .

T - Adjusted A D T - number of heavy vehicles increased by topographic fac tor .

H - Heavy vehicle - (Type B & C t rucks ) .

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If costs are to be compared to the legal axle load or to the unit axle load, then:

D ^ = C u ( W ^ - l ) ( 7 )

NEW CONSTRUCTION TWO LANE NEW CONSTRUCTION

TWO LANE

MAXIMUM COST

MINIMUM COST

4 5 6 7 8 9 10

AXLE LOAD IN TONS

l b )

V MAXIMUM COST

MINIMUM COST

8 10 12 14 A X L E LOAD IN TONS

(a)

F i g u r e 7. Rate o f i n c r e a s e o f annual, c o s t w i t h i n c r e a s e I n a x l e l o a d .

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in which: D = Differential annual cost per mile in thousands of dollars between the unit axle

load'ind W. = Annual cost per mile in thousands of dollars for the unit axle load.

W = Axle load in tons for which differential costs are desired. Values for s are determined as discussed in the preceding and in Equation 5.

Another interesting consideration is the rate of increase of highway costs with axle load. Based upon Equation 4:

dC = CaS W ^ ' ' dW (8) and:

r = CasW^" ' (9) in which:

r = rate al increase of total annual cost responsibility in thousands of dollars per mile per ton (axle load).

A typical plot of Equation 9 is shown in Fig. 7 for Ohio conditions. The implication of Fig. 7 is that for higher axle loads, the rate of cost increase is reduced, particularly for weights in excess of 6-8 tons.

SUMMARY In considering the differential cost studies to date, the problems of developing the

relationship between highway-cost and vehicle-size leads to certain conclusions. The complexities of rationally expressing the relations which are needed prevent too many general statements.

For a truly rational and theoretically sound development of the relation of highway costs to vehicle si;ze a great deal of research is st i l l required. Since so many phases of highway engineering are st i l l empirical and since the elements of highway costs which are rational represent such a small part of the total cost, the values derived from the cost-size investigations are certain to be questioned. On the other hand, studies based upon the methods currently used for design wil l at least reflect present practice and expenditures. Insofar as this type of an answer is suitable, reasonably reliable estimates can be made.

From a research viewpoint, the studies which are most needed for cost-size investi­gations are related to the geometric factors. While it is true that a rational solution to structural elements such as pavements is not available, the empiricism utilized in pavement design is more effectively related to vehicle size than is the design for geo­metric factors.

The shape of the curve of highway costs versus vehicle size appears to be reasonably well established at this time, at least for current design procedures. There is little question but that the curve is basically of the exponential form Fig. 2 rather than the reverse curve frequently used as a qualitative description of the relationship. There is greater question as to the validity of the geometric capacities than for the structural elements.

Considering the complexities of achieving values for cost-size relations, a suggested procedure for estimating differential costs may be quite adequate for many problems. The method proposed involves knowing the dollars per mile which are available for a given highway system. Using the legal load as the axle load for which the system is designed, one point on the cost-size curve is available. Equations for projecting the curve above and below this given point have been suggested (0).

One of the major problems for which little direct research is currently under-way is involved with the problem of solving for the optimum sized vehicle to be used on an existing road network. There are a great many miles of highways in this country, and until i t is possible to evaluate the load-carrying characteristics of these pavements, it wi l l be illogical to extrapolate current expenses for reconstruction and resurfacing.

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The same is true for maintenance costs which are associated with vehicle weight (structural capacity). There is also some qpiestion as to the validity of extrapolating the geometric capacity requirements beyond the current values. Accordii^ to the stand&rd design practice today, the vehicle dimensions make no difference other than on the broad basis of passenger cars and trucks. Thus, changing vehicle dimensions would not appear to change highway costs. It is cjuite obvious that such a statement is not theoretically sound. As an example, a substantially wider vehicle would unquestion­ably increase the geometric capacity requirements. Drastic changes of vehicle height, length, and performance could also affect highway geometries.

ACKNOWLEDGMENTS The basis for the preceding paper was the research at The Ohio State University

undertaken by the writer working closely with Robert Chieruzzi and Richard W. Bletzacker, Research Associates of the Engineering Experiment Station. Most of the philosophies and principles described herein were evolved through many hours of dis­cussion and analyses. In retrospect, it is difficult to determine the source of an idea or its ultimate treatment. The writer is indebted to his two associates for their per­mission to utilize the material presented.

Hie help of the Ohio Trucking Association, as well as the following four trucking companies, through their financial sponsorship is acknowledged with sincere gratitude: B and L Motor Freight of Newark, Ohio; Commercial Motor Freight of Columbus, Ohio; Eastern Motor Dispatch of Columbus, Ohio; and Suburban Motor Freight of Columbus, Ohio.

REFERENCES 1. Mitten, L .G . , Bishop, A . B . , and Rihn, T .A. , "Ohio Highway Finance in 1953."

Bull. 159, Engineering Experiment Station, The Ohio State University, Columbus (1956).

2. Baker, Robert F . , and Karrer, Emmett H . , "A Study of the Relationship of Pavement Cost to Vehicle Weight." Ohio State University, Eng. Exp. Sta., Bull. 161 (1956).

3. Lindley, J. L . , "An Incremental Cost Study of Highway Structures in the State of Ohio." Highway Research Board, Proceedings 36 (1957).

4. Baker, R. F. , "Fundamental Factors Involved with Incremental Cost Studies of Pavement." Highway Research Board, Proceedings 36 (1957).

5. Chieruzzi, R., "Earthwork Incremental Cost Study." Proceedings, Eleventh Annual Ohio Highway Engineering Conference, Columbus (1957).

6. Baker, R.F. , and Chieruzzi, R.; Bletzacker, R.W., "Highway Costs and Their Relationship to Vehicle Size." Ohio State University, Eng. Exp. Sta., Bull. 168 (1958).

7. Pancoast, D. F . , "Allocation of Highway Costs in Ohio by the Incremental Method." Report prepared for Ohio Department of Highways in cooperation with Bureau of Public Roads, Ohio Department of Highways, Columbus, Ohio (1953).

8. "Allocation of Road and Street Costs." Washington State Council for Highway Research (1956).

9. "Highway Use and Highway Costs." Joint State Government Commission of Pennsylvania. Report of General Assembly of Commonwealth of Pennsylvania, Part I , Harrisburg, Pennsylvania.

10. "Financii^ Kentucky's Roads and Streets." Bureau of Business Research, University of Kentucky, Lexington (1956).

11. Koenker, W.E., and Larson, A. J. , "Ecpiitable Highway Cost Allocation in North Dakota." Bureau of Business and Economic Research, University of North Dakota, Grand Forks (1956).

12. Johnson, R.D., "The Montana Incremental Method of Determining Motor-Vehicle Tax Responsibility." Montana Highway Commission (1957).

13. St. Clair, G.P., "Problems Involved in Initiation, Analysis, and Summation of Section 210 Study." Proceedings, WASHO, Arizona Highway Dept. (1958).

Pricing and Financing Highway Services O. H . B R O W N L E E , U n i v e r s i t y of Minnesota

• I N N E A R L Y eve ry d i scuss ion about pub l ic p o l i c y one reads o r hears s tatements r ega rd ing the need f o r m o r e h ighways , m o r e schools , m o r e housing, m o r e defense o r m o r e of a lmos t anything except c e r t a i n a g r i c u l t u r a l c o m m o d i t i e s . These statements a r e t r u e i f they a re i n t e r p r e t e d as meaning that m o r e of each of these v a r i o u s goods and se rv ices , wi thout loss of any other goods o r s e rv i ce , wou ld add to our genera l w e l f a r e . Such statements may not be t r u e , however , when one takes in to cons idera t ion the f a c t that the r e sources r e q u i r e d to produce v a r i o u s goods and se rv ices a re l i m i t e d i n quant i t i es , and t h e r e f o r e , i n o r d e r to get m o r e of one t h i i ^ now one must u sua l ly give up some amounts of o ther t h ings .

Perhaps the w o r d "need" should not be used i n such d i scuss ions . R a r e l y , i f ever , i s t he re a s i tua t ion such that one could not s u r v i v e unless he had m o r e of a p a r t i c u l a r t h i n g . Instead, the p r o b l e m migh t be v i ewed as one of cata loguing the v a r i o u s th ings that could be produced—given the ava i lab le r e sources and ways of conver t ing t hem into product—and at taching va lues to each p o s s i b i l i t y so that one can be compared w i t h another . Some of the p r o b l e m s invo lved i n mak ing such compar i sons w i t h r e f e rence to the p r o b l e m of p r o v i d i n g highway s e r v i c e s a re d iscussed i n t h i s paper . In p a r t i c u l a r , i t i s noted the k i n d of i n f o r m a t i o n that i s r e q u i r e d and some of the i m p l i c a t i o n s a re indica ted f o r highway r e s e a r c h .

Reference has been made to the p r o b l e m of d e t e r m i n i n g how much to produce of highway s e r v i c e , o r schools , o r anything else, as one of evaluat ing a l l the poss ib le bundles of th ings tha t m i g h t be made ava i l ab le . T h i s paper w i l l not pursue t h i s ap­p roach d i r e c t l y . Perhaps i n a c o n t r o l l e d economy t h i s p rocedure i s employed . In the economy of the Uni ted States i t m i g h t be done i n evaluat ing v a r i o u s k inds of defense p r o g r a m s . But to cons t ruc t a comple te catalogue of what m i g h t be produced would be v i r t u a l l y imposs ib l e , and to va lue each co l l e c t i on i n accordance w i t h gene ra l ly accepted evaluat ion procedures—if such exist—also would be v e r y c o s t l y . Instead, one can e m ­p loy a p rocedure m a k i n g use of c e r t a i n condi t ions tha t wou ld be f u l f i l l e d i n o r d e r f o r a co l l ec t ion to be an o p t i m a l one ( tha t i s , a "best" o n e ) . In p a r t i c u l a r use can be made of the m a r k e t sys t em i n obta in ing i n f o r m a t i o n about how a change i n the c o l l e c t i o n of th ings that m i g h t be p roduced w i l l be evaluated by the popu la t ion .

Unless the economy i s o rgan ized i n e f f i c i e n t l y ( i n v o l u n t a r y unemployment i s one k i n d of i n e f f i c i e n t y ) i t costs something to expand the output of a p a r t i c u l a r good o r s e r v i c e . Under c e r t a i n condi t ions t h i s cost r epresen t s the va lue of o ther goods and se rv ices that must be s a c r i f i c e d i n o r d e r to obta in m o r e of the p a r t i c u l a r c o m m o d i t y i n quest ion. Le t the p r i c e that people a r e w i l l i n g to pay p e r un i t of the good represen t i t s va lue . I f p r i c e exceeds the add i t iona l cost pe r u n i t , m o r e of that good and less of the o thers would cons t i tu te an i m p r o v e m e n t , s ince the value of m o r e of the good w o u l d exceed the va lue of l e ss of o ther goods. Converse ly , i f the p r i c e of the c o m m o d i t y i s less than the add i t iona l cos t , m o r e of the c o m m o d i t y and less of the o the r s would make things w o r s e . Compar i sons of p r i c e s and costs can t e l l w h i c h th ings should be produced m g rea t e r quant i t ies and w h i c h i n s m a l l e r ones. One migh t then say, "We need m o r e of something i f i t s p r i c e exceeds i t s cost and less of someth ing else i f i t s p r i c e i s less than i t s c o s t . "

F o r compar i sons of p r i c e s and costs to g ive one a t r u e p i c t u r e about h i s needs, the p r i c e s mus t g ive good app rox ima t ions as to what th ings a re w o r t h , and the costs mus t y i e l d accura te es t imates of what must be s a c r i f i c e d . Some th ings one would not cons ider s e l l i n g , and f o r them a m e a n i n g f u l p r i c e cannot be es tabl i shed. F o r t he r th ings , the p r i c e underes t imates the t r u e v a l u e . The p r i c e that one i s w i l l i n g to pay f o r something that he w i l l use represen t s on ly the va lue to h i m of consuming the p a r t i c u l a r good and excludes the va lue to o ther people of h i s use of that good. E l e m e n t a r y education i s f r e q u e n t l y c i t e d as a case of a s e rv i ce that would be p roduced i n i n s u f f i c i e n t amounts i f one f o l l o w e d the p r i c e - c o s t c o m p a r i s o n because he i s w i l l i n g to pay something f o r

27

28

c h i l d r e n ' s educat ion, but the p r i c e you a r e w i l l i n g to pay doesn' t depend on m y f e e l i n g s about your c h i l d r e n ' s educat ion. F o r s t i l l o ther th ings , the p r i c e ove res t ima tes the va lue because one pe r son ' s w e l f a r e i s in f luenced adver se ly ( o t h e r than by what happens to p r i c e s ) by inc reased consumpt ion of the good by another p e r s o n . Thus, f u e l s tha t con t r ibu te to a i r p o l l u t i o n may be o v e r - p r i c e d ( o r u n d e r - c o s t e d ) . Users wouldn ' t be w i l l i n g to pay as much f o r t hem i f they had to bear p o l l u t i o n cos t s .

Costs also may be poor representa t ions of what has to be s a c r i f i c e d because they include monopoly e lements o r the r e s u l t s of r e s t r i c t i o n s — i n c l u d i n g taxes—imposed by government . However , imag ine that such things don ' t ex is t o r that they can be accounted f o r p r o p e r l y . Then, f o r a c o m m o d i t y whose consumpt ion by one pe r son has no e f fec t on anothers pe r son ' s welfare—except t h rough i t s i m p a c t on pr ice—one can u s e f u l l y t a l k about whether too l i t t l e o r too much of i t i s being produced w i t h r e f e r ence to the r e l a t ionsh ip between i t s p r i c e and i t s cos t .

What does a l l of t h i s have to do w i t h h ighways? One w i l l contend that , f o r the mos t p a r t , h ighway se rv i ce s a re such that i f they w e r e p r i c e d and i f costs were computed a p p r o p r i a t e l y , one wou ld be supply ing h i s "needs" when one produced tha t amount such tha t the pr ice—the amount charged f o r a passage by a p a r t i c u l a r vehicle—equals the cost r e s u l t i n g f r o m tha t passage.

F i r s t , i t should be made c l e a r that the benef i t s f r o m inves tment i n h ighways have p r o p e r t i e s such that a highway inves tment can be evaluated i n the same manner as can

' any inves tment designed to produce goods and se rv i ce s that a r e to be s o l d . To speak of highway se rv i ce s as i f they cons t i tu ted a s ingle homogeneous c o m m o d i t y i s to e r r o r i n the same way as to speak of f o o d as a s ingle good. Discuss ion w i l l be avoided of how such s e r v i c e should be def ined except to a sse r t that some of the d i f f i c u l t i e s i n ana lyz ing highway p r o b l e m s a r i s e f r o m inappropr i a t e de f in i t i ons of highway s e r v i c e . T r a v e l i n g a p a r t i c u l a r d is tance, a t a g iven speed and w i t h g iven c o m f o r t and safety may be as d i f f e r e n t — i n the m i n d of the highway u s e r - f r o m t r a v e l i n g th i s same distance at another speed and w i t h o the r degrees of c o m f o r t and safe ty as a pound of s i r l o i n steak i s f r o m a pound of potatoes . T r u c k t r a v e l d i f f e r s f r o m auto t r a v e l , e tc .

A l though the re a re many d i f f e r e n t k i n d s of h ighway se rv i ce s , n e a r l y a l l of t hem benef i t the highway use r—in the case of s e rv i ce s p r o v i d e d by passenger ca r t r a v e l — o r the bene f i t s a r e passed on to o ther pe r sons f r o m w h o m a c o l l e c t i o n can be made—through c o m m o d i t y p r i c e s , i n the case of t r u c k se rv ices—in the same way as a r e the benef i t s f r o m technolog ica l i m p r o v e m e n t o r add i t iona l c ap i t a l used i n a f a r m o r f a c t o r y . In genera l , h ighway se rv i ce s a re l i k e f o o d i n that one pe r son has no in t e r e s t i n another ' s consumpt ion pa t t e rn (except f o r i t s e f f ec t on p r i c e s ) ^ . The case f o r d i s t r i b u t i n g h i g h ­way s e rv i ce s and f o r d e t e r m i n i n g t h e i r appropr i a t e l eve l s of output by a p r i c e - c o s t mechan i sm i s as s t rong as that f o r any o ther c o m m o d i t y g r o u p .

The statement that highway se rv i ce s c o m p r i s e a c o m m o d i t y group such that p r i c e -cos t c r i t e r i a should guide t h e i r d i s t r i b u t i o n and p r o d u c t i o n does not mean tha t one should set up t o l l s ta t ions at eve ry s t r ee t c o r n e r and eve ry c r o s s r o a d . Because of co l l e c t i on cos ts and inconveniences that m i g h t be m o r e d i s t a s t e f u l than congest ion, t o l l roads can p l a y a v e r y l i m i t e d r o l e i n the h ighway s y s t e m . However , one can es tabl i sh m o t o r f u e l taxes , we igh t -d i s tance taxes , l i cense f ee s , and o ther charges i n a way such tha t the o v e r - a l l f ee schedule y i e l d s a r a t i o n a l a l l oca t ion of whatever road and s t ree t f a c i l ­i t i e s a r e ava i l ab le . A n d , one can account f o r costs and revenues so that he w i l l get about the r i g h t amount of highway inves tment and d i s t r i b u t e i t f a i r l y w e l l geograph ica l ly . In f a c t , the s t r u c t u r e of charges to highway u s e r s a l r eady may be f a i r l y reasonable and i s constant ly i m p r o v i n g , a l though one i s wi thou t some i n f o r m a t i o n r e q u i r e d to cons t ruc t

* That d i f f e r e n t degrees of highway congest ion a r e not a l l equal ly s a t i s f ac to ry to a h i g h ­way u s e r migh t appear to des t roy the a s se r t i on that one man ' s consumpt ion i s of no c o n ­c e r n to o the r men , and v i c e v e r s a . However , i f one cons iders t r a v e l a t one speed, safe ty , e t c . , as a d i f f e r e n t c o m m o d i t y f r o m t r a v e l at another speed, safety , e t c . , t he re i s no c o n t r a d i c t i o n i n the f o r m a l s ta tement . M o r e congest ion i s analogous to the h igher p r i c e f o r steak that w o u l d r e s u l t f r o m an increase i n i t s demand. The highway u s e r wou ld be i n d i f f e r e n t to some h igher f ee w i t h l o w e r congest ion and the low fee w i t h m o r e congest ion.

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a good fee catalogue. The p r o v i s i o n of f a c i l i t i e s p robab ly i s less r a t i o n a l , r e l a t i v e l y speaking, than i s the fee schedule, al though only rough guesses can be made about t h i s f r o m ex i s t i ng data.

Except on t o l l roads , the basic charge f o r the passenger auto should be, and i s , the m o t o r f u e l s t ax . Fue l consumpt ion i s an index of distance t r a v e l e d f o r any v e h i c l e , al though dis tance t r a v e l e d and amount of s e rv i ce a re not un iquely r e l a t ed as long as highways d i f f e r . However , to account f o r highway qua l i ty d i f f e r e n c e by d i f f e r e n c e s i n f u e l s taxes p robab ly i s not f e a s i b l e . Since passage f o r the passenger auto i s the least cos t l y to p r o v i d e the f u e l tax can be used as a k i n d of t o l l . Si)ecial f ees f o r passenger c a r s may be w a r r a n t e d i n l a r g e c i t i e s where congest ion i s a p r o b l e m , such fees being i n accordance w i t h the h igher costs of p r o v i d i n g a g iven l e v e l of s e rv i ce i n areas where land values a re h igh . S i m i l a r l y , spec ia l assessments o r spec ia l l i cense f ees f o r r e s i ­dents of v e r y spa rse ly se t t led areas may be advisab le . In t h i s case, such fees a re i n accordance w i t h the h igh va lue of the s e rv i ce rendered by the h ighway.

F o r t r u c k s and busses, f u e l s taxes a re supplemented by l icense fees in r ecogn i t ion of d i f f e r e n c e s i n costs imposed by passage of veh ic l e s of d i f f e r e n t c h a r a c t e r i s t i c s . However , l i cense fees cannot be v a r i e d s u f f i c i e n t l y to equi tably tax"the many d i f f e r e n t c lasses of weight and distance combina t ions . Weight -d i s tance taxes a re p r e f e r a b l e and could p e r m i t d i f f e r e n t f ees f o r d i f f e r e n t rou tes . In f a c t , weight -d i s tance taxes m i g h t be a d m i n i s t e r e d i n a manner s i m i l a r to that used i n c o l l e c t i n g the pe r sona l income tax f r o m s e l f - e m p l o y e d pe r sons .

Some of the i m p l i c a t i o n s of us ing p r i c e - c o s t compar i sons to a g rea t e r extent in mak ing highway decis ions a r e of i n t e r e s t .

I f p r i c e s and costs a re app rop r i a t e ly de t e rmined , not on ly the highway sys tem as a whole , but each separate en t i ty should "pay f o r i t s e l f " i n an account ing sense when the sys tem i s o p t i m a l (because of i n d i v i s i b i l i t i e s , equa l i ty between imputed revenues and imputed cos ts may not be ach i evab l e ) . Othe rwise sec tors of the sys tem that are "mak ing a p r o f i t " and ought to be expanded may be suppor t ing sec to rs that ought to be con t rac ted . T h i s p o s s i b i l i t y cannot be detected when on ly the revenues and costs of the sys tem as a whole a r e examined .

That highway u se r s should pay f o r the highways has much , though not u n i v e r s a l , suppor t . However , that each c l e a r l y d is t inguishable sector should pay f o r i t s e l f i s less wide ly supported—except poss ib ly f o r t o l l roads . In p a r t i c u l a r , i t i s be l ieved that gen ­e r a l l y there has been r e l a t i v e o v e r - c o n s t r u c t i o n of r u r a l n o n - t r u n k highways , al though th i s be l i e f can ne i the r be adequately supported nor r e f u t e d w i t h ex i s t i ng data .

The p r i c e s that have to be pa id f o r r e sources a re taken as r e l i a b l e es t imates of the va lue of the p roduc t tha t has to be s a c r i f i c e d i n o r d e r to expand p roduc t ion of one good. Government pays the same p r i c e s f o r l abor and m a t e r i a l s as do o ther u s e r s . However , i t b o r r o w s money at m o r e f avo rab l e t e r m s ( a t a l o w e r ra te of in te res t ) than does the t y p i c a l p r i v a t e b o r r o w e r . Th i s l o w e r i n t e r e s t r a t e r e f l e c t s p r i m a r i l y the confidence of the lender i n government ' s a b i l i t y to repay—not i n the r e l a t i v e m e r i t s of the p r o j e c t s . Government can tax ( o r p r i n t money, i f i t i s the f e d e r a l government) to r epay loans . P r i v a t e b o r r o w e r s mus t repay out of ea rn ings . I f government b o r r o w s at, say, 3 p e r ­cent, whereas p r i v a t e p r o d u c e r s b o r r o w at, say, 6 percent , and both government and p r i v a t e p r o d u c e r s use amounts of cap i t a l such that ra tes of r e t u r n a re equal to b o r r o w ­ing costs , government w i l l be us ing too much and p r i v a t e p r o d u c e r s too l i t t l e . Sh i f t ing cap i t a l f r o m the government to the p r i v a t e sector w o u l d expand to t a l p r o d u c t . G o v e r n ­ment also should not inves t i n p r o j e c t s unless they would y i e l d , say, 6 pe rcen t , i f c a p i ­t a l i s to be a l loca ted i n the best manner . Thus, decis ions to b u i l d highways and to make o ther governmenta l inves tments should not be based on the r a t e at w h i c h government can b o r r o w but on the r a t e of r e t u r n on cap i t a l i n o ther uses .

Tax d i f f e r e n t i a l s , as w e l l as d i f f e r e n t i a l s i n costs of b o r r o w i n g a f f ec t the r e l a t i v e p r i c e s of gove rnmen ta l ly produced goods i n c o m p a r i s o n w i t h p r i v a t e l y p roduced goods. In the t r a n s p o r t a t i o n f i e l d a re spec ia l excise taxes a f f e c t i n g some k inds of t r a n s p o r t (bu t not o thers ) that encourage use of the highway sys tem r a t h e r than a l t e rna t i ve f o r m s of t r a n s p o r t a t i o n . These taxes ought to be abol i shed . However , there a re also p r o p e r t y taxes applying to n e a r l y a l l p r i v a t e p r o p e r t y . A comple te evaluat ion of the p r o p e r t y tax i s not cons idered to be app rop r i a t e f o r t h i s d i scuss ion . However , to obta in a be t te r

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d i s t r i b u t i o n of r e sou rces among v a r i o u s k i n d s of t r a n s p o r t a t i o n , i m p u t e d p r o p e r t y taxes on highways ought to be cons idered i n a r r i v i n g at highways costs , j u s t as a "shadow" i n t e r e s t ra te equal to the m a r g i n a l ra te of r e t u r n on cap i t a l i n p r i v a t e inves tment r a t h e r than the cost of b o r r o w i n g ought to be employed .

To t r y to make the las t two poin ts c l e a r e r , imag ine that there a re two se rv ices—ca l l t hem " r a i l t r a n s p o r t " and "highway t ranspor t "—both of w h i c h cou ld be produced at the same constant u n i t cos ts , i f r e source p r i c e s w e r e the same to both i n d u s t r i e s . Assume also tha t the amount of e i ther s e r v i c e demanded v a r i e s i n v e r s e l y w i t h i t s p r i c e and d i r e c t l y w i t h the p r i c e of the compet ing s e r v i c e . W i t h the same in t e r e s t charges and no taxes , the p r i c e s would be iden t i ca l and c e r t a i n amounts of each s e r v i c e would be p roduced . However , i f one i n d u s t r y were charged m o r e f o r cap i t a l than was the o ther and also had to pay taxes p ropor t iona te to the v o l u m e of s e rv i ce produced , i t s s e rv ice would be p r i c e d h igher than that of the o ther i n d u s t r y . Less of i t and m o r e of the o ther wou ld be used than would be economic, that i s , than would be the case i f " t r u e " costs d e t e r m i n e d p r i c e s .

I t should be noted that i f the h ighways were to "pay f o r t hemse lves" i n the sense of y i e l d i n g revenues equal to cos ts , i nc lud ing the impu ted ones, there wou ld be d i v e r s i o n of highway revenues to the genera l governmenta l f u n d . T h i s d i v e r s i o n would be equal to impu ted p r o p e r t y taxes p l u s , say, 2 o r 3 pe rcen t of cap i t a l out lays—this 2 o r 3 p e r ­cent being a rough es t imate of the d i f f e r e n c e s i n b o r r o w i n g costs to government and p r i v a t e b o r r o w e r s .

Al though i t i s not economica l ly f ea s ib l e to co l l ec t t o l l s except on a v e r y s m a l l p e r ­centage of the h ighway sys t em, t o l l s can be equitable r a t i on ing devices and can p e r m i t accura te accounting of the revenues a t t r ibu tab le to a p a r t i c u l a r sector of the highway s y s t e m . F o r these reasons, r a the r than m i n i m i z i n g the number of t o l l roads , one would employ t h e m whe reve r f e a s i b l e . However , c e r t a i n p r a c t i c e s i n a d m i n i s t e r i n g t o l l roads a r e not consis tent w i t h best use of the highway s y s t e m . In p a r t i c u l a r (a) r e ­q u i r i n g that t o l l roads pay f o r themselves out of t o l l s i s uneconomic . M o t o r f u e l s tax r ece ip t s a lso should be c r e d i t e d the t o l l r oads . To do o the rwise w i l l r e s u l t i n u n d e r -u t i l i z a t i o n of such roads and o v e r - u t i l i z a t i o n of o r o v e r - i n v e s t m e n t i n , f r e e w a y s , (b ) t o l l s should be much m o r e f l e x i b l e than t o l l a u t h o r i t i e s have been i n c l i n e d to make t hem i n the pas t . V a r y i n g t o l l s w i t h the demand wou ld smooth the t r a f f i c f l o w and could make i t app rox ima te m o r e c lose ly that f o r w h i c h the r o a d was designed. Idea l l y , t o l l s m i g h t f l uc tua t e as do the odds at p a r i m u t u a l be t t ing booths o r as do stock m a r k e t quota t ions . In a reas such as Manhattan where access i s by tunnel o r b r i d g e , t o l l s to the i s l and c e r t a i n l y should exceed those away f r o m the i s l and d u r i n g the m o r n i n g r u s h hour s , and perhaps v i c e v e r s a d u r i i ^ the evening hours—although i f t he r e a re too many autos i n Manhattan the re i s no reason why en t ry fees should not a lways exceed ex i t f e e s .

F luc tua t ions i n t o l l s not on ly wou ld a id i n c o n t r o l l i n g t r a f f i c f l o w s . They also would p e r m i t - i m p r o v e d es t imates of the demand f o r highway s e r v i c e s . Such data a re r e q u i r e d f o r d e t e r m i n i n g how much inves tment to make i n highway f a c i l i t i e s and v e r y f e w of t hem a re ava i l ab le .

To m i n i m i z e e r r o r s i n loca t ing and inves t ing i n highway f a c i l i t i e s , the demand f o r and costs of p r o v i d i n g v a r i o u s se rv ices must be known . Highway f a c i l i t i e s p rov ide s e rv i ce s o v e r a long p e r i o d of t i m e , and no one can f o r e c a s t w i t h p e r f e c t accuracy , the condi t ions that w i l l p r e v a i l i n the f u t u r e . However , one cou ld make use of m o r e of the a t ta inable cost and demand i n f o r m a t i o n than has been made ava i l ab le .

F i r s t cons ider cos t s . Economis t s d iv ide the elements d e t e r m i n i n g costs in to two c lasses : (a ) The t echno log ica l and (b ) the m a r k e t . The f i r s t c l ass cons i s t s of a d e s c r i p t i o n i n p u r e l y p h y s i c a l t e r m s as to how resources can be conver ted in to p r o d u c t . How to cons t ruc t a f l e x i b l e pavement and a concre te pavement that wou ld c a r r y c e r t a i n loads w i t h a g iven d e t e r i o r a t i o n f o r a g iven p e r i o d of t i m e w o u l d be p a r t of such a de ­s c r i p t i o n . The m a r k e t descr ibes the p r i c e s that have to be pa id f o r r e s o u r c e s . I f the re i s m o r e than one way to do a g iven j o b , the way that i s leas t cos t ly at one set of p r i c e s obvious ly w i l l not be the least expensive at eve ry o ther set of p r i c e s .

A g r ea t dea l of t echno log ica l i n f o r m a t i o n about h ighways i s ava i lab le and m o r e i s be ing assembled . However , i t i s be l i eved that some of t h i s i n f o r m a t i o n i s not i n a f o r m such that i t p e r m i t s r e levan t cost compar i sons , tha t i s , compar i sons of the cost of

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c a r r y i n g one type of v e h i c l e r a t h e r than another . To a p p r o p r i a t e l y assess the m a i n t e n ­ance cost a t t r i bu tab le to the passage of a veh ic l e w i t h p a r t i c u l a r c h a r a c t e r i s t i c s ove r a g iven sec t ion of the h ighway, the wear and t e a r on the r o a d has to be measured i n t e r m s that can be conver ted in to cos t s . The cost of r e s t o r i n g the road sect ion to i t s condi t ion p r i o r to the v e h i c l e passage i s the r e q u i r e d i n f o r m a t i o n , and no way can be seen of conve r t i ng fa t igue data in to the d e s i r e d i n f o r m a t i o n a l f o r m . Compar i sons of cons t ruc t ion cos ts and a t tempts to a l loca te t hem a re numerous . However , i t i s m a i n t e n ­ance p lu s cons t ruc t ion cos ts that a r e re levan t , and m o r e maintenance but less c o n s t r u c ­t i o n becomes economic as i n t e r e s t r a t e s a r e i nc reased .

W i t h r e f e r e n c e to the demand f o r highway se rv i ce s much l ess i s known than about cos t s . I dea l l y one wants to know how much of a p a r t i c u l a r k i n d of s e r v i c e buyers a re w i l l i n g to take at p a r t i c u l a r p r i c e s . F r o m th i s one can d e t e r m i n e , f o r example, how much people be l ieve i t i s w o r t h to be able to t r a v e l w i t h a g iven degree of safety at 50 mph between two poin ts r a t h e r than at 40 m p h . I f the add i t iona l cost of p r o v i d i n g f a c i l ­i t i e s f o r the h igher speed was less than the va lue , these f a c i l i t i e s should be cons t ruc ted .

A s was stated p r e v i o u s l y , v a r y i n g t o l l s p e r m i t s obta in ing demand i n f o r m a t i o n . P e r ­haps a r rangements cou ld be made w i t h selected t o l l r oad au tho r i t i e s so that the e f fec t s of v a r i o u s t o l l s on the t r a f f i c p a t t e r n cou ld be observed .

Another method f o r ob ta in ing demand i n f o r m a t i o n i s th rough ask ing u s e r s how they wou ld behave i f c e r t a i n condi t ions p r e v a i l e d . D r i v e r s m i g h t be asked how much m o r e they wou ld be w i l l i n g to pay p e r t r i p i f the t r a f f i c densi ty were such that they could d r i v e at one speed r a the r than another , f o r example . Such su rveys t y p i c a l l y p e r m i t p resen t ing a w i d e r choice of p o s s i b i l i t i e s than cou ld be presented i n an exper iment such as v a r y i n g the t o l l s on a p a r t i c u l a r r o a d . However , the p o s s i b i l i t i e s a re hypothe t ica l ones and the responses may d i f f e r cons iderab ly f r o m actual behavior imder the c i r c u m ­stances. Never the less , such su rveys have y i e lded i n f o r m a t i o n u s e f u l to business f i r m s t r y i n g to es t imate the demand f o r a new produc t and could be used i n e s t i m a t i n g m o r e accura te ly highway u s e r s ' p r e f e r e n c e s .

To de te rmine whether a p a r t i c u l a r sec tor of the highway sys t em i s "paying i t s w a y " one needs to know i t s t r a f f i c p a t t e r n . Many t r a f f i c counts have been made and one can t e l l a good deal about t r a f f i c pa t t e rns f r o m the wear and tear on a p a r t i c u l a r h ighway. However , much less i s known about the compos i t ion of t r a f f i c on v a r i o u s sect ions of the sys tem than one should know.

S U M M A R Y

In t h i s shor t d i scuss ion , i t has been asse r ted that h ighways compete w i t h o ther a c t i v i t i e s , i n c l u d i n g o ther t r a n s p o r t a t i o n f a c i l i t i e s , f o r the use of r e s o u r c e s . In de ­t e r m i n i n g the amount of h ighway se rv i ce s to p r o v i d e , one should compare the value of these se rv ices w i t h the o the r th ings that cou ld be p r o v i d e d . Highway se rv i ce s a re such that compar i sons of t h e i r p r i c e s — i f they could be pr iced—and t h e i r cos ts—if resources a re obtained f o r p r o v i d i n g such se rv i ce under the same t e r m s as i n o ther uses—could t e l l whether too much o r too l i t t l e i s be ing p roduced .

Employ ing t o l l s to s e l l h ighway s e r v i c e s d i r e c t l y i s economic only on a r a t h e r s m a l l p a r t of the highway s y s t e m . F o r the r e m a i n d e r , the schedule of fees acts as a schedule of p r i c e s . The p r i c e to any veh ic l e i d e a l l y should be the cost i n c u r r e d i n handl ing that v e h i c l e . To put highway se rv ices on the same f o o t i n g as other c o m p e t i t o r s f o r r e -sources , costs should be es t ima ted us ing the same in t e r e s t r a tes and such o ther cost f a c t o r s as p r o p e r t y taxes as these o ther u se r s pay . Thus , some d i v e r s i o n of highway revenues to the genera l f u n d would be j u s t i f i e d .

To make t h i s p r i c e sy s t em f u n c t i o n e f f e c t i v e l y r e s e a r c h i s needed that w i l l p r o v i d e es t imates of the demands f o r highway se rv i ce s , and to know m o r e about costs i s needed. T o l l r oad exper ience can p r o v i d e some i n f o r m a t i o n about demand, and t o l l s m i g h t be v a r i e d s p e c i f i c a l l y f o r t h i s purpose . M a r k e t su rveys also could be employed .

Price Theory and Tax Equity in Highway Finance M . Z . K A F O G L I S , Depar tmen t of Economics , U n i v e r s i t y of F l o r i d a

Highway user taxes act as p r i c e s f o r the use of h ighways , thus i n ­f l uenc ing the a l loca t ion of t r a f f i c ( and resources ) among the v a r i ­ous t r an spo r t a t i on agencies. A s s u m i n g that o p t i m a l use of the t r a n s ­p o r t a t i o n sys t em i s one of the a i m s of pub l ic p o l i c y , i t i s i m p o r t a n t that highway user tax ra tes be cons t ruc ted so as to f o s t e r a t ta inment of t h i s goa l . Al though t h i s c a l l s f o r a p r i c i n g o r m a r k e t approach to highway f inance , i t i s equal ly i m p o r t a n t to segregate, i d e n t i f y and a l l o w f o r those values ( i n d i r e c t benef i t s ) wh ich a re not r e f l e c t e d i n the m a r k e t choices of i n d i v i d u a l s .

I t appears that the t r a d i t i o n a l a l l oca t i on of highway cost between u s e r s and non-use r s does not i n gene ra l represen t a response to i n ­d i r e c t bene f i t s . Rather , i t r e f l e c t s a d m i n i s t r a t i v e p r o b l e m s and c e r t a i n not ions about equi ty o r j u s t i c e . The t h e o r e t i c a l condi t ions under wh ich a non-user share i s app rop r i a t e may be spec i f i ed , but app l ica t ion of the theory r a i s e s d i f f i c u l t p r a c t i c a l p r o b l e m s . N o t ­wi ths tanding these p r a c t i c a l d i f f i c u l t i e s , i t seems c l ea r that the a l ­loca t ion of shares between u se r s and non-users should f o l l o w , not precede , the de t e rmina t i on of p r i c e s f o r highway use . M o r e o v e r , the non-user share should be s c r u t i n i z e d c a r e f u l l y , so that u se r ra tes a re not d i m i n i s h e d o r d i s t o r t e d by deductions f o r i n d i r e c t benef i t s w h i c h acc rue i n the f o r m of r en t s , w i n d f a l l s and su rp luses . Such i n ­d i r e c t benef i t s mus t be cons idered i n the l i gh t of gene ra l s tandards of tax equ i ty .

Economica l l y e f f i c i e n t highway use r tax r a t e s t r u c t u r e s can be cons t ruc ted by adher ing to the economic p r i c e c r i t e r i o n : P r i c e should equal m a r g i n a l cos t . F o r an o p t i m a l l y u t i l i z e d h ighwayp lan t , " p r o g r a m cos t " i s a reasonable a p p r o x i m a t i o n of m a r g i n a l cos t . A n equal ly s a t i s f a c t o r y a p p r o x i m a t i o n f o r roads wh ich have excess ca­p a c i t y and low m a r g i n a l costs i s not ava i l ab le . However , such roads may be f i n a n c e d economica l ly t h r o u g h use of the " t w o - p a r t t a r i f f " . The t w o - p a r t t a r i f f combines a low p r i c e which v a r i e s w i t h use w i t h a l u m p sum tax wh ich does not v a r y w i t h use .

To p r o v i d e p r a c t i c a l guideposts f o r app l ica t ion of the m a r g i n a l cost s tandard, highway design, p r i c e t heo ry and f i n a n c i a l a d m i n i s ­t r a t i o n may be i n t e r r e l a t e d and in t eg ra ted in to an opera t iona l f r a m e ­w o r k o r " m o d e l " . The c r u c i a l e lement i n es tabl i shment of the " m o d e l " i s the separa t ion of specia l o r i n c r e m e n t a l pavement cost f r o m common o r g e o m e t r i c des ign cos t . Speculation concern ing the i m p a c t of the f r a m e w o r k suggests the p o s s i b i l i t y of es tab l i sh ing the gasol ine tax r a t e so that gasol ine tax " ea rn ings" on the p r i m a r y roads cover p r i m a r y r o a d common cos t . A d d i t i o n a l o r i n c r e m e n t a l pavement cost may be r e c o v e r e d th rough the use of lump sum r e g i s t r a t i o n taxes o r weight dis tance t axes . L i g h t l y t r a v e l l e d roads may be f i nanced th rough the use of gasol ine tax " ea rn ings" supplemented by lump sum l icense taxes on l i g h t veh ic l e c lasses . The genera l conclus ion i s tha t i t i s poss ib le t o manage the highway f i n a n c i a l s t r u c t u r e i n the i n t e r e s t of economic e f f i c i e n c y wi thou t c r e a t i n g se r ious inequ i t i e s .

• W I T H I N the past f e w yea r s the not ion that h ighways should be f i nanced "equ i t ab ly" has been supplemented by the v i e w tha t the highway user tax s t r u c t u r e should also

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f o s t e r the economic u t i l i z a t i o n and development of the highway p lan t . Th i s change i n e m ­phasis i m p l i e s a p a r t i a l s h i f t f r o m theuse of e th ica l s tandards of tax equity to the use of m o r e o r less ob jec t ive standards of p r i c i n g i n the development of the highway f i n a n c i a l s t r u c t u r e . The a i m of t h i s paper i s to set f o r t h the r e l a t ionsh ips between p r i c e and t ax s tandards as they apply to highway f inance and to es tabl ish c r i t e r i a f o r the combina t ion of p r i c e s and taxes in to a comprehens ive sys tem of charges f o r the f i n a n c i n g of h ighways .

A b s t r a c t economic theory has es tabl ished the p r i n c i p l e that , w i t h i n the l i m i t s of a g iven d i s t r i b u t i o n of income , m a x i m u m economic w e l f a r e i s approached when p roduc t ion and consumpt ion a re ad jus ted so that m a r g i n a l cos t and p r i c e become equal ( l ) . I f i n ­come r e d i s t r i b u t i o n i s not an e x p l i c i t a i m of the highway u s e r tax s t r u c t u r e , i t m i g h t be appropr ia t e to eschew benef i t and a b i l i t y - t o - p a y s tandards of t axa t ion ai^d to es tab l i sh highway use r taxes i n r e l a t i o n to a m a r g i n a l cost p r i c i n g s tandard . One of the i m p l i ­cat ions of a p r i c i n g o r " m a r k e t " approach i s the assumpt ion that the benef i t s o r u t i l i ­t i e s re levant to highway f inance acc rue , i n one f o r m o r another , d i r e c t l y to highway u s e r s . However , cons idera t ion of the i n d i r e c t o r so -ca l l ed non-user benef i t s wh ich accrue to v a r i o u s i nd iv idua l s may lead to a sys t em of taxa t ion based on the p r e m i s e that i nd iv idua l s should pay i n p r o p o r t i o n to " b e n e f i t s - r e c e i v e d " . Simultaneous a p p l i ­ca t ion of both p r i c e and tax standards may in t roduce c o n f l i c t in to the o v e r - a l l f i n a n c i a l s tructure—what i s pa id as a tax by the non-user does not have to be pa id as a p r i c e by the highway u s e r . The p o s s i b i l i t y of u n w a r r a n t e d subsidy to one group o r another i s obvious , h i o r d e r to an t ic ipa te t h i s p r o b l e m , the d i scuss ion begins w i t h a cons ide ra t ion of the t r a d i t i o n a l a l l oca t ion of cost between highway u s e r s and non-use r s .

T H E NON-USER QUESTION

A recent p r i c i n g p roposa l set f o r t h by Brownlee and H e l l e r demons t ra tes the v a l i d i t y of a p r i c i n g approach i n s o f a r as p r i m a r y o r " t r u n k " r o a d f inance i s concerned ( 2 ) . However , there have been objec t ions to t h i s p roposa l f r o m proponents of a u s e r - n o n -use r a l loca t ion of highway cost who ma in t a in that the p r i c i n g p roposa l abs t rac t s the mos t d i f f i c u l t p a r t s of the problem—the r e l a t i onsh ip of i n d i r e c t o r soc ia l benef i t s to secondary road f inance ( J ) . Some p r o g r e s s i n the way of c l a r i f y i n g t h i s issue can be made by r ecogn iz ing e x p l i c i t l y that the a l loca t ion of a share of secondary r o a d cost to non-users i s m o r e a response to a d m i n i s t r a t i v e p r o b l e m s than to i n d i r e c t bene f i t s . R i c h a r d Ze t t e l ( J ) , among o the r s , has noted that p r o p e r t y taxes , spec ia l assessments and other f o r m s of revenue a re s i m p l y a c rude means of c o l l e c t i n g d i r e c t l y f r o m the highway u s e r that p o r t i o n of h i s highway b i l l that cannot be co l l ec t ed th rough the use of o r d i n a r y use r charges . The expendi ture of "gene ra l " o r non-user funds f o r highway purposes does not nece s s a r i l y i m p l y that highways y i e l d i n d i r e c t benef i t s n o r does i t i m p l y that highways ought to be f i nanced i n t e r m s of tax equi ty . M o r e o v e r , the a d m i n i s ­t r a t i v e p r o b l e m of c o l l e c t i n g f r o m the use r does not c a l l f o r an a l loca t ion of highway cost between u s e r s and so -ca l l ed non-use r s o r i n d i r e c t b e n e f i c i a r i e s . B a s i c a l l y , the cost a l l oca t i on i s among those who use the h ighway.

Recogni t ion of the a d m i n i s t r a t i v e bas i s f o r non-user revenue sources does not r e ­solve the economic i ssues r a i s e d by v a l i d i n d i r e c t bene f i t s . In o r d e r to examine the economic basis of a non-user share, i t i s necessary to examine the condi t ions under which v a l u e - o f - s e r v i c e o r b e n e f i t s - r e c e i v e d a l loca t ions of cost a r e a p p r o p r i a t e . The re a re two such s i tua t ions : (a ) j o i n t cost o r supply and ( b ) j o i n t o r c o l l e c t i v e demand. Joint supply c rea tes a p r o b l e m of cost ass ignment because two o r m o r e p h y s i c a l p r o ­ducts emerge f r o m a s ingle app l ica t ion of r e s o u r c e s . Joint o r c o l l e c t i v e demand creates the p r o b l e m of d i s t r i b u t i n g the cost of a s ingle p roduc t (whose cost i s de t e r ­minate) among m o r e than one b e n e f i c i a r y . A n examinat ion of these two p o s s i b i l i t i e s may p r o v i d e the t h e o r e t i c a l s tandards f o r evaluat ing a l loca t ion of cost between u se r s and non-use r s .

Joint Cost

Joint cost a r i s e s when p roduc t s cannot be p roduced separa te ly . The c lass ic ex­ample i s the case of beef and hides; the re a re two d i s t i n c t p roduc t s whose separate costs a re i nde t e rm ina t e . I t appears to be se t t l ed that the " s o l u t i o n " i n such cases r e -

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qu i re s an a l loca t ion of t o t a l cost on the bas i s of the v a l u e - o f - s e r v i c e o r va lue - in -use of the separate p roduc t s (_5). Highways do c rea te some j o i n t p roduc t s , and t h i s m i g h t j u s t i f y an a l l o c a t i o n of cost to non-use r s o r genera l t axpaye r s . Highways crea te f i r e stops, openings f o r l i g h t and a i r and v a r i o u s o ther phys i ca l p roduc t s wh ich have v a l u e . These examples of jo in tness do not appear to weigh heav i ly i n the usual a l l oca t ion of cost to non-use r s . M o r e o v e r , the phys i ca l b y - p r o d u c t s of highway development do not appear to p l ay a s i gn i f i c an t r o l e i n dec is ions concern ing expansion and con t r ac t i on of the p lan t . On the whole , h ighways a re b u i l t f o r ac tua l o r po ten t i a l highway use and l i t t l e m o r e . I t appears tha t the p h y s i c a l b y - p r o d u c t s of highway development do not p r o v i d e an i m p o r t a n t bas i s f o r a non-user share . On the o ther hand, these e lements should be cons idered , e spec ia l ly when s t ree t p r o g r a m s a re a f f ec t ed by plans f o r m u n i c ­i p a l redevelopment .

Jo in t Demand

Jo in t demand a r i s e s when one i n d i v i d u a l gains o r r ece ives benef i t f r o m the consump­t i o n of another . Economis t s desc r ibe such phenomena as " e x t e r n a l e c o n o m i e s . " A pe r son who p rov ides f o r the p h y s i c a l p r o t e c t i o n of h i s own p r o p e r t y a lso p r o v i d e s i n ­d i r e c t l y f o r the p r o t e c t i o n of h i s ne ighbors ' p r o p e r t y . S i m i l a r l y , a f a r m to c i t y h i g h ­way wh ich i s cons t ruc ted and p a i d f o r by f a r m e r s i n d i r e c t l y benef i t s merchan t s , l a n d ­owners and o thers loca ted i n the c i t y . Al though the f a r m e r s w i l l use the road , o thers stand to benef i t f r o m that use . Since only f a r m e r s use the road , cos ts may be a l l o ­cated d i r e c t l y to f a r m e r s . The quest ion that a r i s e s re la tes to the c i r cums tances under w h i c h downtown merchan t s and o thers wou ld ( o r should) subsid ize the f a r m e r s ' use . In v i e w of the f a c t tha t downtown merchan t s r ece ive many and v a r i e d benef i t s , i t may seem " f a i r " that they share the r o a d b i l l . Th i s not ion of j u s t i c e , that i s , the benef i t t heory of t axa t ion , m i g h t l ead to an i n i t i a l a l l oca t i on of cost between use r s and non-u s e r s . In addi t ion to being i n c o r r e c t t e chn i ca l l y , such an a l l oca t i on r e q u i r e s a c o n ­s iderab le amount of r e s e a r c h t i m e and cos t . A f a r be t te r approach wou ld r e q u i r e a t ­tent ion to these quest ions: (a) I s i t necessary to subsidize the u se r? (b ) Is i t " f a i r " tha t i n d i r e c t b e n e f i c i a r i e s shoulder a p a r t of the b i l l ? The f i r s t ques t ion can be e v a l u ­ated i n t e r m s of ob jec t ive s tandards; the second r e q u i r e s the adoption of a s tandard of j u s t i c e .

SUBSIDY TO T H E USER

F i g u r e s 1-3 depict the u se r -non -use r r e l a t ionsh ips r e l evan t to highway f i nance . In o r d e r to s i m p l i f y the p resen ta t ion , i t i s assumed that : ( a ) highway cost v a r i e s d i r e c t l y w i t h some u n i t , say v e h i c l e - m i l e s , (b ) there i s on ly one c lass of veh i c l e , ( c ) highway s e r v i c e i s p roduced under condi t ions of constant average and m a r g i n a l cos t . Another s i m p l i f i c a t i o n i s made by employ ing s t r a igh t l ines f o r the demand cu rves of i n d i v i d u a l s . These assumpt ions and s i m p l i f i c a t i o n s do not a f f e c t the gene ra l i t y of the g r a p h i c a l p r e ­senta t ion . Three s i tua t ions a r e presented: (a ) No i n d i r e c t benef i t s of highway use; ( b ) I n d i r e c t benef i t s w h i c h r e q u i r e a non-user share , and ( c ) I n d i r e c t benef i t s which do not r e q u i r e a non-use r share .

No I n d i r e c t Benef i t s

In F i g u r e 1 the h o r i z o n t a l ax i s measures veh ic l e m i l e s , Mf. r epresen ts the p r i c e o r m a r g i n a l cos t , D ^ represen t s the demand of i n d i v i d u a l A f o r highway use . D ^ depicts the quant i t ies of veh ic le m i l e s that i n d i v i d u a l A w i l l purchase at each of a se r i e s of p r i c e s . I f t he r e i s no i n d i r e c t b e n e f i c i a r y , the charge i s P, and i n d i v i d u a l A pays the e n t i r e highway b i l l . The t o t a l payment made by A i s shown by the a rea OQRP. The p r o p e r p rocedu re , t o be d e s c r i b e d i n a subsequent sec t ion , r e q u i r e s t ha t u s e r t a x r a t e s be es tabl ished i n accordance w i t h m a r k e t o r p r i c e s tandards .

I n d i r e c t B e n e f i t s Which Requi re a N o n - U s e r Share

F i g u r e 2 r ep resen t s the s i tua t ion when i n d i v i d u a l B i s a non-user who r ece ives i n ­d i r e c t benef i t s because of i n d i v i d u a l A ' s use of the h ighway. I n d i v i d u a l B may represen t

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a downtown merchant , r e a l estate p r o m o t e r o r some governmenta l agency wh ich has an i n t e r e s t i n encouraging highway use . I t i s i m p o r t a n t to note that i n d i r e c t benef i t s accrue to B only i f the highway i s used. The m e r e exis tence of a highway does not c rea te i n d i r e c t benef i t s , al though i t does crea te the j o i n t p roduc ts p r e v i o u s l y desc r ibed . Ind iv idua l B , the non-user who rece ives i n d i r e c t benef i t s , a lso has a demand f o r t r a v e l between the same two po in t s as i n d i v i d u a l A . A s a non-user , however , B does not use the road d i r e c t l y . The demand, D^^, of the non-user i s f o r A ' s d i r e c t use of the h i g h ­way . Both demands may be measured along the same h o r i z o n t a l ax i s because both de­mands r e l a t e to the same u n i t of s e r v i c e . F i g u r e 2 m i g h t r ep resen t the r e l a t i onsh ip between f a r m e r s and downtown bus inessmen. I f the c u r r e n t p r i c e i s P , and the i n d i v i ­

duals do not ( o r cannot) take t h e i r i n t e r d e ­pendence in to account, A w i l l purchase Q veh ic l e m i l e s . Since B i s a non-user he can purchase none. In r ecogn i t i on of the interdependence, however , B may o f f e r a subsidy to encourage A ' s use of the h i g h ­way . I nd iv idua l B has a l ready r ece ived a w i n d f a l l i n the f o r m of i n d i r e c t benef i t s be ­cause he wou ld have been w i l l i n g to pay a p r i c e P Q f o r each veh ic le m i l e that A has t r a v e l e d . Th i s w i n d f a l l i s depic ted by the a rea O Q S P Q . Indeed, B stands to gain i f he o f f e r s to subsidize A ' s purchase of a n ­other v e h i c l e - m i l e . I nd iv idua l A i s w i l l i n g

Quantity

Figure 1. Private demand (The User Share),

to purchase an addi t iona l u n i t at a p r i c e s l i g h t l y be low P , wh i l e the va lue of an a d d i ­t i ona l un i t to B i s a pos i t i ve quant i ty s l i g h t l y below P Q . A s s u m e that B o f f e r s an amount U to i n d i v i d u a l A i n o r d e r to en­courage A ' s use of the h ighway. W i t h t h i s o f f e r , the p r i c e of an add i t iona l u n i t to A i s P - U , and A w i l l i nc rease h i s purchases to q . I nd iv idua l B w i l l increase the sub­s idy o f f e r e d as long as add i t iona l un i t s a r e f o r t h c o m i n g at a subsidy p e r un i t below h i s demand p r i c e f o r those quan t i t i e s . S i m ­i l a r l y , A w i l l continue to purchase a d d i ­t i o n a l un i t s u n t i l quant i ty Q' i s reached such that h i s ( A ' s ) demand p r i c e f o r Q' p l u s B ' s subsidy o f f e r ( B ' s demand p r i c e f o r Q') become equal to P , the going p r i c e . The e q u i l i b r i u m i s depic ted by po in t M

« o

Q.

P Pb u

V

sA, \ X \ M M C

1 I X

1 1

1 1 1

Q q a Figure 2.

Quantity

Collective demand (The Non-User Share).

where the respec t ive con t r i bu t ions of A and B t o w a r d the purchase of Q' a r e P^ and and Pb ( Pa + Pb = P) • The t o t a l amounts pa id by A and B a re depic ted by the areas OQ'WPa and O C ' V P ^ , r e s p e c t i v e l y . I t should be noted that the u se r charge i s below m a r g i n a l cost r e f l e c t i n g the genera l o r soc i a l d e s i r a b i l i t y of inc reased highway use .

Other po in ts l i k e M cou ld be d e t e r m i n e d by assuming a d i f f e r e n t m a r k e t p r i c e . T h i s se r i e s of po in t s de t e rmines the j o i n t o r co l l ec t i ve demand ( D Q ) f o r highway use . Dc

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can be cons t ruc ted d i r e c t l y by a v e r t i c a l s u m m a t i o n of and . When the econom­i c s of the m a r k e t p lace i s cons idered , the demands of i nd iv idua l s ar^; summed h o r i z o n ­t a l l y (6) . However , when a s e r v i c e y i e l d s i n d i r e c t benef i t s i t takes on a " p u b l i c " o r " c o l l e c t i v e " cha rac t e r because a l l i n d i v i d u a l s demand the same p h y s i c a l p r o d u c t . P o ­l i c e p r o t e c t i o n , na t iona l defense and many o ther p r o g r a m s i n s t i t u t ed i n the pub l i c i n t e r ­est may be conceptual ized th rough a v e r t i c a l summat ion of i n d i v i d u a l demands. The p rocedure s employed i n F i g u r e 2 were set f o r t h o r i g i n a l l y i n Sweden by W i c k s e l l and l i n d a h l and have been developed r e c e n t l y i n the Uni ted States by H o w a r d Bowen (T) and Paul A . Samuelson {8). I m p l i c i t i n the so lu t ion i s a " n e u t r a l " t heo ry of taxa t ion r e ­f l e c t i n g the v o l u n t a r y choices of i nd iv idua l s i n a c o l l e c t i v e contex t .

The a l l o c a t i o n of shares depic ted i n F i g u r e 2, i s a k i n , but not i d e n t i c a l , to the t r a ­d i t i o n a l a l l o c a t i o n of cos t between u s e r s and non -use r s . A c t u a l d e t e r m i n a t i o n of the non-user share poses s i g n i f i c a n t p r o b l e m s of measurement . The subsidy w i l l not be o f f e r e d by the non-user un less i t b r i n g s about increases i n A ' s use of the h ighway. That i s , i f a subsidy o f f e r i n the f o r m of a non-user share w o u l d r e s u l t i n no o r i n neg­l i g i b l e change, the subsidy i s super f luous and charges f o r the road a r e assessed against the u s e r s of the r o a d . A l though the downtown merchan t may benef i t f r o m the use of the road , i t does not ( o n economic grounds) f o l l o w that he should d e f r a y p a r t of the cost of the f a r m to c i t y s y s t e m . I t i s a lmos t c e r t a i n that r en t s and w i n d f a l l s of v a r i o u s s o r t s

w i l l a cc rue to many i n d i v i d u a l s . H i e i n ­c lu s ion of these e lements i n the highway f i n a n c i a l s t r u c t u r e may lead only to a r e d i s ­t r i b u t i o n of i ncome f r o m those r e c e i v i n g w i n d f a l l s to highway u s e r s . However , i f a l m s a re to be g iven , the re may be o the r s who occupy a h ighe r p lace on our scales of p r e f e r e n c e .

Silence on the p a r t of i n d i r e c t b e n e f i c i ­a r i e s i s evidence that the i n d i r e c t benef i t i s of a su rp lus cha rac t e r and does not have to be cons ide red i n a f r a m e w o r k of econom­ic e f f i c i e n c y . I f the subsidy i s r e q u i r e d , bus inessmen and o the r s w i l l e x e r t p r e s s u r e on the l e g i s l a t u r e o r the highway au tho r i t y to p r o v i d e expanded f a c i l i t i e s . A s a gen­e r a l r u l e , c o l l e c t i v e o r p o l i t i c a l ac t ion of some s o r t w i l l be r e q u i r e d . The task of the highway analys t i s to r econs t ruc t the p r e s s u r e s and the c o l l e c t i v e ac t i on . The highway f i n a n c i a l analyst r ece ives an e x ­pend i tu re p r o g r a m along w i t h the r e c o r d of l e g i s l a t i v e and execut ive hear ings and o ther evidences of c o l l e c t i v e ac t i on . The p r o g r a m i s a r e s u l t o f t r a f f i c s tudies i n i ­t i a t e d by the highway au tho r i t y and the v i e w s of v a r i o u s non-user groups w h i c h

a r e a f f e c t e d . A s c r u t i n y of the p r o g r a m and the hear ings may ind ica te the i n d i r e c t bene f i t s wh ich ought to p l a y a r o l e i n highway f inance . By i n f e r ence , the highway ana­l y s t can a t tempt to r e c o n s t r u c t r e l a t ionsh ips invo lved i n the c o l l e c t i v e ac t ion and w i t h i n w ide l i m i t s may be able to de te rmine appropr i a t e paymen t s . B e f o r e h i m a r e a lways the f o l l o w i n g quest ions: ( a ) Does t h i s group o r i n d i v i d u a l r ece ive an i n d i r e c t benef i t ? ( b ) I f so, i s a payment by the i n d i r e c t b e n e f i c i a r y a necessary cond i t ion f o r r e c e i p t of t h i s i n d i r e c t benef i t ? ( c ) What i s the m i n i m a l amount that he would have to pay to b r i n g about a s i tua t ion that y i e ld s t h i s amount of benef i t ? The p r o b l e m s a r e d i f f i c u l t , bu t not i n su rmoun tab l e . A l though p e r f e c t i o n may be i m p o s s i b l e , i t i s f e l t that the ap­p r o a c h suggested i s s u p e r i o r to the b r o a d and of ten i l l u s o r y conception of i n d i r e c t o r " s o c i a l " bene f i t s so f r e q u e n t l y brought in to highway f i n a n c i a l ana ly s i s . M o r e o v e r , the opposite e x t r e m e of o v e r l o o k i n g i n d i r e c t benef i t s e n t i r e l y i s avoided. A t leas t a f e w

Quantity Q

Figure 3. Windfall (Equity).

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l i m i t s have been set and some c r i t e r i a have been es tab l i shed .

I n d i r e c t B e n e f i t s Wi thout a N o n - U s e r Share

F i g u r e 3 r epresen t s the s i tua t ion when t he re a r e i n d i r e c t benef i t s wh ich have no s ign i f i cance unless a s tandard of tax equi ty i s adopted. The h o r i z o n t a l summat ion of Da and E)u y i e l d s the c o l l e c t i v e demand, D ^ . A t p r i c e P, both D ^ and y i e l d a quant i ty Q. A t output Q the demand of B , the non-user , f o r add i t iona l i n c r e m e n t s of t r a f f i c i s z e r o . A n inc rease i n t r a f f i c beyond Q does not y i e l d any add i t iona l advantages to the i n d i r e c t b e n e f i c i a r y . No subsidy i s o f f e r e d and A pays f o r the h ighway . The shaded a rea i n F i g u r e 3 represen ts a w i n d f a l l o r r en t wh ich may o r may not be ex­t r a c t e d f r o m the i n d i r e c t b e n e f i c i a r y depending on equi ty . These ren t s and w i n d f a l l s , of cou r se , w o u l d p r o v i d e an excel lent source of revenue f o r r e d i s t r i b u t i v e purposes . However , the no t ion that " l i k e th ings should be t r e a t ed a l i k e " a long w i t h p r i n c i p l e s of tax equi ty such as " n e u t r a l i t y " o r "reasonable c l a s s i f i c a t i o n " , i m p l y that r e n t s and w i n d f a l l s associa ted w i t h the highway f u n c t i o n should be t r e a t e d i n the same manner as any o the r r en t s o r w i n d f a l l s . On a d m i n i s t r a t i v e and oppor tun i s t i c grounds , the case f o r the e x t r a c t i o n of such ren t s i s much s t ronge r . F o r example , the uncap i t a l i zed r en t s associa ted w i t h a new highway p r o g r a m a re easy to measu re and i n t h i s w r i t e r ' s op in ion represen t an excel lent source of gene ra l tax revenue. Th i s op in ion i s based on oppor tun i s t i c and a d m i n i s t r a t i v e grounds coupled w i t h a no t ion about j u s t i c e . However , such oppor tun i s t i c t axa t ion should not be r e l a t ed to the highway tax s t r u c t u r e wi thou t f i r s t assess ing the i m p l i c a t i o n s of r educ ing the share assigned to u s e r s .

Perhaps the mos t s i g n i f i c a n t p r a c t i c a l conc lus ion i s tha t the t r a d i t i o n a l a l l oca t i on of cost between u s e r s and non-use r s i s p r i m a r i l y a response to an a d m i n i s t r a t i v e p r o b l e m . However , the p r o p e r p lace to consider a d m i n i s t r a t i o n i s a f t e r cos t s have been a l loca ted , not b e f o r e . The f i r s t s tep i n highway f i n a n c i a l ana lys i s should es tabl i sh the cost of h ighway use . I f the " s o c i a l l y " des i r ab le amount of h ighway s e r v i c e ( d e ­p i c t e d by Dj j ) " c l e a r s the m a r k e t " at a c o s t - d e t e r m i n e d p r i c e , a non-user share i s not r e q u i r e d . K the " s o c i a l l y " des i r ab le amount does not " c l e a r the m a r k e t " , h ighway use mus t be encouraged th rough subsidy i n the f o r m of a non-user sha re . Equ i ty may also c a l l f o r a non-user share; t h i s r e q u i r e s evaluat ions concern ing the d i s t r i b u t i o n of i n ­c o m e . Al though the a t t a inment of equi ty i s des i r ab le , i t does not p r o v i d e a p r i n c i p l e f o r the d e t e r m i n a t i o n and a l l o c a t i o n o f h ighway cos t . The p r a c t i c e o f i n c o r p o r a t i n g e i the r a " b e n e f i t " o r " a b i l i t y to p a y " t heo ry of t axa t ion w i t h i n the a n a l y t i c a l f r a m e w o r k of cos t a l l oca t ion may se rve only to reduce the amounts assessed against u s e r s , and cou ld lead to an u n w a r r a n t e d subsidy d i sgu ised i n the f o r m of a " s c i e n t i f i c " a l l oca t i on of cos t . The r e s u l t m i g h t w e l l be a m i s a l l o c a t i o n of r e sources and t r a f f i c i n the domes­t i c t r a n s p o r t a t i o n s y s t e m .

H I G H W A Y P R I C I N G

I t has been suggested that the d e t e r m i n a t i o n o f p r i c e s f o r the use of h ighways ought to be the f i r s t , not the second, step i n highway f i n a n c i a l ana ly s i s . I n the abs t rac t , the appropr i a t e p r i c e i s f o u n d at the po in t on the t h e o r i s t ' s m a r g i n a l cos t c u r v e w h i c h c o r ­responds to the quant i ty of s e r v i c e t aken . T h e o r e t i c a l m a r g i n a l cost cu rves a r e i n ­t e r e s t i n g a n a l y t i c a l t oo l s , u s e f u l i n d e m o n s t r a t i i ^ the p r i n c i p l e , but of l i t t l e help i n app l i ca t i ons . The ensuing d i scuss ion d e l i b e r a t e l y eschews the t r a d i t i o n a l t h e o r e t i c a l m a c h i n e r y i n f a v o r of an app l i ed i n t e r p r e t a t i o n of the m a r g i n a l cost s tandard .

M a r g i n a l cost has been def ined as the d i f f e r e n c e i n t o t a l cost a t two consecut ive l eve l s of output {9). A l t e r n a t i v e l y , i t i s the cost w h i c h cou ld be avoided i f an a d d i t i o n ­a l u n i t , b lock of u n i t s , o r c lass of un i t s w e r e not p roduced . A c c o r d i n g to James E . Buchanan ( 1 0 ) , t he r e a r e two components of m a r g i n a l cost r e l evan t to highway f i nance : (a ) The d i r e c t m a r g i n a l money cost imposed by a u se r and ( b ) the i n d i r e c t add i t iona l burdens i m p o s e d on o t h e r u s e r s , tha t i s , de lays and inconveniences assoc ia ted w i t h congest ion. D i r e c t m a r g i n a l money cost i s " that p o r t i o n of t o t a l maintenance costs wh ich v a r y d i r e c t l y w i t h r o a d usage . " I n d i r e c t o r " r e a l " m a r g i n a l cost cannot be t r a n s ­l a t ed eas i ly in to a money equivalent . E m p l o y i n g t h i s two-p ronged concept ion of m a r ­g i n a l cos t , Buchanan concludes tha t :

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1 . Secondary r o a d u se r s who cause l i t t l e congest ion should be r e q u i r e d to pay less p e r ton o r veh ic l e m i l e than p r i m a r y r o a d u s e r s .

2. Heavie r and l a r g e r veh ic l e s should be charged h igher ra tes than l i g h t e r and s m a l l e r ones because bo th the d i r e c t and i n d i r e c t components of m a r g i n a l soc ia l cost a r e g r ea t e r .

3. Slower veh ic l e s w h i c h add m o r e to congestion should pay h i g j i e r r a t e s than f a s t e r v e h i c l e s .

4. V e h i c l e s known to t r a v e l m o r e d u r i n g congested t i m e p e r i o d s should be charged h igher r a t e s . Higher ra tes should be charged on week-ends and hol idays and d u r i n g r u s h h o u r s .

One d i f f i c u l t y w i t h Buchanan's conception of m a r g i n a l cost i s the assumpt ion that maintenance cost i s the re levan t m a r g i n a l money cos t . Th i s e l imina t e s cons t ruc t ion expendi ture f r o m the p u r v i e w of the highway p r i c e s t r u c t u r e . Al though the cost of sunk, f i x e d o r p r e v i o u s l y c o m m i t t e d resources i s not m a r g i n a l ( 1 1 ) , i t does not f o l l o w tha t cons t ruc t ion cost i s wi thout s ign i f i cance to highway p r i c i n g ( T 2 ) . Expansion and c o n t r a c t i o n of the highway p lan t t h rough v a r i a t i o n s i n cons t ruc t i on expendi ture i s a d a i l y occurence . Al though such expendi tures become sunk costs , new cons t ruc t ion ex­pendi tu res a r e con t inua l ly being made and, t h e r e f o r e , a r e m a r g i n a l . T o have any r e a l s ign i f i cance , m a r g i n a l cost mus t r e f e r to those r e sources wh ich a re c u r r e n t l y a v a i l ­able f o r o ther uses and w h i c h management may o r may not choose to a p p r o p r i a t e . I n a s i m i l a r v e i n , L e r n e r main ta ins that m a r g i n a l costs "are costs the i n c u r r e n c e of wh ich i s i n ques t ion" ( ^ 3 ) .

"Costs the i n c u r r e n c e of wh ich i s i n ques t ion" a re found i n the p r o g r a m o r p l an of the a u t h o r i t y . The p r o g r a m i s con t inua l ly i n question and represen t s both p roduc t ion and p lann ing ( s h o r t and long run ) costs ; i t does not inc lude costs tha t have been i n ­c u r r e d p r e v i o u s l y . I f the p r o g r a m i s w e l l conceived, i t i s geared as evenly as poss ib l e t o the demand tha t i s expected to p r e sen t i t s e l f at a s e r i e s of f u t u r e dates. I f the de ­mand develops as an t ic ipa ted , the highway p l an t w i l l operate as near to the o p t i m u m as poss ib l e . F r o m t i m e t o t i m e the p r o g r a m w i l l be r e v i s e d i n response to changes i n the out look, and p r o g r a m cost w i l l e i the r be inc reased o r decreased . K demand decl ines and add i t i ona l c o n s t r u c t i o n i s not r e q u i r e d , p r o g r a m cos t w i l l dec l ine t o the l e v e l of maintenance; i f demand inc reases , p r o g r a m cost w i l l i nc rease so as to inc lude the cos t of added capac i ty .

The d i f f i c u l t y w i t h p r o g r a m cost i s obvious . I t i s a v a l i d i n t e r p r e t a t i o n of m a r g i n a l cost on ly on the assumpt ion that the p r o g r a m r e f e r s to an o p t i m a l l y ad jus t ed p l an t . T h i s assumpt ion may be quest ioned. P a r t i c u l a r roads o r the sys tem as a whole may be c h a r a c t e r i z e d by congest ion (excess demand) o r u n d e r - u t i l i z a t i o n (excess s u p p l y ) . In the event of u n d e r - u t i l i z a t i o n , add i t iona l t r a f f i c can be handled at a v e r y low a d ­d i t i o n a l cos t . On the o ther hand, congest ion c rea tes a s i tua t ion wh ich i s c h a r a c t e r i z e d by h igh m a r g i n a l costs some of w h i c h a r e exceedingly d i f f i c u l t to measure . Such c o n ­d i t ions may a r i s e because of (a ) shor t r u n o r t e m p o r a r y excess supply o r demand (b) i n d i v i s i b i l i t i e s , tha t i s , the p h y s i c a l i m p o s s i b i l i t y of ad jus t ing the p lant and ( c ) peak load . Al though these condi t ions a re c lo se ly i n t e r r e l a t e d , each may c a l l f o r a p a r t i ­c u l a r k i n d of p r i c e p o l i c y .

B e f o r e examin ing these s i tuat ions i t may be h e l p f u l to d i s t ingu i sh between " t e m p o r a r y " and "permanen t" i n d i v i s i b i l i t i e s of the highway p l an t . T e m p o r a r y i n d i v i s i b i l i t i e s a r e those that can be e l i m i n a t e d by increases o r decreases i n demand o r supply . F o r example, a d d i ­t i o n a l lanes a r e added i n an t i c ipa t i on o f the demand a f e w y e a r s hence. T h e r e i s excess supply of a t e m p o r a r y na ture because of the i n a b i l i t y to make f r equen t and s m a l l ad jus tmen t s . P e r ­manent i n d i v i s i b i l i t i e s appear on secondary roads . T y p i c a l l y , such roads have excess supply because of an inadequate demand coupled w i t h the f a c t that roads mus t have c e r t a i n m i n i m u m design f ea tu re s to wi ths tand the e lements and to p r o v i d e a reasonable m i n i m u m qua l i ty of s e r ­v i c e . In the ensuing d i scuss ion , permanent i n d i v i s i b i l i t i e s ( secondary roads) a r e t r e a t e d separa te ly . However , t e m p o r a r y i n d i v i s i b i l i t i e s a r e t r e a t e d a s a s h o r t - r u n m a l a d j u s t m e n t .

Short Run Excess Supply o r Demand

If t he re w e r e no peak load p r o b l e m o r pe rmanen t i n d i v i s i b i l i t i e s , excess supply o r

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excess demand could be r e m o v e d th rough appropr ia t e ad jus tment of the p lan t . However , the p lant cannot be ad jus ted i m m e d i a t e l y . A n a t tempt to e l i m i n a t e congest ion o r ex­cess capaci ty i m m e d i a t e l y th rough p r i c e v a r i a t i o n s involves d i f f i c u l t a d m i n i s t r a t i v e p r o b l e m s . M o r e o v e r , i t i s poss ib le to ma in t a in that p r i c e d i s c i p l i n e i s not a necessary condi t ion f o r e f f ec t i ve shor t r u n u t i l i z a t i o n of the highway p l an t . An ad jus tment to t e m ­p o r a r y excess capac i ty o r congest ion o c c u r s m o r e o r l e ss a u t o m a t i c a l l y because t r a f ­f i c has a tendency to d i s t r i b u t e i t s e l f so as to r e f l e c t m a r g i n a l r e a l cos t . Congestion r a i s e s r e a l cost to the m o t o r i s t ; excess capaci ty reduces such cos t . The m o t o r i s t , i n r educ ing r e a l cos t , w i l l a t t empt to select tha t t i m e and rou te wh ich has the l o w e r m a r g i n a l r e a l cos t . Of course , t h i s automat ic ad jus tment f o r excess capac i ty and c o n ­ges t ion i s l i m i t e d , e spec ia l ly i n r u r a l a reas , by the number of a l t e r n a t i v e s ava i l ab le to m o t o r i s t s . Another aspect of t h i s ad jus tment i s the f l u c t u a t i o n i n u se r tax ea rn ings . I f u se r tax r a t e s a r e es tabl ished on the assumpt ion of o p t i m a l opera t ions , congest ion w i l l r e s u l t i n " p r o f i t s " to the highway au tho r i t y w h i l e excess capac i ty w i l l lead to " l o s s e s . " The accumula t ion of p r o f i t s may be i n t e r p r e t e d as a r e f l e c t i o n of r i s i n g m a r g i n a l cos t w h i l e the i n c u r r e n c e of losses may r e f l e c t d e c l i n i n g m a r g i n a l cos t .

The ad jus tment desc r ibed above may also be i n t e r p r e t e d as a r e f l e c t i o n of the i n t i ­mate r e l a t ionsh ip between the vo lume o r density of t r a f f i c and the qua l i ty of s e r v i c e . Al though ra tes a re not v a r i e d , the m o t o r i s t r ece ives a l o w e r qua l i ty of s e rv i ce on a congested highway and a h igher qua l i ty of s e rv i ce on a highway which has excess capaci ty . The e f f ec t i s much the same as that w h i c h wou ld be obtained i f the qua l i ty s tandard were main ta ined and p r i c e v a r i a t i o n s w e r e used to ad jus t the v o l u m e of t r a f f i c . Instead o f p r i c e v a r i a t i o n s , the ad jus tmen t may occur p a r t i a l l y th rough qua l i ty v a r i a t i o n s wh ich a re " b u i l t - i n " to the sys t em.

In pass ing , another i m p l i c a t i o n should be noted. The addi t ion of a veh ic l e imposes add i t iona l " r e a l " costs on o ther veh ic l e s , a l though the add i t iona l money out lay o f the highway a u t h o r i t y i s qui te l o w . These " r e a l " costs may be measured by cons ide r ing the i m p a c t of the v e h i c l e on the " p r a c t i c a l " capac i ty of the h ighway. P r a c t i c a l capac i ty has been def ined i n the Highway Capaci ty Manual (_14) as: "the m a x i m u m number of veh ic l e s tha t can pass a g iven po in t on a roadway o r i n a designated lane d u r i n g one hour wi thou t the t r a f f i c densi ty being so g rea t as to cause unreasonable delay, haza rd o r r e s t r i c t i o n to the d r i v e r s ' f r e e d o m to maneuver under the p r e v a i l i n g roadway and t r a f f i c c o n d i t i o n s . " E v e r y d i m i n u t i o n of ava i l ab le capac i ty can r ep resen t an i n c r e m e n t of cos t imposed on other v e h i c l e s . Thus , the m a r g i n a l cost imposed by each veh ic le i s a f u n c t i o n of veh ic l e s inconvenienced o r even d i sp laced ( r e d u c t i o n i n c a p a c i t y ) . Since eve ry veh ic l e i s m a r g i n a l , p r i c e s cou ld be es tabl ished on the bas i s of r e l a t i v e capac i ty u t i l i z e d on the assumpt ion that the m o r e capaci ty u t i l i z e d by a p a r t i c u l a r v e ­h i c l e , the m o r e the p r a c t i c a l capaci ty i s r educed . The capaci ty approach p r o v i d e s a means f o r t r a n s l a t i n g r e a l cost in to money cos t . However , i f the road i s capable of handl ing add i t iona l t r a f f i c , wi thout any i m p a c t on p r a c t i c a l capaci ty , the m a r g i n a l cos t can be no g rea t e r than that p o r t i o n of maintenance cost w h i c h v a r i e s d i r e c t l y w i t h road 11 use .

The burden of the a rgument i s tha t highway u se r s who do not bear the b r u n t of h igh m a r g i n a l costs i n t e r m s of h igher u se r tax ra tes mus t s t i l l bear r e a l cost i n t e r m s of delay, inconvenience and f r u s t r a t i o n . A p o l i c y of m a i n t a i n i n g r a t e s at the p r o g r a m cost l e v e l has m o r e to c o m m e n d i t than the a rgument of a d m i n i s t r a t i v e f e a s i b i l i t y . A l though m o r e r e f i n e d r a t e v a r i a t i o n s i n response to t e m p o r a r y excess supply and ex ­cess demand wou ld be d i f f i c u l t to a d m i n i s t e r , i t may be des i r ab le i n some instances to add p r i c e d i s c i p l i n e to the " b u i l t - i n " ad jus tment a l r eady de sc r i bed .

Permanent I n d i v i s i b i l i t i e s

F requen t ly i t i s i m p o s s i b l e to ad jus t the h ighway p lan t to the demand f o r i t s use and t he re i s a pe rmanen t condi t ion of excess capac i ty . None of the poss ib le ad jus tments desc r ibed i n the p reced ing sect ion can be made. M a r g i n a l cost on a l i g h t l y t r a v e l e d road i s w e l l below the u n i t p r o g r a m cost f o r that r o a d . However , the m a r g i n a l cost a rgument f o r l o w ra t e s i s not espec ia l ly s t rong as the demand f o r such roads p r o b a b l y i s r e l a t i v e l y ine las t i c ; t h e r e f o r e , the excess capaci ty cannot be r e m o v e d th rough i n -

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creases i n t r a f f i c b rought about b y l o w m a r g i n a l cost p r i c e s . Never the less , a f o r m a l adherence to the p r i c i n g s tandard r e q u i r e s l ow ra tes f o r l i g h t l y t r a v e l e d roads .

M a r g i n a l cost p r i c i n g r e q u i r e s that secondary roads having excess capaci ty be o p ­era ted at a " l o s s . " I n a sense t h i s o f f e r s an excel lent t h e o r e t i c a l r a t i o n a l i z a t i o n f o r a non-user share on secondary roads . The quest ion of " losses" due to m a r g i n a l cost p r i c i n g has been discussed by many w r i t e r s ( 1 5 ) . One so lu t ion to the p r o b l e m i s the " t w o - p a r t " t a r i f f ( 1 6 ) . Under t h i s p roposa l the consumer pays a low m a r g i n a l cost p r i c e at the t i m e of purchase . I n add i t ion , l u m p sum charges independent of use a re employed to cover the losses that a r i s e . A n appl ica t ion of t h i s idea to highway f inance leads to a l u m p sum tax not to exceed the v a l u e - o f - s e r v i c e to the user , combined w i t h a l ow user charge based on m a r g i n a l cos t . The gasol ine and weight distance taxes a re appropr i a t e candidates f o r the m a r g i n a l ra te w h i l e l i cense taxes , d r i v e r ' s l i cense f ees , p r o p e r t y taxes on au tomobi les , spec ia l assessments against those abut t ing p r o p e r t y owners who use the road and many o the r s appear to be sui table f o r the l u m p sum charge . I t i s f e l t that l icense taxes and d r i v e r ' s l i cense fees a re best sui ted f o r t h i s purpose b e ­cause t h e i r purchase i s v o l u n t a r y . Thus , the payment does not exceed v a l u e - o f - s e r v i c e . Of course , t h i s does not p rec lude the use of any other l u m p sum tax p r o v i d e d i t i s p a i d by the use r and does not exceed v a l u e - o f - s e r v i c e .

Peak Loads

E l i m i n a t i o n of peak load does not invo lve conceptual p r o b l e m s that have not been de­s c r i b e d by Buchanan and o the r s , bu t app l i ca t ion to highways does i n v o l v e s i g n i f i c a n t a d m i n i s t r a t i v e p r o b l e m s . Al though there a re oppor tun i t i e s f o r peak load p r i c i n g that ought to be examined by highway a d m i n i s t r a t o r s , i t i s l i k e l y that the genera l p r o b l e m i s solved as w e l l as i t can be by the " b u i l t - i n " ad jus tmen t . M o t o r i s t s do not d r i v e head­long in to congest ion un less t h e i r demand i s h igh ly ine las t i c ; i t poss ib le , they tend to a r range t h e i r a f f a i r s i n o r d e r to avo id the t r a f f i c . Reasonable r a t e d i f f e r e n t i a l s p r o b ­ably wou ld have l i t t l e impac t on the peak load p r o b l e m , al though o ther so lu t ions of a m o r e gene ra l na tu re a r e poss ib l e , e . g . , subs id ized t r a n s i t sy s t ems . I n r e a c h i n g t h i s conc lus ion r e l a t i v e to the peak load p r o b l e m , i t i s not i m p l i e d tha t peak load p r i c i n g should be abandoned. In some instances, appropr i a t e peak load p r i c e p o l i c y of the s o r t advocated by Buchanan m i g h t r e s u l t i n a m o r e e f f e c t i v e u t i l i z a t i o n of the highway s y s t e m . The p r o b l e m s r e l a t i v e to peak load a r e a d m i n i s t r a t i v e , not conceptual .

T H E F R A M E W O R K O F A P P L I C A T I O N

I t has been suggested tha t a highway use r tax s t r u c t u r e consis tent w i t h the m a r g i n a l cost s tandard m i g h t be based on p r o g r a m cos t . T e m p o r a r y congestion and excess capac i ty a r e e l i m i n a t e d p a r t i a l l y by a " b u i l t - i n " ad jus tment desc r ibed e a r l i e r . I f such condi t ions p e r s i s t f o r any length of t i m e , they w i l l have an i m p a c t on p r o g r a m cost and w i l l lead e i the r to h ighe r o r l o w e r ra tes u n t i l the p lan t i s ad jus t ed . I f i t i s p r a c t i c a l , a sys tem of peak load and s h o r t - r u n p r i c e s may be i n c o r p o r a t e d in to the f i n a n c i a l s t r u c ­t u r e . M o d i f i c a t i o n s f o r l i g h t l y t r a v e l e d roads wh ich have h igh average p r o g r a m costs but l ow m a r g i n a l cos ts a r e also r e q u i r e d . A f t e r a l l ad jus tmen t s have been made, the r e v i s e d p r i c e s t r u c t u r e may deviate cons iderab ly f r o m the i n i t i a l p r i c e s t r u c t u r e based on p r o g r a m cos t .

The bas ic e lement i n the es tab l i shment o f the p r i c e s t r u c t u r e w i l l be an i n c r e m e n t a l a l l oca t ion of p r o g r a m cos t . The usua l i n c r e m e n t a l cost a l l oca t ion invo lves a d i r e c t ass ignment of specia l cos t to v e h i c l e c lasses a l o i ^ w i t h an appor t ionment of c o m m o n cost among a l l v e h i c l e s . To have e m p i r i c a l v a l i d i t y , these cost ass ignments u sua l ly a re based on engineer ing design c r i t e r i a . These "des ign-cos t " ass ignments o r "cos t r e s p o n s i b i l i t i e s " mus t be conver ted into economic c o s t - p r i c e r e l a t i o n s h i p s . F i n a l l y , c o s t - p r i c e r e l a t ionsh ips mus t be combined w i t h a d m i n i s t r a t i v e r e l a t ionsh ips i n o r d e r t o p r o v i d e a workab le so lu t ion . The p r o b l e m i s l a r g e l y one of a r r a n g i n g v a r i o u s ca tegor ies in to a s ingle f r a m e w o r k that in tegra tes the f a c t o r s imp ing ing on the t o t a l highway p r o g r a m . The r e l a t ionsh ips that sha l l be cons idered f a l l in to t h r ee c lasses :

1 . Design-Cost—Cost o f supply ing h ighway s e r v i c e s d e t e r m i n e d f r o m highway de ­s ign c r i t e r i a .

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2 . C o s t - P r i c e — P r i c e s f o r highway s e r v i c e s de t e rmined i n accordance w i t h the m a r g i n a l cost c r i t e r i a .

3. P r i c e - A d m i n i s t r a t i v e — C o l l e c t i o n of p r i c e s i n accordance w i t h a d m i n i s t r a t i v e c r i t e r i a .

Des ign-Cos t Rela t ionships

A l l v a r i a t i o n s i n h ighway design due to v a r i a t i o n s i n e i ther t r a f f i c v o l u m e o r to the s ize , weight and p e r f o r m a n c e of veh ic l e s can be r e l a t ed e i the r to pavement r e q u i r e m e n t s o r t o g e o m e t r i c des ign . Pavement des ign r e f e r s t o pavement cha rac t e r i s t i c s—sur face , base and subbase; geome t r i c design deals w i t h length , w i d t h , c u r v a t u r e , g rad ien t and a l inement . Fundamenta l ly , the geome t r i c design of a highway i s a f u n c t i o n of (a ) the v o l u m e of a l l c lasses of t r a f f i c , ( b ) the d imens ions and speeds of v e h i c l e s and ( c ) the qua l i t y of s e r v i c e (speed, ease of d r i v i n g , r i s k , e t c . ) that has been se lected. A s s u m i n g g iven s o i l and weather condi t ions , pavement design i s a f u n c t i o n of the axle load of v e ­h i c l e s and, pos s ib ly , of the number of r epe t i t i ons of the ax le load ( v o l u m e of p a r t i c u l a r weight c lasses of t r a f f i c ) .

V o l u m e r e l a t ionsh ips re levan t to the geomet r i c design have been establ ished by studies of highway capaci ty (_14). These r e l a t ionsh ips a re not so " l u m p y " as one w o u l d suppose. When a two- l ane highway becomes congested, the j u m p to a f o u r - l a n e highway i s not i n e v i t a b l e . The two lanes may be widened, grades and c u r v a t u r e may be reduced and many o ther e lements of geome t r i c design may be v a r i e d i n an a t tempt to ad jus t the geome t r i c design to the t r a f f i c . Of course , the p o s s i b i l i t y of ad jus t ing the p lant on the d r a w i n g boa rd i s a d i f f e r e n t p r o b l e m f r o m ad jus t i ng the p lan t i n an economic sense. M o r e o v e r , the p o s s i b i l i t y of m a k i n g ad jus tment i n the geome t r i c design i s severe ly l i m i t e d w i t h r e g a r d to f a c i l i t i e s wh ich c a r r y a v e r y low v o l u m e of t r a f f i c because of the m i n i m u m design f o r m necessary to p r o v i d e a reasonably s a t i s f a c t o r y s e r v i c e .

V o l u m e o r quant i ty r e l a t i onsh ips f o r pavement th ickness a re not as w e l l es tabl ished as those f o r geome t r i c des ign . The pavement th ickness , f o r example , may be a f f ec t ed by the number and f r equency of r epe t i t i ons of a p a r t i c u l a r ax le l o ad . However , pave ­ment design does not cons ider t h i s r e l a t i onsh ip i n a manner such that a de f in i t e r e ­la t ionship between number o f r epe t i t i ons and pavement th ickness can be de t e rmined ( 1 7 ) . The chief d i f f i c u l t i e s i n i s o l a t i n g weigh t r e l a t e d pavement cos t s appear i n the l o w - v o l u m e roads which a r e not designed f o r " i n f i n i t e " r epe t i t i ons of a m a x i m u m p e r m i s s i b l e ax le load (_17). A s a r e s u l t of these p r o b l e m s , d i f f e r e n t methods and a cons iderable amount of judgment a r e r e q u i r e d i n o r d e r to i so l a t e w e i g h t - r e l a t e d cos t s f o r a h ighway sys t em having both h igh and low v o l u m e roads . I n o r d e r to s i m p l i f y the d i scuss ion , i t w i l l be assumed tha t the sys tem of highways i s composed of two c lasses of r o a d each designed i n accordance w i t h the f o l l o w i n g s tandards , l i m i t a t i o n s and assumpt ions :

1 . P r i m a r y o r h i g h - v o l u m e roads a r e designed f o r an i n f i n i t e number of r epe t i t i ons of a l e g a l l y p e r m i s s i b l e m a x i m u m ax le l oa d . I n c r e m e n t a l weight cos ts can be c a l c u ­la ted and assigned to the v a r i o u s weight c lasses u s i i ^ the road ( 1 8 ) .

2. Secondary o r l o w - v o l u m e roads a re designed to the h igher of two standards: (a ) To wi ths tand the e lements over a g iven p e r i o d of yea r s o r (b ) to wi ths tand the m a x i m u m axle load wh ich appears w i t h a s u f f i c i e n t f r equency to a f f e c t design s tandards . Secondary road pavements a r e capable of handl ing m i x e d t r a f f i c i n p r o p o r t i o n s that a r e not known . P r o v i d e d they appear i n " l i m i t e d " n u m b e r s , heavy veh ic les do not impose measurab le i n c r e m e n t a l weight cos ts (IT) •

I t should be noted that these s tandards , l i m i t a t i o n s and assumpt ions w i l l v a r y de­pending on the state of engineer ing knowledge . Al though a m o r e sophis t ica ted s e r i e s of design r e l a t ionsh ips cou ld be d e r i v e d , those that have been presented a r e s u f f i c i e n t f o r the ana lys i s which i s to f o l l o w . I t i s a lso w o r t h no t ing that geome t r i c design c rea tes highway capaci ty w h i l e pavement th ickness c rea tes the a b i l i t y to bear loads . Since h i g h ­way capaci ty i s c rea ted on behalf of a l l veh ic l e s , geomet r i c design may be i n t e r p r e t e d as i m p o s i n g on ly common cos t . I n t e r p r e t e d i n t h i s manner , the geomet r i e s of the ex t r a f o o t o r two o r d i n a r i l y associa ted w i t h t r u c k t r a f f i c i s a common , not a spec ia l cost , be ­cause the add i t iona l capac i ty i s ava i lab le to a l l v e h i c l e s . I f the ava i lab le h ighway c a -

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pac i ty i s e i the r inc reased o r decreased, the condi t ions under wh ich a l l veh ic l e s operate a re changed because of the e f f e c t on congest ion. T h i s does not ho ld f o r pavement t h i c k ­ness wh ich imposes spec ia l cos t . The r e m o v a l of an i nc r emen t of weight o r axle load ( s i z e , speed and v o l u m e of t r a f f i c r e m a i n i n g constant) reduces highway cost , but does not a f f e c t the condi t ions under w h i c h a l l veh i c l e s opera te .

A s s u m i n g that the pavement of p r i m a r y highways i s designed to wi ths tand " i n f i n i t e " r e ­pe t i t ions of a m a x i m u m axle load , the m a r g i n a l cost of pavement i s zero because the a d d i ­t i o n of one m o r e veh ic le does not increase the t o t a l cost of pavement . On the o ther hand, i f a continuous r e l a t i onsh ip i s es tabl ished between the numbers (and f requency) of a p a r t i c u l a r axle load and the pavement r e q u i r e m e n t , m a r g i n a l pavement cost can be de t e rmined by e v a l ­ua t ing the i m p a c t of an add i t iona l v e h i c l e on the pavement th ickness r e q u i r e m e n t . The en ­suing d i scuss ion proceeds on the assumpt ion that a continuous r e l a t ionsh ip between r e p e t i -t i o n a l loading and pavement th ickness has not been es tabl i shed. However , the i m p l i c a t i o n s of t h i s p o s s i b l e r e l a t i o n s h i p w i l l be noted i n the course of the d i scuss ion .

W i t h t h i s background i t i s poss ib le to es tab l i sh a se r i e s of tenta t ive r e l a t ionsh ips around wh ich a sys tem of highway f inance may be cons t ruc ted . The re l a t ionsh ips de­s c r i b e d below are of t w o sor t s—geomet r ic and pavement; they a re deduced f r o m the assumed c r i t e r i a f o r highway des ign .

A . G e o m e t r i c Rela t ionships

1 . G e o m e t r i c design p r o v i d e s capac i ty . 2 . Capacity i s u t i l i z e d by a l l v e h i c l e s . T h e r e f o r e , geomet r i c design imposes

c o m m o n cos t . 3. Changes i n geome t r i c design crea te m a r g i n a l costs which do not inc lude i n c r e ­

men ta l ( s p e c i a l o r we igh t - r e l a t ed ) pavement cos t s .

B . Pavement Rela t ionships

1 . Specif ic o r f i n i t e changes i n vo lume of t r a f f i c a re not cons idered i n the de te r ­mina t ion of the pavement s t r u c t u r e .

2 . Because of " i n f i n i t e " des ign, the m a r g i n a l cost of pavement s t r u c t u r e i s p r e ­sumed to be ze ro on p r i m a r y roads . However , l a r g e i n c r e m e n t s of pavement can be ass igned to a l l weight c lasses be low the l e g a l m a x i m u m on p r i m a r y roads .

3. Inc remen t s of pavement s t r u c t u r e cannot be assigned on secondary roads where heavy veh ic l e s appear i n " l i m i t e d " n u m b e r s . I n so fa r as design i s concerned a l l costs on such roads a re c o m m o n cos t s .

4 . The pavement s t r u c t u r e ( b u t not the geomet r i e s ) of a secondary r o a d i s equiva­len t to the pavement s t r u c t u r e of a p r i m a r y road designed f o r the same weight c lass of t r a f f i c .

These r e l a t ionsh ips p r o v i d e the basic ingred ien t s i n the development of a m a r g i n a l cost sys tem of highway f i nance . By r e l a t i n g the sys tem to highway design, the p r o b l e m i s p laced i n an e m p i r i c a l o r appl ied se t t i ng .

C o s t - P r i c e Rela t ionships

The s t a r t i n g po in t i n an ana lys i s of c o s t - p r i c e r e l a t ionsh ips i s the segregat ion of spec ia l pavement co s t . One may assume that t h i s specia l i t e m has been segregated i n ac -cordance w i t h the usua l i n c r e m e n t a l cost p r o c e d u r e . W i t h the e l i m i n a t i o n of spec ia l pave ­ment cost , the s i m p l i f i e d h ighway ne twork under cons ide ra t ion i s d e s i g n e d f o r a s ingle weight c lass of t r a f f i c , al though i t s t i l l cons iders d i f f e r ences i n d imens ions and speeds of v e h i c l e s . The pavement i s designed e i the r to wi ths tand the e lements o r to wi ths tand i n f i n i t e r e p e t i t i o n s o f the f i r s t o r l i gh tes t v e h i c l e c l a s s . W i t h t h i s "bas ic" s t r u c t u r e , t h e l i m i t s wh ich have s ign i f i cance to both design and economic ana lys i s a r e geomet r i c i n na tu re . These geome t r i c r e l a t ionsh ips have a spec ia l s ign i f i cance to highway p r i c i n g .

The m a r g i n a l cost bas i s f o r the a l loca t ion of common o r geomet r i c cost by evalua t ing the i m p a c t on p r a c t i c a l capaci ty was desc r ibed e a r l i e r . A n addi t iona l i n c r e m e n t of t r a f f i c on a f u l l y u t i l i z e d f a c i l i t y d imin i shes i t s p r a c t i c a l capaci ty and r e q u i r e s i m p r o v e -

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ments in the geometric design. Since every vehicle is marginal, marginal cost is the cost of improving the geometric design, that is,.adding capacity. Capacity relation­ships are ideal f o r marginal cost pr ic ing. The elimination of one unit provides capacity f o r a l l other units; the addition of one unit displaces others. Marginal cost of a par­ticular use can be determined by evaluating these displacements.

It appears that data are available f o r establishing prices consistent with the view that has been presented. According to the Highway Capacity Manual (14) : "approxi­mately the same operating conditions w i l l prevail on an expressway through rol l ing terra in when there are 1,500 passenger cars per lane per hour as when there are 115 trucks and 1,040 passenger cars per lane." Thus, 115 trucks displace 460 passenger vehicles. In this particular case, passenger vehicles are responsible f o r about two-thirds (1 ,040/1 , 500) of total common (geometric) cost, while commercial vehicles are responsible for about one-third (460/1, 500). This is an "opportunity cost" basis f o r the determination of marginal cost. The addition of a single commercial vehicle displaces capacity f o r four passenger vehicles. Such ratios are available in the High­way Capacity Manual which lays the foundations f o r the marginal cost pricing of high­way services. In addition to the common costs described above, commercial vehicles w i l l receive an assignment of special pavement cost to be defrayed either through lump sum or use taxes depending on the relationship between pavement thickness and number of repetitions of the axle load.

There are many elements of cost that are not considered in highway design. Thus, design provides almost no empirical basis fo r the allocation of cost of administration and maintenance. However, these costs may be either special or common and they may or may not vary with incremental additions of t r a f f i c . To the extent that these costs do vary with t r a f f i c , they may be added to the marginal costs implied by design c r i t e r i a i n order to a r r ive at a total pr ice to be charged on the basis of use. To the extent that they do not vary with incremental additions to t r a f f i c , marginal cost is zero and "losses" w i l l have to be covered through lump sum taxes.

The relationships described above do not hold when there is a significant amount of under-utilized capacity. In such instances an additional vehicle w i l l have no measurable impact on the practical capacity or design of the highway. However, i t might be held that any increase in t r a f f i c imposes marginal " rea l" costs on other t ra f f ic even if i t does not affect highway design or practical capacity. Since workable distinctions of this sort are d i f f icul t to maintain, the ensuing discussion of secondary road finance adheres to a money cost interpretation.

The determination of marginal money cost on secondary roads which have excess capacity raises dif f icul t problems. An additional vehicle has no impact on highway de­sign, although i t might have some impact on maintenance. In short, marginal cost is fa r below design cost. Although marginal cost would be exceedingly di f f icul t to calcu­late in such situations, adherence to the pricing standard requires that these roads be operated at a "loss". An examination of applied marginal cost pr ic ing proposals re ­veals that the so-called two-part t a r i f f includes a variable or marginal charge based on operating expense (maintenance cost) and a fixed charge based on overhead (19 ) . Strictly speaking, maintenance expense is not a marginal cost. But this seems to be the only interpretation of marginal cost that can be applied realist ically in excess capacity situations. A more satisfactory term f o r this concept is "out-of-pocket" cost. A l l serious attempts at realistic applications of the marginal cost standard rely on the out-of-pocket concept. This is not acceptable under increasing cost situations, but i t probably comes close when there is obvious permanent excess capacity. One now has two crude, but workable, marginal cost standards fo r two types of road. These are summarized below:

1. Program cost (exclusive of special weight cost) represents an approximation to pr imary road marginal cost. If the road is f u l l y uti l ized, this cost may be allocated among vehicles on the basis of the proportion of capacity util ized by each vehicle.

2. Maintenance cost represents an approximation of secondary road marginal cost.

The two standards suggested above determine two extreme points on the traditional marginal cost curve; one f o r a "high" volume road, the other f o r a "low" volume

44

road. Highway financial analysts are not without experience in "smoothing out" or " f i l l i n g i n " the missing l inks. Meanwhile, the discussion is based on the extremes.

I t is necessary now to consider the pricing cr i ter ion to be employed for vehicles which impose special pavement costs. The special weight cost applicable to a given weight class is a common cost with respect to the vehicles in that class and other heavier weight classes. On the assumption that these weight costs do not vary with the number of repetitions of load there is no justification f o r penalizing additional use of these pavement increments. Insofar as the marginal cost standard is concerned, the use of such increments by heavy vehicles should be encouraged through lowprices. (Of course, any encouragement that this might offer fo r increaseduse of the highway may be o f f ­set by the impact of additional heavy vehicles on congestion, that i s , geometric requirements.) Pursuitof a low or zero pricepolicy fo r the pavement component wouldinvolve "losses" due to economical or marginal cost pr ic ing. These losses would be equal to special pavement cost. If the service is to be continued, beyond the design l i fe of such highways, these losses must be recouped. The losses on each increment maybe recoveredfrom the operators of the heavy vehicles requiring such increments, through the use of lump sum charges.

These conclusions concerning pr ic ing fo r special weight increments do not hold if a relationship can be established between number of repetitions of axle loads and pavement cost. If pavement cost is a continuous function of number of repetitions, an additional vehicle w i l l impose additional pavement cost and a price based on use should be em­ployed. It seems possible that a relationship might be established between special weight cost and axle miles. In this event, the axle-mile standard f o r the inter-class allocation of special pavement cost might be appropriate. This appears to be the cur­rent practice. This is an interesting example of the relationship between the state of engineering knowledge and highway pr ic ing. The assumption of " inf in i te" design leads to lump sum taxes while the assumption of "continuous" design leads to prices which vary with use such as axle-mile or ton-mile taxes.

Tentative Price-Administrative Relationships

The usual procedure in establishing the highway user structure involves the calcu­lation of a " b i l l " (cost responsibility) f o r the motoriat. Once cost responsibility is calculated, various taxes and tax rates are adjusted so that this amount is collected f r o m each user. In attempting to administer the system of highway finance without t o l l gates, one may take advantage of any fortuitous relationships that w i l l fur ther his pur­pose. The ensuing discussion suggests two possible price-administrative relationships that do not have as strong a foundation as the design-cost and cost-price relationships. Nevertheless, the relationships that shall be suggested appear to have enough validity to qualify as tentative hypotheses awaiting empirical ver i f icat ion. The two price-ad­ministrative hypotheses are:

1. If there is but one weight class of vehicle, a single price f o r the use of both pr imary and secondary systems is more likely to conform to marginal cost principles than to f u l l or average cost principles, that i s , cost responsibility.

2. Gasoline consumption provides as adequate a measure f o r pr ic ing in accordance with capacity util ized as can be had without the use of to l l gates or elaborate reporting devices.

To evaluate the f i r s t hypothesis one may recall the two pr ic ing c r i t e r ia established in the cost-price section. These are: (a) Marginal cost on the pr imary system is determined by unit program cost, and (b) marginal cost on the secondary system is determined by unit maintenance cost. Unit program cost on the secondary system is considerably above unit program cost on the p r imary system. However, average main­tenance cost on the secondary system is considerably below unit program cost of the secondary system. Thus, unit program cost on the pr imary system may have a closer relationship to unit maintenance cost on the secondary system than to unit program cost on the secondary system. If one translates theoretical cost curves into metaphor, this involves saying that the marginal cost of a small plant operating with excess capacity is l ikely to have a closer relationship to the marginal cost of an optimally operating

45

large plant than the average cost of the small plant has to the average cost of the large plant. This relationship assumes that average cost declines over the range embracing the small and large plants. A graphical demonstration is not necessary to grasp the nature of the relationship between the average and marginal costs of small and large plants operating under conditions which involve a large proportion of f ixed costs. This possible relationship between the two marginal costs provides a means fo r rationalizing the administrative problem. If i t is hypothesized on the basis of the possible relation­ships described above that the two marginal costs are roughly equal, i t follows that a single price can be charged f o r both pr imary and secondary roads m the absence of heavy axle loads.

The second hypothesis is suggested by a proposal set fo r th by Leland James ( 2 0 ) . Although James' figures and theory have been questioned {20), no one appears to have disputed the existence of the gasoline consumption-capacity uti l ized relationship. A comparison of relative gasoline consumption and space occupancy ratios indicates that this relationship might have considerable validi ty. An empirical test is not attempted in this paper, although the design fo r such a test involves no diff icul t ies . In order to demonstrate the possibilities, i t shall be adopted as an hypothesis f o r administrative purposes. In addition to providing another possible tool for marginal cost pricing, gasoline consumption makes possible a significant analytical short-cut. If the relation­ship between gasoline consumption and capacity ut i l ized were "perfect", the common (geometric) cost of pr imary roads would not have to be apportioned directly among vehicles. Af te r special pavement cost is assigned, the task would be completed by establishing a gasoline tax rate such that gasoline tax "earnings" on the pr imary system would cover its common cost. It seems that there is a good possibility of achieving two ends in one maneuver: (a) Establish marginal cost rates and (b) obviate the calculation of total cost responsibility fo r each vehicle. Only special cost responsibility would have be to calculated. Moreover, if marginal pavement cost is presumed to be zero (because of " inf in i te" load bearing capacity), the problem resolves itself into the determination of a gasoline tax and the establishment of a system f o r recovering losses through lump sum taxes.

SUMMARY OF TENTATIVE RELATIONSHIPS

It is now possible to bring the relationships that have been developed into a complete, albeit speculative, system of highway finance and administration. The more important relationships are:

A . Design-Cost Relationships

1. Changes in geometric design create measurable marginal costs. 2. Changes in pavement thickness create special cost. 3. The pavement structure (but not the geometry) of the secondary system is

equivalent to the pavement structure of the f i r s t increment of the p r imary system.

B . Cost-Price Relationships

1. Price should be established at the marginal cost level. 2. Common (geometric) cost may or may not be significant to highway pricing de­

pending on the amount of capacity available, (a) If there is under-utilization, the economic cost of providing additional service is below the design-cost of providing additional capacity. Maintenance cost represraits a reasonable approximation of marginal cost, (b) If there is f u l l util ization the economic cost of providing additional service is at least equal to the design-cost of providing additional capacity. Program cost is a reasonable approximation of marginal cost f o r applied purposes.

3. Marginal cost of special pavement structure may be either zero or some positive quantity depending on the l imi t s of engineering design.

4. Losses due to marginal cost pr ic ing must be recovered f r o m users in the f o r m of lump sum taxes not to exceed the value of service.

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C. Price Administrative 1. If there is but one class of vehicle, a single price charged f o r the use of both

(pr imary and secondary) faci l i t ies is more l ikely to conform to marginal cost standards than to f u l l or average cost standards.

2. Gasoline consumption provides as adequate a measure fo r pricing in accordance with capacity util ized as can be had without the use of to l l gates or elaborate reporting devices.

I t is important to note that the relationships are integrated. Highway design, price theory, and financial administration are now parts of a single model. The three sets of relationships described above may be arranged in whatever manner appears to suit the institutional fabric and may be extended, refined and validated through further re ­search and testing. It is f e l t that they represent a reasonable application of an abstrac­tion, the marginal cost principle, to highway design, highway pricing and highway ad­ministrat ion. In order to demonstrate a possible application of these relationships, a provisional synthesis is offered.

A SYNTHETIC SYSTEM OF HIGHWAY FINANCE

Assume at the outset that special pavement cost, along with the axle loads to which i t applies, i s isolated ( A 2 ) . (Notations refer to the relationships described in the p re -ceeding outline.) Now, the pavements of p r imary and secondary systems are structur­ally equivalent ( A 3 ) . Uniform rates established at the marginal cost of the pr imary system w i l l result roughly in marginal cost prices on the secondary system ( C I ) . Now, set the gasoline tax rate so that "earnings" on the p r imary system cover the common cost of the pr imary system (C2) . The result is approximate marginal cost prices on a l l systems.

Gasoline tax earnings on the p r imary system w i l l cover a l l but special pavement costs of the p r imary system. Gasoline tax earnings on the secondary system may cover maintenance costs but this is not assured. If the pr imary road system is congested, "prof i t s" w i l l be earned at the established gasoline tax rate. If highways are provided under long-run increasing cost conditions, revenue yielded at the established rate may prove inadequate fo r optimal expansion. In this event, (a) the gasoline tax rate w i l l have to be raised or (b) "intolerable" conditions may persist unt i l an adequate surplus is accumulated. If there is persistent excess capacity on the pr imary system, losses w i l l occur and the plant must be contracted. Secondary roads w i l l incur losses because of permanent excess capacity. The amount of secondary road losses w i l l be the d i f f e r ­ence between secondary road program cost and secondary road gasoline tax earnings. Such losses w i l l be large or small depending on the amount of excess capacity. Where marginal cost i s lowest, the losses w i l l be greatest.

Regardless of the specific conditions under which they arise, losses due to conform­ance with the marginal cost standard call fo r lump sum taxes levied on the user. These taxes cannot exceed value-of-service or the direct benefits accruing to the user. A l ­though any lump sum tax may qualify f o r this purpose, license taxes are indicated. Their imposition would not interfere greatly with use and they cannot exceed value of service because they are voluntarily purchased. Since p r imary roads tend to operate under optimal or congested conditions, losses w i l l be incurred on secondary roads where excess capacity is prevalent. Therefore, the license tax on light vehicles may be re ­served f o r secondary road purposes.

Special pavement costs must now be considered. In this simplif ied system, such costs are incurred on the p r imary system. The current state of engineering knowledge indicates that the marginal cost of pavement is either zero or some positive quantity. If marginal pavement cost is presumed to be zero, additional lump sum taxes may be imposed on appropriate vehicle weight classes. If marginal pavement cost is positive, axle-mile or other third-structure taxes may be indicated. I t is possible that a com­bination of lump sum and th i rd structure taxes may be required. To a large extent a specific solution to this problem depends on the state of engineering knowledge and on administrative and jurisdictional considerations. To summarize this synthetic system:

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Pr imary road finance relies on gasoline taxes levied on the assumption that a l l vehicles are of the lowest weight class and on lump sum and/or third-structure taxes designed to recover special pavement cost imposed by heavier vehicles. Secondary road finance relies on gasoline tax earnings fo r a l l or a portion of maintenance expense and on local license taxes on light vehicles in order to recover the balance.

SOME SPECULATIONS RELATIVE TO HIGHWAY FINANQAL POLICY

Assuming that the basic relationships on which the model rests bear the scrutiny of students and administrators, i t is interesting to consider some of the possible impl ica­tions to public policy. If the direct benefits to users exceed the cost of the highway pro­gram, a "user pay a l l " policy can be established. Surpluses, rents and other windfalls may be considered by those responsible f o r justice or equity in the tax system as a whole. However, as a practical matter the highway analyst may have to make the value judgment concerning the appropriation and disposition of these surpluses. If the direct benefits accruing to users do not exceed the cost of a given program, payments establish­ed on the basis of the foregoing principles w i l l not cover cost. This does not imply that the highway system is overexpanded. However, the highway program w i l l have to be r e ­viewed in the light of the indirect benefits which may have played a role in the investment decision, but which have not yet played a role in the financial structure. Appropriate non-user taxes to cover the "losses" due to "social" expansion of the plant may be de­termined in accordance with the theory of joint demand presented at an earlier point. An appropriately determined non-user share results in an adjustment of user taxes to a level below marginal cost. To economic theorists this represents the adjustment for "external economies" or social value. In this wr i te r ' s opinion this adjustment would be minimal .

The motorist or truck operator probably w i l l pay a higher price because the bulk of the present non-user share has been eliminated. However, the non-user funds released would be available to finance other governmental programs of a more "general" nature. It is possible that the present non-user share which is devoted p r imar i l y to secondary roads w i l l be roughly equivalent to any increase in gasoline or license tax revenue for secondary road purposes. Secondary road users might simply trade one f o r m of tax f o r another. This study may lead only to a rearrangement of administrative relation­ships, especially those having to do with the jurisdictional distribution of centrally collected funds. The validity of such a rearrangement ultimately rests on factors other than those with which this paper is concerned. On the other hand, i f the present non-user share has led, on one way or another, to a distortion of the pr imary or commercial rate structure, there is a possibility that the present allocation of resources is i n e f f i ­cient. This raises again the questions of the proper level of commercial truck rates and the propriety of uti l izing rents, windfalls, and surpluses f o r highway purposes. Because such surpluses appear to have been restr icted to secondary road finance, i t i s l ike ly that the impact on the commercial rate structure may have been minimal .

Although some exceptions have been made to the analyses, procedures and techniques that are employed in the establishment of the highway user tax structure, i t appears that the highway user tax structure has survived and remains a powerful tool f o r the attain­ment of economic efficiency. I t is reasonable to agree with Zettel (_4) that: "When we consider that user taxation was conceived in expediency, born of necessity and nurtured of poli t ics, i t is surprising that the offspring is as healthy and works as well as i t does to serve sound economic objectives. " The chief concern, however, is not with the de­cisions that have been made in the past, but with those that are about to be made f o r the fu ture . A vastly expanded Federal Highway Program has been inaugurated. The means f o r the financing of this program are s t i l l tentative. The Congress and students of high­way problems are now awaiting completion of studies undertaken by the Bureau of Public Roads. This w i l l represent the th i rd federal study of highway problems, and like the Coordinator's Report, probably w i l l establish a nation-wide pattern for a host of state and local investigations. The concressional request f o r investigation and research is broad enough to allow f o r either a benefits-received or pricing approach to highway prob­lems. If one reads between the lines of the F i r s t Progress Report of the Bureau of Public

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Roads, i t is possible to distinguish some disenchantment with the benefits-received approach and a renewed interest in economic efficiency. The decisions now being made w i l l have an important bearing on the possibilities for the attainment of economic efficiency in the highway user tax structure.

REFERENCES

1. Reder, Melvin A . , "Studies in the Theory of vVelfare Economics." New York: Columbia University Press, 1947, p . 35.

2. Brownlee, O . H . , and Heller, Walter W. , "Highway Development and Financing." American Economic Review, Proceedii^s, X L V I (May, 1956) pp. 232-51.

3. Groves, Harold M . , in Brownlee, O. H.,and Heller, Walter W. , ibid, pp. 251-2. Ross, Wil l iam D . , in Brownlee, O . H . , and Heller, Walter W. , ibid, pp. 258-9.

4. Zettel, Richard A . , "Objectives and Concepts of Highway-User Taxation." HRB Bu l l . 92, Highway User Taxation, Washington: 1954, pp. 7,14.

5. Wallace, Donald H . , "Joint and Overhead Cost and Railway Rate Pol icy ." Quarterly Journal of Economics, X L V I H (August, 1934)pp. 583-619,

6. Stigier, George, "The Theory of P r i ce . " New York: The Macmillan Company, (1947) p . 91 .

7. Bowen, H . D . , "The Interpretation of Voting in the Allocation of Resources." Quarterly Journal of Economics, L V I I I (Nov. 1943), pp. 27-43.

8. Samuelson, Paul A . , "Diagrammatic Exposition of a Theory of Public Expen­d i tu re . " Review of Economic Statistics, XXXVII (Nov. , 1955), pp. 350-56.

9. Samuelson, Paul A . , "Foundations of Economic Analys is ." Cambridge: Harvard University Press, (1948), p . 241.

10. Buchanan, James E., "Pricing of Highway Services." National Tax Journal, V (June, 1952), pp. 97-107.

11. Hotelling, Harold. , "The General Welfare in Relation to Problems of Taxation and of Railway and Uti l i ty Rates." Econometrica, V I (July, 1938), pp. 242-69.

12. Troxel , C. Emery. , "Economics of Transport ." New York: Rinehart & Co., Inc. , (1956).

13. Lerner, Abba P. , "Statics and Dynamics in Socialist Economics." Economic Journal X L V I I (June, 1937), p . 250-70.

14. Bureau of Public Roads, "Highway Capacity Manual." Washington, (1950),-p . 57.

15. Ruggles, Nancy., "The Welfare Basis of the Marginal Cost Pricing Pr inc ip le ." Review of Economic Studies, Vo l . X V I I (1949-50) pp. 24-46.

16. Lewis, W . A . , "The Two Part T a r i f f . " Economica, VIE (1941), pp. 249-70. 17. Baker, Robert F . , and Karrer , Emmett H . , "A Study of the Relationship of

Pavement Cost to Vehicle Weight." Columbus, Ohio: The Ohio State University Experiment Station, (1956).

18. Pancoast, D . F . , "Allocation of Highway Costs in Ohio." Report prepared for Ohio Department of Highways in cooperation with the Bureau of Public Roads, Ohio Department of Highways, Columbus, (1953).

19. Coase, R. H . , "The Marginal Cost Controversy." Economica, X I I I (August 1946), pp. 173-4.

20. Bureau of Public Roads, "A Factual Discussion of Motortruck Operation Regulation and Taxation." Washington, (1951).

Use of Economic Criteria for Highway Investment Planning

TILLO E. KUHN, Economic Policy Division, Department of Transport, Ottawa, Ontario, Canada

# ROAD AND bridge building—one of the finest manifestations of man's ingenuity and peaceful, constructive endeavour—is team work par excellence. It represents a most complex productive effort , extending f r o m the gathering of the basic data through the survey and planning work right to the payment of the f ina l b i l l and to the settlement of the last legal c la im. In this process use is continually being made of a great many ex­perts in different f ields: of surveyors, draftsmen, location and soils engineers; of h i j h ly skilled specialists in the various construction phases; of t r a f f i c and safety ex­perts; of appraisers; statisticians, geographers, planners, financial and legal talent; above a l l of decision-makers throughout.

What part can economic analysis play in this process? This paper attempts to ap­praise cr i t ica l ly some of the basic economic assumptions, ideas, and working techni­ques which might be used in this intriguing sphere of highway planning and finance. To maintain logical continuity, the discussion follows decision-making in investment plan­ning, step by step, f r o m broad, general issues down to detailed technical problems.

BASIS OF INVESTMENT DECISIONS

A private entrepreneur's decision to invest in a factory of other productive asset w i l l arise f r o m the expectation that such investment w i l l prove profitable. The busi­ness man w i l l carry out the new venture when the anticipated returns f r o m the invest­ment are at least equal to the costs of borrowing the necessary money. Hence, the i n ­centive to a l l private investment arises f r o m a l l business men's assessment of the prof i tabi l i ty of investment related to the rate of interest on money f o r investment.

Keynes (_1) called the expected prof i tabi l i ty of new investment the "marginal e f f i ­ciency of capi ta l ." In this connection "marginal" refers to the returns f r o m producing one more capital asset (the marginal one). Logically, the entrepreneur or promoter, confronted with a whole range of possible new projects, w i l l choose the one which can be expected to yield the highest rate of return over cost. Therefore, the marginal efficiency of capital w i l l denote, at any given moment of time, the highest net rate of return f r o m the most promising of a l l projects to be found in the entire economy. In ordinary language i t might be called the expected annual prof i t rate on the most promis­ing of a l l real investments.

It i s , f i r s t l y , important to appreciate the dynamic nature of Keynes' concept of mar­ginal efficiency of capital and the way in which i t provides a link between the present and the future . Many entrepreneurs and potential promoters of capital investment schemes w i l l simultaneously turn their attention to a great variety of ventures. They w i l l , by market research, forecasts or by sheer guess-work, t ry to foresee the future and the performance of the projects under consideration. They w i l l reject ventures which show a combination of high r isk, slow maturing and low returns, in favour of those with the opposite characteristics. In interaction, each entrepreneur individually and a l l of them collectively w i l l therefore in effect establish a system of project p r i o r ­ities at any given t ime, with the most profitable venture taking top place and a l l the others b e i i ^ ranked according to their mer i ts . Investment funds w i l l then be borrowed and the projects carr ied out unt i l the expected rate of p rof i t f r o m the least profitable scheme equals the rate of interest at which capital can be attracted. In equilibrium, the marginal efficiency of capital, expressed in percent per year, w i l l be equal to the rate of interest on money.

I t is important, secondly, also to note the inherent tendency to self-adjustment of this process. The business promoters w i l l compete, as i t were, fo r a necessarily l imited number of feasible new projects. The supply of worthwhile ventures at any

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50

time depends on a great variety of technological and environmental factors: fo r ex­ample growth of population and markets, the rate of technical progress and innovation, trends in income, employment and purchasing power. As over time more and more new projects are realized there w i l l be a tendency fo r the marginal efficiency of capital to decline; but then growth and technological progress may again provide better invest­ment opportunities and hence raise the schedule f o r the marginal efficiency of capital. On the whole, however, the marginal efficiency of capital w i l l adjust downward to the money rate of interest, itself determined by factors which need not enter into discussion at the moment.

Thirdly, i t is important to appreciate the monopolistic nature of the investment plan­ning process. Whatever project the entrepreneur contemplates, i t must be something which his competitors cannot emulate, at least not fo r the time being. Hie venture may involve the introduction of an entirely new commodity or service, in which case the en­trepreneur w i l l attempt to protect his monopolistic position by patents "and commercial strategy. If the product or service sponsored by h im is not entirely novel, he w i l l at least endeavour to create a 'mental' monopoly, by advertising, introduction of a brand name and so on. In addition he w i l l attempt to build spatial or functional monopolies, by seeking government protection and licensing, supply and sales franchises and ex­clusive rights within a t e r r i to ry , or by oligopolistic maneuvers.

The ne tp rof i t s that accrue to the entrepreneur or his f i r m are the result of many heterogenebus factors: gains f r o m risk-taking and uncertainty-bearing; the presence of a favourable market and technological environment; outstanding managerial and organizational ability; and perhaps a good deal of luck, bearing in mind Goethe's maxim that only the able enjoy consistent luck. But always there w i l l be a strong element of monopoly present in the process which determines investment and, in interaction with the rate of interest, the marginal efficiency of capital.

PLANNING OF INDIVIDUAL PROJECTS

A synthesis of the general investment process with the planning of individual projects must now be attempted. In other words, i t remains now to describe how a l i s t of worth­while projects might be drawn up and how the profi tabi l i ty and performance of each one of them might be judged.

Basically, the prospective entrepreneur w i l l select f r o m equally risky alternative ventures, fo r f i r s t consideration, the one with the highest potential net yield. Similarly, he w i l l prefer the least r isky one of a number of ventures which promise to yield iden­t ical returns over t ime. This implies that he has knowledge of net returns (that is , gross revenues less costs) over the planning period f o r a number of ventures.

How can the most profitable combination of price, cost and output for an individual project be achieved? This problem, demonstrated in Figure 1, resolves itself into the process of maximizing the difference between total gross revenues and total costs, in other words maximizing net revenues; if that position is reached then the most advan­tageous outputs (quantities of goods or services) are also being produced.

On the revenue side, fundamentally, one w i l l have to assume the presence of one very important aspect of monopolistic market strategy: "price discrimination, " also called "charging what the t ra f f ic w i l l bear, " or euphemistically, "differential pr ic ing, " the te rm preferred by A . M . Milne (2) in his excellent textbook on transport economics.

Assuming that this can be done, through market analysis, motivation research or experimentation, the entrepreneur w i l l attempt to assess the potential maximum bene­f i t s derived by each user or group of users f r o m the consumption of the new product, and the total quantities of this product provided cumulatively at each point. These ben­efits can at the same time be taken to represent the maximum differential charges which can be extracted f r o m each user, as long as the basic condition "benefits offered are at least equal to prices charged, " is satisfied.

Curve DBM in Figure 1 represents such an assessment of marginal differential ben­efits and prices charged. It shows that gross revenues w i l l be maximized i f total quantities OM of goods or services are supplied and charges identical to the ordinate values of the benefit (marginal revenue) curve DBM are imposed. Total gross re -

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venue—which is the integral of the demand function—will tend to become equal to the area under the arc DBM as the number of users approaches inf in i ty .

Is Perfectly Different ial Pr icing Permissible?

Gross revenues are charges multiplied by quantities; in this case the sum of an i n ­f ini te number of rectangles, each of a height corresponding to pr ice charged and with an infinitesimally small base representing quantity consumed ( F i g . 1 ) . It is sometimes argued that such a rate policy, with infinitely small variations of prices charged, would not only be unethical, but also at least impractical . The latter contention may be true

MARGINAL COSTS a I REVENUES

MARGINAL REVENUE (BENEFIT) CURVE

EARNINGS

Fxgure 1

QUANTITIES OF GOODS a SERVICES

and in the real world i t may be more convenient to let rates go down in definite "steps". As a matter of fact, many electric power companies employ rate structures that go down in such steps after certain quantities of consumption are exceeded. But this does not in the least detract f r o m the validity of the revenue maximization formula . The same electric power companies would not hesitate to apply i t , were i t not for the fact that the extra revenues thus obtained would be more than offset by the additional ad­ministrative and organizational expenses of a perfectly variable t a r i f f system. Analyt­ical ly, one might accommodate this phenomenon by calculating gross revenues net of collection costs. Diagrammatically then a whole series of marginal gross revenue curves would be obtained, one f o r each pricing system adopted, consisting of a series of "steps" and in the extreme case consisting of a straight l ine. The one marginal re­venue curve which encloses the largest gross revenue area—and hence the one with the greatest number of steps—will represent the best solution.

Very l i t t l e remains of the other arguments against differential pricing once the moral and emotional disguises have been removed. Of course a l l economic l i fe i s ruled by the supreme rule of "charging what the t ra f f ic w i l l bear." It is applied with great vigour on as many occasions as possible by a l l sellers of goods and services. Whenever feasi­ble i t is presented as a price reduction and advertised as "quantity discount, " "loyalty discount, " "off-peak inducement t o l l " and the l ike . Another method would be to vary service qualities, including differ ing treatment in the granting of credit fac i l i t ies , while holding direct money prices constant.

Only because generations of economists have been brought up on the quite unrealistic assumptions of pure and perfect competition have wr fome to regard the uniform market

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price, set at the marginal cost level, as the rule rather than the exception. Partly this has been due, as Schumpeter (_3) points out, " . . .to the specific bias of the eco­nomic theorist that has nothing to do with poli t ical preference, the bias f o r easily man­ageable patterns." One learns slowly that the so-called imperfections, the monopolies, duopolies, oligopolies, are all-prevasive, that advertising, control of entry, licensing, government regulation, brandnames, special service features, credit terms, even such market strategy as the opening of a re ta i l store in a part icular ly favoured location, are a l l very logical attempts to create l i t t l e economic "niches" which are sheltered f r o m the ch i l l winds blowing across the desolate market place of pure and perfect competition.

It is very important f o r the subsequent discussion of specific highway problems to accept the principle of differential pr ic ing (which is really the same as differential benefit assessment), at least as an investment planning tool . A quotation f r o m Milne may give this principle of discriminatory pr icing, which is so part icularly important in the f i e ld of transport economics, some fur ther theoretical respectability: "The phrase 'charging what the t r a f f i c w i l l bear' can assume two meanings. F i r s t i t may mean that prices are to be fixed in such a way that in respect of each t ra f f i c carr ied the maximum revenue is obtained regardless of the particular costs involved. In ac­cordance with this interpretation of the principle no t r a f f i c should be charged a lower rate or fare when i t w i l l bear a higher rate or fa re . The second meaning of the phrase —the meaning which is relevant to our discussion.. . —can be more conveniently couched in negative terms and can be expressed in the f o r m that no t r a f f i c should be charged a price which i t w i l l not bear when, at a lower price, the t r a f f i c would be prepared to move. When interpreted in this second way the principle may promote a greater u t i l i ­zation of indivisible and f ixed resources and may thereby permit indivisible and fixed costs to be spread over a larger volume of t r a f f i c . In this way the practice of dis­criminatory pr ic ing may confer economic benefit, a benefit represented by the fact that transport rates and fares are rendered lower than they would be in the absence of discriminatory pr ic ing (3) ."

Further proof how economies can be brought about by differential pr ic ing w i l l be provided in the following sections. (Judging f r o m information contained in studies by Owen and Dearing {i), Dearing (_5), Duzan (6) and others, t o l l roads in the United States appear to apply differential pr ic ing. This point is pursued in detail by Ruhn (_7), Chapter IV " T o l l Road Model -F ina l Consideration.")

Cost Analysis and Output Determination

By contrast f r o m the marginal benefit (and differential price) curve DBM in Figure 1, the marginal cost curve ABN requires only brief explanations. Due to the amazing interest taken in the United States in marginal cost pricing (or incremental cost charg­ing) of highway services and the great volume of l i terature produced on the subject, l i t t l e needs to be said on the topic.

No significance should be attached to the way the marginal cost curve ABN is drawn in Figure 1; i t is assumed here that marginal costs of providing the f i r s t few quantities of goods or services are relatively high and that they then f a l l as economies of scale are reaped or in i t ia l f ixed costs are spread over a greater number of production units. For purposes of i l lustrat ion i t is fur ther assumed that at very large output quantities marginal costs rise again, due to diseconomies of scale, the bidding up of factor prices and so on. Neglecting indivisibi l i t ies of factors of production—(This is a somewhat unrealistic assumption, but the main line of reasoning presented here does not depend on i t . The theoretical problems posed by indivisibil i t ies of factors of production, f ixed and variable costs, etc. can be resolved f a i r l y easily (8).) —and thus implying that i n f i n ­i tely small additions to output requiring infinitely small incremental cost doses are possible—a smooth marginal cost curve w i l l be obtained.

The most advantageous output to be produced and consumed, f r o m the entrepreneur's point of view, w i l l be determined by the intersection of the marginal cost and revenue curves (at point B in Figure 1) and w i l l be quantity OC. Marginal costs associated with the production of the different quantities of output are identical to the ordinate values of the marginal cost curve. Total costs w i l l tend to become equal to the area

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OABC under the curve AB as the number of goods or services supplied approaches i n ­f in i t y .

If the cost and revenue conditions depicted in Figure 1 prevai l , the entrepreneur w i l l choose to supply OC quantities of goods or services, since he cannot increase his net earinings by supplying any other quantities of output. At output level OC the extra cost of supplying the additional last, very small increase in quantity of goods or ser­vices, is equal to the benefit enjoyed by the additional user of that last unit of output. Since under a regime of "charging what the t r a f f i c w i l l bear" pr ice equals benefits, i t follows that at output OC the marginal cost of supplying the last unit is equal to marginal benefit derived f r o m that unit, and hence to pr ice .

If this is so, then the optimum position f r o m the entrepreneur's point of view has been reached. If he were to increase his output to (say) OF, the costs incurred by him in order to supply the quantity increment CF would be equivalent to the area CBHF. At the same time additional benefits conferred upon users, and hence charges collected would only be equivalent to CBGF. The loss to the entrepreneur of supplying additional quantities CF would therefore be equal to the area of the curvilinear triangle BHG.

Similarly, i f he were to decrease his output by (say) quantity CI he would stand to lose. At output OI the marginal cost of supplying the last unit would be only IK, but benefits conferred would be as much as I L . At output OI his total net earnings would only be equivalent to the area A D L K . Compared with the optimum output OC, deter­mined by the intersection of the marginal cost and marginal revenue curves, the entre­preneur would therefore lose net earnings equivalent to the area of the curvilinear triangle L K B .

While output OC is the optimum one f r o m the entrepreneur's point of view, is i t also a logical one as fa r as the users are concerned? K OC units of goods or services are being offered and consumed no user could possibly be worse off than p r io r to the operation of the new factory or fac i l i ty , since benefits w i l l be equal to charges. Users are not compelled to buy the new goods or services and their choice is a purely volun­tary one. They cannot be 'overcharged' since the slightest over-a l l increase of the rate schedule over and above the maximum level of the benefit schedule would presumably induce them a l l to r e f ra in f r o m the purchase of the goods and services offered.

Is output OC the optimum one f r o m the community's point of view? W i l l adoption by the entrepreneur of the particular production and investment plans associated with out­put OC lead to the best allocation of scarce resources within the economy as a whole?

It might be argued f r o m a social or community point of view that the entrepreneur, by pursuing ruthless "charge what the t r a f f i c w i l l bear" practices, w i l l be reapi i^ ex­cessive monopolistic prof i t s to the detriment of the public. It might be said that the entrepreneur would actually be "underproducing" and hence "under-employing" p ro ­ductive resources, since at outputs larger than OC his total gross revenues would s t i l l exceed total costs, and consequently net revenues would s t i l l be accruing to h im . For example, he might be compelled by government decree to operate, in the public interest, at output level OM in order to satisfy a l l demands f o r the proposed goods and services. True, in that case quantities OC to OM would be provided at a loss equivalent to area BMN (the difference between cost area CBNM and benefit-marginal revenues area CBM) . But the loss sustained by providing these additional units of production would be more than offset by the excessive prof i ts (equivalent to area ADD) made on the preceding units of output. In other words, i t might be argued that thr entrepreneur would s t i l l be in business as long as the potential loss f r o m providing services to the community at less than cost (area BMN in Figure 1, f o r instance), wis smaller than the net earnings extracted at lower output levels (area A D B ) .

This line of reasoning, within the framework of the prr sent analysis, must be re ­jected absolutely. It is most misleading since i t introduces different c r i te r ia , such as income distribution desiderata, monopoly pricing and control problems which were de­liberately not brought into the discussion at this stage. The line of reasoning is p r i ­mar i ly directed at the implications and consequences of a regime of "charging what the t r a f f i c w i l l bear." I t seeks to attack the fact that a potential consumers' surplus (area ADB in Figure 1) is priced away and is turned into a producers' surplus. The argument in the preceding paragraph is thus concerned with the alleged "excessive" size of net earnings or the "unreasonably high" rate of p rof i t accruing to the entrepreneur.

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Desirability of Investment Decision It i s important at this point in the analysis to obtain a reliable answer to the question

whether or not the entrepreneur or entrepreneurs w i l l plan the investment of productive resources in the most efficient and socially most worthwhile way. I t may help to b r ie f ly recapitulate the conclusions previously arr ived at:

1. In an economy where there is freedom of investment planning, entrepreneurs w i l l promote projects which promise returns in excess of the rate of interest on money for investment. Since ventures which show the highest relative returns at equal r i sk w i l l logically be selected f i r s t , an order of project pr ior i t ies based on expected p ro ­f i tabi l i t ies w i l l be established.

2. niis process is continuous and self-adjusting. The entrepreneurs w i l l be 'com­peting' fo r the necessarily l imited number of investment opportunities, the 'supply' of which is determined by technical innovation and progress, the extent of the market, population and income growth, geographical expansion, etc. The marginal efficiency of capital—the expected rate of return f r o m producing the most promising additional capital asset at any one t ime—will have a tendency to decline. There w i l l be no more investment once the marginal efficiency of capital fa l l s to the level of the prevailing interest rate.

3. For purposes of project selection entrepreneurs w i l l carry out demand and cost studies f o r a l l proposed ventures. Different ial charging, made possible by the mono­polistic characteristics inherent in the situation, w i l l be applied whenever practicable. Thus gross revenues w i l l be determined by the maximum charges which can be extracted f r o m the purchasers of various output quantities. Then costs associated with the v a r i ­ous output levels w i l l be ascertained.

4. The output at which marginal costs exactly equal marginal revenues (themselves equal to the benefits conferred upon the user of the marginal unit of goods or services) w i l l be the most profitable one f r o m the entrepreneur's point of view. At this point the expected net revenues (that is , the difference between gross revenues and costs) f r o m the proposed project w i l l be maximized.

Once these prel iminary steps have been completed each entrepreneur individually and a l l entrepreneurs collectively w i l l have compiled l is ts of profitable ventures. These w i l l be arranged in order of logical p r ior i t i es , for example by relating net revenues either to capital investment, or to total costs. (A good discussion of highway p r io r i ty calculations and appropriate arithmetical methods is contained in a paper by van Gl in -stra Bleeker {9).) Entrepreneurs w i l l select the projects with the highest p r io r i ty ra t ­ing, that is , those promising to yield the highest (marginal) efficiency of capital, f o r most immediate implementation. Projects f r o m which lower returns are expected w i l l be carr ied out subsequently unt i l f inal ly the marginal efficiency of capital invested in new ventures w i l l have been brought down to the rate of interest on investment money.

Thus in the sequence of events as described, investment w i l l not lead to high prof i t s , but rather high prof i t expectations w i l l induce investment and this in turn w i l l , in the long run, cause realized prof i ts to f a l l . The so-called "unreasonably high rate of p ro ­f i t s " i s , therefore, in the planning stage, nothing but an indication that exceptionally good investment opportunities exist within the economy.

It is certainly most desirable f r o m the community's point of view that entrepreneurs should invest in those projects, and select those particular output levels, which promise to yield the greatest benefits relative to costs. For the economy as a whole aggregate investments w i l l then also produce maximum benefits relative to costs; thus the de­sired objective fo r the allocation of scarce resources fo r productive purposes w i l l be fu l ly met.

PRIVATE VERSUS PUBLIC INVESTMENT ACTIVITIES

Having established the economics of the purely private investment process, i t now remains to introduce investment activities of the State. Two problems arise: not only must public investment planning per se be analysed, but the conflicting desires of p r i ­vate and public agencies in allocating scarce resources to promising capital investment projects must be reconciled.

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To deal with the latter problem f i r s t , one can very crudely state that the most e f f i ­cient allocation of investment resources w i l l be achieved when a l l projects—regardless of their private or public characteristics—are assessed on their meri ts in the same way and are carried out in order of expected rates of net return. In other words, public projects should compete, as i t were, on equal terms with private ones and logical p r i ­ori t ies for a l l of them should be based on the expected efficiencies of capital for the various ventures.

Such an approach, although useful as a starting point, represents gross over -s impl i ­fications. I t ignores the institutional setting and behaviour of private and public agen­cies and unrealistically-implies either the complete planning of a l l mvestment by the State, or the voluntary and successful adoption of private enterprise behaviour by public authorities. I t further presumes that the returns f r o m a public investment project can be measured and compared directly with those f r o m a private venture—again an entirely untested condition.

The problem of the proper delimitation of private and public spheres of influence in economic l i f e is perhaps one of the most pressing at the present time and should cer­tainly receive more attention in economic research than in the past. ( I t should be noted that recently an expansion of the supply of public goods and services, rather than of private ones, has been advocated by Galbraith (10) and others. It is argued that in North America man is approaching the l imi t s of physiological needs, that the greatest gains in standards of l i v i i ^ can be made in the area of things consumed in common and that therefore the wealth-producing machinery of the modern economy should be used increasingly fo r the provision of needed social faci l i t ies and services.) It is impossible, within the l imi ted scope of this paper, to do the question justice. At the same t ime, as w i l l be shown in the next section, highway provision clearly is a proper function of pub­lic authorities, and therefore an attempt must be made to at least sketch the basic theoretical f ramework. Since, except fo r the technical features, there is nothing special about highways f r o m the economic theory point of view, the following remarks generally pertain to ^Vhat might be called "the economics of public works" and apply with equal force to the planning of investment in public airports , docks and harbours, sewage systems, water works and the l ike .

It is self-evident that society as a whole cannot at any time use up—whether by cur­rent consumption or by capital investment—more goods and services than the economy produces; in effect, for the entire economy, output and income must be equal. At any given level of employment total income is necessarily equal to incomes created by p ro ­duction of investment goods and services plus incomes created by the production of con­sumers goods and services. Investment is total current output less output of consump­tion goods. Similarly, savings are total aggregate income less consumption expendi­tures. Therefore investment must be equal to savings, because both are in turn equal to output ( = income) less consumption.

As Keynes shows, investment has a key role in the economic process. If investment fa l l s short of savings then there w i l l be a reduction in output and a f a l l in employment unt i l , with lower savings put aside f r o m lower incomes, aggregate investment again equals aggregate savi i^s . Conversely, i f investment increases, then income w i l l i n ­crease unti l savings out of the higher incomes w i l l once more be equal to higher i n ­vestments. It is usually assumed that the volume of aggregate savings is a f a i r l y pre­dictable and stable function of national income. Investment, on the other hand, because i t requires predictions about the unknown future and is based on such dynamic factors as the state of business confidence, population growth, technical progress, etc., is autonomous and subject to violent, erratic fluctuations.

Most governments are now dedicated to policies of f u l l employment. To individual enterprise wage payments are just l ike ordinary variable costs which do not have to be met once there is no employment. To society as a whole, on the other hand, payments to labour—either in f o r m of wages or welfare support—go on regardless of the degree of employment and they are therefore really like unavoidable f ixed costs. If so, the argument goes, i t is better to let workers contribute to national income by productive employment, than to let them be idle. Or, more concisely, i t is argued that the mar­ginal cost to the economy of employing otherwise idle labour is zero or almost zero.

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In addition there are, of course, many humanitarian, poli t ical and social reasons f o r pursuing the economic objective of f u l l employment.

From the foregoing discussion i t w i l l have become clear that there is a fundamental difference between private and public investment planning: as private investment auton­omously and errat ical ly moves up and down, the State (provided the bureaucratic appa­ratus is in possession of the facts) w i l l normally attempt to adjust i ts own public works programs in such a way that f u l l employment is attained. Thus, as private invest­ment goes down, public investment w i l l normally be increased, and conversely. This process can be f a i r l y well accommodated within our earlier concept of a mixed p r io r i t y l i s t of worthwhile private and public investment projects: as through a decline in the businessmen's confidence and promotional fervour, etc., more and more private ventures drop out, the opportunities f o r the realization of public projects w i l l become greater. "Diis i s , of course, the idea behind the so-called 'shelf of public works'—quite a sound one whatever the practical drawbacks of this device may be. The l imi t ing cases, at f u l l employment, w i l l be a l l public and no private investment, or, at the other extreme, only private and no public investment at a l l . But normally, in a f ree society, bothforms of investment w i l l be represented in varying degrees and this brings with i t a l l the com­plications of a mixed system.

Great diff icul t ies of measurement arise when one begins to compare the net returns f r o m a public investment with those of a private project . How could one ever hope to assess in identical units of measurement the social returns f r o m , f o r example, a new court house and f r o m a new steel plant? In the latter case money net returns, based on money gross revenues less money costs at the optimum output level, w i l l be the appropriate index. But although the costs of constructing the court house can be stated in money, i t would be very d i f f icu l t to direct ly translate the social advantages flowing f r o m the administration of justice and the maintenance of law and order into dollars and cents.

Conceptually the steel plant and the court house are poles apart, but very serious efforts should be made to reduce the analytical gap between them. From the entire community's point of view i t would be advisable to broaden the very narrow cost and revenue concepts used in the steel plant planning process, by including social costs (those which the entrepreneur escapes and imposes on the community at large, that i s , smoke and noise nuisance, deterioration of a residential neighborhood, e t c . ) . Similarly, some ways and means might be found to calculate more accurately the true returns f r o m social investments. Usually l i t t l e analytical difference is foimd between private and public investment planning in the f ie ld of transportation and this may be part icularly true of highway provision. (An analytical t o l l road 'model ' , discussed in Chapters I I , ni and IV by Ruhn (_7) can be used to demonstrate the great s imilar i t ies between private and public highway investment planning, provided the to l l road entrepreneur has a wide enough planning horizon and the highway authority is a c t i i ^ eff icient ly.) In this way, by empirical and theoretical research, social and private planning c r i te r ia might even­tually be made more compatible thus leading to a more efficient allocation of scarce resources.

There s t i l l exist diff icul t ies on the money (o r resources) supply side of investment planning. I t was shown earlier that private investment w i l l normally continue unt i l the marginal efficiency of capital declines to the interest rate level. In terms of Keynesian economics, the interest rate is determined by "liquidity preference" (the desire of people to hold cash fo r a number of motives, rather than to tie i t up in investments) and the amount of money. Since the amoimt of money is set by the monetary authorities and normally cannot be influenced by private enterprise forces, the rate of interest becomes a price or reward for the "not-hoarding" of cash and equates the demand f o r ready money with the supply.

The circumstances are quite different in the case of public bodies. In the f i r s t place they can and do expand or contract the amount of money by printing bank notes or by withdrawing them f r o m circulation. Secondly, the State can by taxation simply withdraw f r o m the private sector funds which would have been used f o r consumption or investment. I t can then, thirdly, either increase or decrease i ts own ordinary or capital spending, frequently without balancing tax receipts and government disbursements.

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Consequently, whereas private enterprise is subject to money market forces in i ts investment planning, the State does not experience automatic checks and controls to the same extent. As an over-a l l policy, as was mentioned before, the objective of f u l l employment w i l l normally be pursued. However, even so the freedom of action of the State within those given terms of reference are very great; thus during a recession taxes might be reduced, or government spending be increased, or the amount of money be enlarged, or these methods be used joint ly with differ ing emphasis.

In the last analysis reliance has to be put on a blend of poli t ical and economic forces to bring about rational solutions in this very complex f ie ld of public finance. The an­guish of the taxpayers f e l t when remitt ing money to the income tax department—some­how collectively expressed—may be just as effective a force as the "liquidity prefer ­ence" of private individuals i n the Keynesian model of the economy. The desire to avoid large budget deficits and/or inflationary price trends w i l l also constitute power­f u l restraints to State action. Efficiency of government operations and spendii^, f i n a l ­ly , may best be promoted by vigilant parliamentary control, by informed c r i t i c i sm and by the evolution of better economic, planning, statistical and accounting tools. A use­f u l f i r s t step in the right direction would be f o r government departments to show ex­pected net social and money returns fo r each major public investment project that lends itself to such analysis. Only those ventures which show anticipated net returns in ex­cess of the p r eva i l i i ^ rate of interest should be considered f o r implementation.

THE ECONOMIC PROBLEMS OF PUBLIC HIGHWAYS

The general investment process, both in the public and the private sphere, has been described in some detail in order to fu l ly understand the poli t ical , institutional and economic framework within which road investment planning has to operate. Next the rationale of public, rather than private, provision of highways must be established.

Should Highway Provision Be a Public Function?

It can be observed in the world at large that the provision of roads and streets is overwhelmingly entrusted to public bodies. There are some exceptions, especially a number of t o l l roads and bri(fees, but even those are subject to a great degree of State control or support. The institutional arrangements vary, f r o m the ubiquitous govern­ment highway departments to the public authorities in the United States, or the Crown Corporations as these organizational devices are called in Canada and the United King­dom. But essentially a l l these highway organizations are creatures of the State.

There are compelling reasons f o r this state of af fa i rs and these should be examined.

Prevalence of Monopolistic Conditions

In practice the public highway and street system enjoys a largely unchallenged mo­nopoly position. Admittedly, there is some competition on certain segments where the otherwise captive motorist customer can turn to air , r a i l , water transport and in rare instances to to l l roads. However, on most sectors, part icularly in the sphere of urban arteries, residential streets and sidewalks, local access and farming roads, develop­ment and mining highways, there are no substitutes whatsoever to the public road.

The proposition can therefore be accepted that public highway authorities exercise a very wide degree of monopoly power and that, indeed, this monopoly power is prob­ably greater than that of a private monopoly which tends at least to be l imited by the threat of potential competition, public control or nationalization. The prevalence of monopoly conditions means that one w i l l have to employ monopoly theory and that i t would be misleading to introduce spurious comparisons with competitive situations into analyses of highway economics.

Absence of Market in Highway ^ h e r e

Linked to the existence of monopoly conditions is the fact that there is no real market in which highway services are sold and bought. Reasons are: f i r s t l y , the lack of com­pulsion f o r the monopoly supplier to sell his services since revenue would be f o r t h -

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coming f r o m general f i sca l funds in any case; secondly, the fact that almost insuper­able technical and administrative obstacles arise when the attempt is made to negotiate sales of individual highway service units with the respective purchasers.

The absence of a market f o r highway seryices means that one is confronted with the absence of a l l the economic checks, balances, controls and procedures which are nor­mally associated with the working of the market mechanism. To f ind practicable sub­stitutes f o r these market forces is one of the key issues in highway economics.

The System Aspect of Public Highways

The "system" aspect is one of the most important characteristics of public highways; yet i t is a concept which is very di f f icul t to define and which has received relatively l i t t l e attention in the l i terature.

By a system i t is meant a heterogeneous set of things and parts, which, when con­nected, f o r m a complex whole. The individual components of the system are joined together because thus arranged they function more efficiently and render better ser­vice.

This principle can be widely observed in the f ie ld of so-called "public enterprises." K many electric power stations are linked together by means of a gr id system they are jointly able to provide better services at lower unit costs, than when they are operating separately. In the connected network the power consumption load can be distributed more widely over many generating plants; peaks of demand fo r electricity on one r e ­gion are offset by troughs in other distr icts; coal-burning plants are able to make up f o r hydro-electric power deficiencies created, fo r instance, by a drought. In addition to these economies of scale of production, very substantial economies of marketing and distribution w i l l also accrue to an electric power system. If every user had to be connected individually to the power plant by means of separate cables and transformers, electricity distribution costs alone might prove prohibitively high. Since, however, whole distr icts can be served by one main connection f r o m the power plant, mass con­sumption at low unit costs fo r a l l users becomes possible. Similar considerations ap­ply to almost a l l other public or publicly regulated enterprises—sometimes called "natural monopolies"—such as water, gas, sewerage, urban transportation, telephone and railway systems.

The same principles f i t the public road system: as private laneways are joined to the street, as other streets are added, as important points of t ra f f ic attraction develop and these in turn are connected, by main thoroughfares and long-distance highways, to focal points in other distr icts and cities, the various combinations of t ra f f ic or igin, destination and routing which the system as a whole w i l l make possible are increased to staggering proportions. Ultimately, the public road system w i l l serve a l l users which can be reached by land and w i l l provide access to an almost unlimited number of points. In economically more advanced countries practically every house, f a r m and place of work has road access and almost every citizen draws to some degree on road services every day.

Does the Integrated Public Road System Possess Inherent Demand and Supply Advantages?

From the users' point of view, the services rendered by a well-developed public highway system are infinitely superior to those provided, f o r example, by a number of separate roads which connect only a few points each. The integrated public road net­work allows users to choose f ree ly f r o m a great variety of routings and at any moment of time—given knowledge of conditions—users w i l l tend to fol low the most rational t r a f ­f i c f low pattern, that is , the one which minimizes total road transport costs for a l l t r a f f i c . Very important are, fur ther , the economies derived by a l l t r a f f i c f r o m the joint use of the highway faci l i t ies : large commercial vehicles, f a r m trucks, delivery vans and passenger cars w i l l a l l be users of the highways, thus contributing jointly to the costs of construction and maintenance of the roads at lower unit cost shares fo r each of them. Again, this is made possible by the highway system which attracts and serves such diverse forms of t r a f f i c .

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On the supply side the economies of scale and operation to be reaped f r o m treating highways as an integrated whole, rather than as so many road bits and pieces, are also very important. In many cases these economies have probably not yet been fu l ly ex­ploited by public highway authorities. By standardizing technical processes, specifi­cations, materials and equipment, by centralizing certain functions which serve a l l segments of the system, such as planning, research, purchasing, by generally using mass production methods, very great savings in unit costs of rendering highway ser­vices can be realized.

It might be noted that sometimes in the past the negative aspects of the system char­acteristics of highways seem to have received undue attention. This may part ly be due to some misunderstandings and misapplications of economic theory. Instead of assess­ing and promoting the economies of joint use of highways by trucks, vans, buses and automobiles, a formidable amount of research work has been devoted to the punitive aspects, such as the minute economics of cost allocation between one vehicle and an­other. This does not detract, of course, in any way f r o m the great contributions such analyses are making to engineering knowledge.

Furthermore, i t appears to be misleading to ignore the Tremendous economic ad­vantages to be d erived f r o m an integrated road system and to express concern that certain secondary roads and streets "are not paying their way"; surely, the contribu­tions these subsidiary feeder faci l i t ies are making to the system as a whole cannot be ignored. (For appropriate assessment techniques see (J), pp. 196-202.)

Finally, some very real system economies to be reaped f r o m the f ree f low of t r a f ­f i c , taxed and regulated in a reasonably uniform way, have been lost in many instances by a veritable jungle of weight, size, safety, licensing, rate and taxation provisions. Some of the objectives promulgated, such as dipstick laws, corridor area concepts, regional boundary control and the l ike , seem to belong more appropriately to the era of petty European principalit ies than to the motor age and the great North American Continent. Due to determined efforts over many years this "balkanization" of highway transport has been reduced considerably, but many people would claim that there is s t i l l great scope for improvements in the interest of the highway system as a whole.

To conclude: a highway system can be regarded as a combination of many different parts which, when working jointly, produce greater quantities and better qualities of highway services at lower total costs, than when being operated separately. The u l t i ­mate economic l imi t s of the system w i l l be reached when the last (marginal) network extension or improvement w i l l yield benefits which are equal to the costs attributable to the marginal project.

Highways Operated "In The Public Interest"

Very closely linked to the system concept is the fact that roads are supposed to be operated by government bodies " in the public interest ." It i s d i f f icu l t , though, to de­r ive precise working rules f r o m so vague a concept. Broadly speaking, promotion of the public interest means that available resources are used in such a way that they yield the greatest aggregate benefits relative to costs for the community at large. This definition compels an answer to such questions as "What exactly are 'aggregate benefits'?"; "How are they to be measured?"; "What do costs mean in this con­nection?".

As soon as one sets out to promote the public interest one leaves behind cash prof i t maximization, the basic motive guiding the actions of private entrepreneurs. From the economics of private enterprise and the profi t -making f i r m , such as described under the headings "Basis of Investment Decisions" and "Planning of Individual Pro­jects" and il lustrated in Figure 1, onemustturn, fo r better or f o r worse, to the so-called "economics of wel fa re . " (This te rm, originally coined by Professor Pigou of Cam­bridge, is now generally accepted. Basic works on the subject are by Pigou, Li t t le , Baumol, Phelps-Brown, and others.)

New Investment Planning Methods and Cri ter ia

This implies that the planning horizon must now be set as wide as possible—certainly

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wider than that of the private entrepreneur; the reasons are, f i r s t l y , that the promo­tion of the public interest is entrusted to a self-perpetuating, permanent body and secondly—if perfect knowledge of the future is assumed—that public interest should know no time l imi t s , but only p r io r i t i e s .

It fur ther follows that activities or works which create external economies must be promoted and those which cause external diseconomies must be discouraged. Finally, works which are too big f o r individual enterprise must be undertaken as long as they are economically worthwhile; in that case the State performs a 'catalyst' function.

In short, the maximization of social benefits and the minimization of social costs within a very wide planning horizon must be the aim of highway development. Highway investment must be conducive to economic growth and development generally. Hence, highway investment c r i t e r ia must be equally applicable to an urban expressway project, to an in ter -c i ty highway, or to resource development roads in the Yukon or in Central A f r i c a . The state of economic development is a relative te rm: City slums or densely settled but congested industrial regions may be just as 'under-developed' in the econom­ic sense as pioneer areas with unexploited resources. The economic cr i te r ia f o r high­way investment planning must therefore be comprehensive enough to lead to the max­imization of net returns on social capital in a l l these varied situations.

This calls f o r a redefinition of the working variables employed in "Basis of Invest­ment Decisions" and "Planning of Individual Projects" and in Figure 1 of this paper. A l l activities external to the private entrepreneur, which were favourably or unfavour­ably influenced by his activities, are now internal to the economy as a whole and hence of direct concern to the highway department. Hence a l l benefits attributable to and a l l costs caused by public highway provision must be taken into account in road investment planning. Examples of factors to be taken into account are given below.

Highway Benefits (Curve DBM in Figure 1 ) . —Savings in t ime, cost, inconvenience, etc., realized by road users direct ly .

Transportation cost, production cost and distribution cost savings accruing to the entire economy.

Employment-creating effects of highway investment. Beneficial effects on land use, growth of secondary industries, development of

natural resources, tourist trade. Increases in the range of choice f o r users by opening new possibilities of travel,

products, etc. Enlargement of supply and marketing areas fo r products and services. A l l other social benefits.

Highway Costs (Curve ABN in Figure 1 ) . —Direct costs incurred by highway department.

Highway dust, fumes, noise. Accident costs. Detrimental effects on land use, values, etc. A l l other social costs. (The more rapid depreciation in the value of existing f ixed

assets, e.g. railway installations, due to the introduction of a highway fac i l i ty i s not a true social cost factor, but belongs to the category of historical costs and is there­fore i r re levant . )

Practical Problems of Cost and Benefit Measurement

Br ie f ly , in common sense terms, highway planning—like a l l other economic plan­ning—must therefore take a l l relevant circumstances into account. It must not be f o r ­gotten that the transport industry is a service industry and that the provision of high­ways should serve some wider economic, social and pol i t ical purposes beyond the mere mechanical conveyance of vehicles f r o m one point to another.

With some justification the c r i t i c i sm can be put forward that such broad definitions of highway costs and benefits are unrealistic, simply because there are no measuring techniques available to match these wide definitions. Admittedly, there w i l l be p rac t i -

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cal diff icul t ies in assessing a l l benefits and a l l costs to a great degree of accuracy in a l l circumstances, but this does not mean that the aims should not be set high. One must start off with the cost and benefit assessments f r o m the safe but narrow base of measurable items, such as savings and losses in t ime, vehicle operating costs, acci­dent costs; this w i l l eliminate at least some areas of doubt which might adversely af­fect the highway investment decision making. It should then be the pr ime aim to nar­row down fur ther the scope of guesswork by improving the measuri i^ techniques.

F i rs t Progress Report of the Highway Cost Allocation Study (11)

I t appears that the Highway Cost Allocation Study, which is currently being conducted in the United States, proceeds in this way f r o m the well-known and well-established facts into new spheres where ignorance s t i l l prevails . This is gratifying, because so many times investigations in this f i e ld seem to start off f r o m a very wide basis, with sweeping terms of reference to inquire into the general economic nature of roads and road transport; but then, in order to produce tangible results quickly, the scope of research is narrowed more and more—partly by taxonomy—until the f ina l conclusions are a l l but useless since they apply to such a l imited aspect only of the original sub­ject.

There is a strong tendency running through much of the l i terature on highways and highway economics to cling to things which are measurable. Bearing called i t a " fu t i le quest f o r arithmetic certainty ( 1 2 ) . " No doubt the strong engineering flavour of the subject of highways has something to do with i t . This should be overcome, as was sug­gested, by proceeding f r o m the narrow area of measurable costs, benefits and other ascertainable economic facets, to broad and general concepts. There are great op­portunities f o r co-operation between engineers and economists in this f i e l d . Already a substantial body of information has been built up on the favourable effects which high­way improvements have on direct vehicle operating costs.

To quote but one example of many possible ones: Controlled tests conducted in the United States have established the very marked effects which rises and fa l l s in the high­way prof i le have upon fue l consumption and travelling time of motor vehicles, par t icu­la r ly of heavy t rac tor - t ra i le r combinations. As soon as one takes the next step and t r ies to assess in money terms the savings made possible by, f o r example, a reduction in the rate of r ise and f a l l of the highway prof i le , one moves into the realm of econom­ics. As the F i r s t Progress Report points out, the economic character and importance of the load which can thus be carr ied more efficiently has to be assessed; time savings have to be translated into money savings by taking into account the faster turnover of vehicles, reductions in overhead costs (license fees, insurance charges, etc.) per ton-mile or per vehicle-mile, proportionate reductions in labour costs and so on; allow­ances also have to be made for the use of lighter tractors made possible by lower power requirements, fo r differences in services performed (l ine haul versus pickup and de­l ivery) , differences in ratios of payload to tare weights and fo r many other factors.

It can readily be seen that there is great scope fo r further research, part icularly in view of the fact that so f a r relatively l i t t le information has been compiled which goes beyond basic vehicle operating test and engineering data. The f ie ld f o r f r u i t f u l inquir­ies widens even more when one takes into account broader social benefits, such as re ­ductions in accident costs, industrial development, improvements in land use, creation of better marketing possibilities and decentralization of population.

I t i s impossible within the scope of this paper to deal exhaustively with a l l the meth­ods which could conceivably be employed to assess the beneficial or detrimental effects of road development. Changes in property values should certainly be studied, since they lend themselves easily to estimation. The creation of business opportunities brought about by highway improvements, on the other hand, cannot be measured very simply and special techniques may have to be evolved. I t is suggested that the effect of road and street improvements in large urban centers offers a part icularly profitable f i e ld f o r investigation in the widest sense. In urban areas the social costs caused by the lack of efficient road transport faci l i t ies appear to be quantitatively especially i m ­portant, as fo r example the readily observable decay of the central core of many a large city test if ies.

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Quite clearly other scientific disciplines, such as economic geography and history, should also be brought to bear on the subject. Location theory may make valuable con­tributions to highway planning. Advanced statistical and mathematical techniques are already being used in the f ie ld of t r a f f i c engineering. Town-planners, architects, social scientists have a great stake in urban problems. No doors to future scientific inquiries in this f i e ld should remain unopened.

PUBLIC HIGHWAY INVESTMENT PLANNING-FINAL CONSIDERATIONS

The scene is now set fo r the completion of the highway investment analysis. The vexing problems of the proper delimitation of spheres of government activity and those which should r ightful ly be reserved f o r private enterprise were touched upon earl ier . Let i t be assumed now that the levels of both total taxation and of total government ex­penditure are optimum, in the sense that a higher or a lower level of either would re ­sult in an economically less advantageous situation, or in poli t ically less preferred circumstances, fo r the community as a whole.

Re-stated, the problem of the State under these assumptions is therefore the optimum allocation of disposable funds or resources, the total level of which is optimum, to d i f ­ferent government functions. In the abstract, the most beneficial allocation of r e ­sources and the maximum contribution to the social product w i l l be achieved when the marginal net returns f r o m marginal government outlay on Function A are equal to the marginal net returns f r o m an equally large outlay on Function B, and when both are equal to net returns f r o m government outlay in a l l other spheres.

As a concession to reali ty one has to admit right at the outset that a large proportion of government outlay, because of the f ami l i a r diff icult ies of measurement, w i l l not be subject to the economic cost/net return calculus and w i l l thus presumably be deter­mined by collective poli t ical judgment. It may well occur that in this economic-polit­ical sphere of government budgeting each department w i l l be vying with the others for fund allocations and a l l w i l l have as their opposing counterpart the Minis t ry of Finance which t r ies to keep the taxes down.

Going further , two divisions within one department may be competing with each other fo r funds, fo r example the one responsible fo r airport development with the high­way department or the waterways authority. How are the inherent conflicts of interest to be resolved? Pseudo-competition, as "an excellent antidote to bureaucracy and vested interest, " between the various agencies concerned with transportation in the United States has, fo r example, been suggested by Pagrum (13) . Li t t le (14) , on the other hand, favours the over-al l planning approach provided the central board adopts suitably efficient policies.

Similar problems and their solutions are, of course, also to be found in the sphere of private enterprise. A comparable dilemma exists when the budget of a large com­pany is to be allocated between, say, advertising, research, new production faci l i t ies and so on. In the f ina l analysis the department which can most effectively "sel l" i ts proposals w i l l obtain the largest fund allocation. Similarly, inside government: The agency whicli succeeds in presenting the most convincing case w i l l l ikely get the largest budget allocations. It is fo r these politico-economic reasons that the so-called "high­way needs studies"—which serve simultaneously as internal masterplans f o r highway departments and as documents to guide legislators in the allocations of funds fo r high­way purposes—have been so eminently successful in the United States and elsewhere. (The f i r s t Canadian needs study, prepared with the help of the Automotive Safety Foun­dation of Washington, D. C., was completed by the Ontario Department of Highways in 1956. It has been most successfully implemented and extended since then.) It is sug­gested that any improvements in the technical quality and competence of plans prepared by the highway department, whether in f o r m of a ful l -scale needs study or otherwise, should influence government policy in favour of road spending. The adoption of e f f i ­cient planning, management and housekeeping arrangements within the highway depart­ment w i l l therefore in most cases also result in the allocation of desired funds. In that way the public authority finds itself in a situation rather comparable to that of a private company which has to attract capital in the money market by showing proof of successful and efficient operations.

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Road Revenue-Expenditure Equation as Guide to Public Policy

It has been seen that highway budget allocations w i l l be part ia l ly or completely sub­ject to poli t ical decisions. Would i t be possible, though, to let actual or potential road user revenues determine the highway budget allocations? Could one not, by drawing on the example of public u t i l i t ies , run highways as a self-supporting activity and stipulate that the highway authority spend no more and no less than i t intends to collect?

If we employ revenues collected f r o m road users in f o r m of motor fuel taxes, license fees and other imposts as the cr i ter ion f o r the "social prof i tab i l i ty" of highway expend­itures, then the underlying assumption is that the existing imposts are related to bene­f i t s and that they are at the "ideal" level. As Winch (15) shows, these assumptions are inadmissible: F i r s t ly , user revenues do not always measure benefits; f o r example, certain road improvements may actually decrease tax receipts although project benefits may be great; secondly, highway account deficits may either mean that taxes are too high and therefore discourage t r a f f i c which might otherwise pay project costs, or that taxes are too low so that users pay less than their share although they might be wil l ing to pay more.

On the theoretical level of discussion, therefore, no a p r i o r i reasons exist to be­lieve that: (a) highway user revenues should determine highway expenditures, (b)de­f i c i t s indicate the curtailment of road spending, and (c) surpluses dictate increases in road expenditures.

In practical terms i t i s also interesting to note that this allegedly ideal balancing of road expenditures and road revenues is by no means universally practised. In Europe highway tax receipts generally greatly exceed expenditures. In Great Br i ta in , during the period 1948 to 1955, fue l tax and vehicle duty revenues of about L 1,680 mil l ion accounted f o r nearly 800 percent of highway expenditures, which were only h 219 m i l ­l ion . Good arguments could be put forward f o r increasing road expenditures in Great Britain—on social investment grounds—and also f o r lowering road user imposts—on taxation grounds. But i t would not fol low that balancing the outlays and revenues would be either good investment policy or good taxation procedure. Also, i t does not neces­sari ly follow that i n Canada, where road user revenues f a l l considerably short of road expenditures, urgently needed highway and bridge projects should be cancelled, or that license fees and fue l tax rates should be raised.

Proper Sequence of Decisions in Highway Sphere

It is suggested that the determination of the magnitude and pr ior i t ies of road p ro ­jects must come f i r s t . How this might be done by means of cost and benefit analyses has already been discussed at length. The proposed highway development program, complete with cost and benefit estimates, must then be reconciled with the claims f o r funds of other government departments. Within the over-a l l l imi t s imposed by (a) total planned public expenditures, (b) expected revenues, and (c) the government's f iscal policies, a l l projects which promise to yield net social benefits over and above social costs should be considered. Since the total proposed expenditures on worthwhile pub­lic projects may exceed total budgeted government expenditures, a proper sequence of pr ior i t ies must be worked out. Government p r io r i t y planning procedures w i l l resemble closely those employed, f o r example, by the entrepreneurs when calculating project p r io r i t i es , except that in the public sphere costs, benefits and other variables are i n ­terpreted in the widest social sense.

In other words, a l l the techniques and analyses described earlier as applying to private investment planning, w i l l basically be val id . The only changes in Figure 1, f o r example, w i l l be that the horizontal axis now denotes "quantities of highway ser­vices" and the ver t ica l one "marginal social costs and benefi ts ." Hence curve DB can be called "marginal social benefit curve ," curve AB "marginal social cost curve" and the difference between the two "net social benefits" or "net social re turns ." Again, projects yielding the highest net returns relative to capital investment or to total costs w i l l be given f i r s t p r io r i t y consideration.

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Subsidiary Highway Planning Decisions Once worthwhile projects have been selected in this way and have been given ap­

propriate pr ior i t ies , many subsidiary technical and managerial problems have to be settled within the basic framework of the main investment decisions. An example of such secondary planning problems is the precise determination of the appropriate high­way design and construction standards according to the weight, volume, speed, dimen­sional, etc., characteristics of the t r a f f i c to be served (see ( 7 ) , Chapter in, f o r a three-dimensional diagram analysis i l lustrat ing these problems).

Another group of problems calling f o r technical or managerial decisions a r i ses f rom the fact that certain given quantities and qualities of highway services can be produced with different admixtures of f ixed and variable costs, since these are inversely related to each other. The same output results over time may be achieved, f o r example, by high f ixed costs ( i n other words, very durable highway construction) coupled with low maintenance expenditures; o r alternatively by low in i t ia l construction e^enditures combined with high costs of upkeep. Provided that no deteriorations of service quali­ties or diminutions of service quantities are incurred, the combination offering the lowest total costs including interest on money invested over the project planning period w i l l be chosen. Appropriate methods f o r ar r iv ing at solutions are analytically f a i r l y simple and need not be discussed here.

Fluctuations in Traf f ic Demand Over Time Yet another category of problems is introduced when fluctuations in demand f o r high­

way services over time are taken into account. Great variations in highway travel w i l l normally be experienced over a period of 24 hours. Daily t r a f f i c volumes w i l l , fo r ex­ample, show sharp hourly peaks between 8 and 9 a . m . , possibly between 12 noon and 1 p . m . and f inal ly during the traditional 5 to 6 p . m . "rush-hour". There w i l l also be weekly, monthly and seasonal variations. Superimposed on top of each other these t ra f f i c variations may produce exceptionally high compound peak t ra f f i c volumes. ( A good example of a combined daily, weekly and seasonal peak is quoted in the Ontario Department of Highways' study "A Plan for Ontario Highways:" " . . .on Sunday, July 10th, 1955, between 8 p . m . and midnight, only 720 motor vehicles traveled northwards on Highway 400 f r o m Toronto towards Barr ie , but 12 times as many vehicles, a total of 8,700, traveled in the opposite direction. This i s in marked contrast to the general experience on most other routes where the peak volume of t ra f f ic going one way is usually not more than twice as high as that in the opposite direction {16)." In addition to these repeated fluctuations there w i l l be a long-term secular growth (or a secular decline) of t r a f f i c . B one w i l l take an extreme view, each year, each month, each week or day, and in the last analysis each hour or even minute, w i l l therefore have i ts own, unique demand schedule fo r highway services. Consequently, there w i l l be d i f f e r ­ent sets of desirable output values, depending on the demand concUtions and cost r e ­quirements of the various t r a f f i c peaks. The question then obviously arises which one of the many demand schedules should be selected f o r investment and production plans.

D . M . Winch in his "The Economics of Highway Planning" (17) demonstrates ably how the different demands for highway services which arise when " t ime" is introduced can be reconciled and how the most economical f i na l output solution can be found. The guiding basic principle is that of cost minimization and u t i l i ty ( i n our case, benefit) maximization. A number of different plans w i l l be drawn up, each showing the optimum volume of t r a f f i c as determined by the point of intersection of the specific demand (marginal benefit) and marginal cost curves. Thus there may be a plan f o r morning t r a f f i c , one f o r noon t r a f f i c , one fo r afternoon rush-hour t r a f f i c and one f o r midnight t r a f f i c ; s imi la r ly , weekly, monthly and seasonal variations may be introduced by p r e ­paring additional plans to cover the various situations. Finally, i t is pointed out by D . M . Winch, these plans "must be reconciled, and the optimum compromise w i l l be that plan which involves the least total unnecessary costs at times when i t i s not the optimum (_18)." And: "Thus by this method of totalling unnecessary costs of sub-optimum solutions at each time one can calculate the best compromise solution, and the problem of the peak can be solved mathematically (_19)."

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Secular growth of traf f ic i s treated in a s i m i l a r way, with the difference that unnec­e s s a r y costs of each plan in future y e a r s "must be discounted at the current rate of i n ­terest to a r r i v e at its current capitalized value ( 1 ^ ) . " D . M . Winch points out that over longer periods of time compound solutions become possible, such as a plan which c a l l s for land acquisition for a 4-lane divided highway and construction of only a 2-lane road now, with the second 2-lane road to be constructed later when needed. He finally states: "However many plans, compound and single, are considered over whatever per ­iod of t ime, with whatever complex peak and growth patterns of demand, this method wi l l always give one method as the best. In complex cases the calculations wi l l be com­plicated, or rather there wi l l be a very large number of s imple calculations, but there w i l l a lways be a determinate optimum solution for any given set of data ( J O ) . "

By extending these analyses it w i l l also be possible to work out, for example, so lu­tions which apply simultaneously for different choices of traff ic routing, a s well a s for var ious traff ic peak and growth situations. Planning of highway systems can also be expedited in this way. However, enough has been said to indicate the general nature of the methods which can be used. ( T h e mathematically inclined student of highway planning problem should re fer to Studies in the Economics of Transportation {21), Part I , for further detailed discussions of the subject matter . ) There i s certainly great scope for the prac t i ca l application of these techniques in the f ie ld of highway transport and determinate solutions to very press ing problems could thus be obtained. A s D . M . Winch concludes: "Given a l l the data there i s no problem so complex that it i s not capable of theoretical solution, and working on the above principles there i s no reason why the detailed calculations could not be delegated to an electronic computer (22)."

It now only remains to d i scuss highway pric ing a s the appropriate tool for the at ­tainment of the desirable leve ls of output allowed for in the investment planning phase. T h i s i s done in the following section.

S O M E N O T E S ON P R I C I N G O F HIGHWAY S E R V I C E S

In the preceding part s of this paper economic analyses and techniques were evolved which wi l l enable an entrepreneur or a highway department to achieve optimum invest­ment, pr ior i ty and output solutions. In conclusion some attention must be given to the closely related sphere of highway pr ic ing problems. Since pric ing of highway serv ices i s a subject fraught with controversy, a careful and systematic approach i s indicated.

In connection with the o v e r - a l l allocation of funds for highway purposes, i t was de­cided ear l i er to treat the provision of public roads and streets as one of a number of government functions. In part icu lar , no direct f i s c a l or bookkeeping link between road expenditures on the one hand and road user revenues collected by the government on the other hand was established. Subject to some other c r i t e r i a s t i l l to be discussed, there therefore exists almost complete freedom to adopt any pric ing policy which ap­pears expedient as far a s the revenue-producing side of highway taxes i s concerned. T h i s init ial lack of f i s c a l encumbrances wi l l greatly facil itate c lar i ty and directness of the highway pr ic ing analyses .

It was seen ear l i e r that optimum output for any one highway, or segment of the road plant, w i l l be achieved when marginal costs of the last serv ice unit rendered a r e equal to the marginal revenues and hence to the p r i c e charged for the last imit. F o r brevity's sake "marginal cost -pric ing rule" shal l be r e f e r r e d to in the future, which, when ap­plied to extreme output values , determines the optimum quantities of s erv i ce s to be rendered. The marginal cost-pric ing rule does not re s t r i c t one v e r y much as f a r a s the pr ic ing of intermediate serv ice units (those between zero output and optimum out­put) a r e concerned. Here the maximum l imit of charges i s determined by "what the traff ic wi l l b e a r . " If the p r i c e for highway serv i ce s exceeds this ceil ing, then traf f ic wi l l be lost and the careful ly planned highway plant wi l l be operating below the optimum level of output. At the optimum output point the "charges the traff ic wi l l bear" a r e , of course , identical to marginal costs .

A s f a r a s the consumption-rationing side of highway pric ing is concerned, the c h a r g ­ing policy therefore has to adhere to two r u l e s . The f i r s t rule ca l l s for the rationing

of highway use to optimum output by means of marginal cost-pricing of the last (or ex­treme) service unit . The second rule demands that no highway service unit should be priced at more than "the t r a f f i c w i l l bear." Subject to these two prime rules, which apply simultaneously, and under a l l circumstances, there is freedom to set highway prices as desired, since thus there w i l l be no interference with the objectives of invest­ment planning and optimum output operation.

Extraneous Pricing Objectives

In addition to these simple rules and objectives, which really f o r m an integral part of optimum resource allocation f o r highway purposes, there are a host of other pricing objectives. Some of them lead f a r afield into pol i t ical , legal, f i scal and—in connection with the conept of "equity"—pseudo-ethical spheres. They are s t r ic t ly extraneous ob­jectives as f a r as this analysis is concerned and they shall therefore be subordinated to the two pr ime rules which were stated before. This does not mean that they may not be useful and desirable objectives in their own r ight . However, they should not be con­fused with the pr imary economic objectives.

In the following paragraphs some outstanding examples of extraneous objectives which can be encountered in the highway sphere w i l l be discussed. This w i l l set the stage f o r a subsequent demonstration of the many different pricing policies a public highway authority may conceivably adopt.

Maximization of Government Revenue

Maximization of government revenues is probably the simplest and most straight­forward pr ic ing objective a public authority or a public enterprise can pursue. It amounts to "charging what the public w i l l bear" in the widest sense, with limitations set by pol i t ical and economic considerations. Imposts on road users and other highway beneficiaries are simply treated as lucrative sources of revenue for the government. Unless there are weighty poli t ical considerations which dictate a more moderate course of action, the upper l imi t s of charges are identical to those found in a perfectly dis­criminatory monopoly situation.

Competitive Neutrality

Sometimes the attempt is made to adjust the taxation system in such a way that "competitive neutrality" between r i va l economic activities prevails . In the f i e ld of transportation i t is held, fo r example, that each agency "must pay i ts way" and that one f o r m of transportation must not "subsidize" the other. This opens up the very wide f i e ld of competition in transport which cannot be discussed here; may i t suffice to say that under the most frequently encountered working definition of "competitive neutral­i t y " each individual user is charged exactly according to costs of providing the service —not more and not less—and f o r the transport activity as a whole, revenues must exact­ly equal costs.

Encouragement of Maximum Use of a Public Service

In cases where the social benefits conferred by one particular government activity are widely dispersed throughout the whole community, where no one user or group of users is part icularly favoured, or where the provision of the service leads to very large external economies, the service is sometimes rendered free in order to encourage maximum use. Examples are the f ree provision by the State of parks, playgrounds, education, l ibrar ies , ar t galleries and in some cases—alas not in North America—of broadcasting services. The costs of these services are borne f r o m general tax re ­venue, ideally f r o m income tax sources.

Equity of Pricing

Equity of pricing is an objective which is very frequently pursued in the highway sphere; i t is unfortunately also the one objective which is most d i f f icul t to define, since

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i t involves principles of justice, ethical judgments, and social policy decision. Just to i l lustrate the complex nature of the equity concept, i t might be noted in passing that one wr i te r found i t worthwhile to devote an entire book to the study of fairness and equity in the f i e l d of public u t i l i ty operation.

In one sense a perfectly dissimilar charging regime might be regarded as achieving complete and universal equity, since every user pays exactly the price of "what the service is worth to h i m . " Even social justice is served since the poor man w i l l pay l i t t l e and the r i ch man w i l l pay a great deal.

This is , however, not the way in which "equity of taxation" is most commonly i n ­terpreted in discussions on highway pr ic ing matters. Sometimes charging on the basis of costs is regarded as equitable, in which case the "competitive neutrality" require­ment is also satisfied. Sometimes taxation equity is interpreted as implying equal charging fo r a l l service units regardless of costs. Since the cost charging case is a l ­ready covered under the "competitive neutrality" objective, the second interpretation of taxation equity shall be used fo r the subsequent discussion.

Other Objectives

Various other taxation objectives can be encountered in practice. There is the public u t i l i ty approach, which calls fo r an over-al l balancing of revenues and expendi­tures, but may leave freedom of charging fo r individual service units to the manage­ment of the enterprise. Sometimes subsidization of some users is prescribed fo r social or poli t ical reasons. Yet, another approach calls f o r the simulation of private enterprise behaviour in s imilar circumstances. Finally, there is pricing on the basis of benefits received; the last objective is sometimes interpreted as "equalization of charges f o r a l l service units, " sometimes as "charging what the t ra f f ic w i l l bear."

Usually a number of these objectives are combined when solutions to highway taxation problems are sought. Thus the Fi rs t Progress Report remarks with reference to ex­perience in the United States: "Each State, when confronted with the mounting need f o r funds to modernize its highways, has found i t necessary to review its road-user tax structure f r o m the double standpoint of productivity and equity."

These introductory remarks and definitions w i l l have shown what a great variety of highway pricing policy objectives can be pursued. Some of these objectives conflict with each other, others can be reconciled. I t is absolutely essential in any considera­tion of road user taxation problems that the policy objectives are stated clearly; only in this way can appropriate solutions be found.

Equipped with prel iminary working definitions and bearing in mind the two pr ime rules which satisfy optimum output requirements, one can now proceed to a demonstra­tion of possible pricing policies which could be adopted by a public highway authority.

Possible Pricing Policies of Highway Authority

The analytical apparatus and the diagrammatical techniques employed in the subse­quent section are the same as those used throughout this paper; they therefore require no special introduction. Likewise, the concepts "costs" and "benefits"—unless other­wise stated—are to be interpreted as "social costs" and "social benefits", as defined ear l ier . This means that "pricing of highway services", or "charging fo r highway services" does not only include the imposition of fees on direct road users, but also covers taxation of other direct and indirect beneficiaries, such as adjacent land owners.

It i s assumed that the highway authority or other government body responsible for the highway function, has complete freedom of charging in any fashion i t desires fo r the services i t provides and that i t i s only bound by the objectives i t sets i tself . The results of the various pricing policies w i l l be judged entirely in the light of these ob­jectives.

Case 1: Simulation of Private Enterprise Behavior-Monopoly

Possibility (a) —Dissimilar Charging (Figure 2 ) . —This simply calls f o r "charging what the t r a f f i c w i l l bear", following the procedures of the private entrepreneur. Out­put is optimum OD, net revenue is ABC.

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Results and Objectives Achieved. —Optimum output, maximization of government revenues, equity in the sense that each user pays "what the service is worth to h i m . "

Objectives Not Achieved. —Public u t i l i ty requirements (since excessive prof i t s are being reaped), competitive neutrality, charging on the basis of costs, equalization of charges f o r a l l service units.

Possibility (b) —Uniform Charging (Figure 3 ) . —In this case the highway authority w i l l f i x output and uniform price in such a way that the area between the marginal r e ­venue and marginal cost curves i s maximized. Output i s sub-optimum OE, price is OH, net revenue is AFGH.

Results and Objectives Achieved. —Large—although not maximum—government r e ­venues, equalization of charges fo r a l l service units.

|MC,MR 8( PRICE

Objectives Not Achieved. —Optimum out­put, public u t i l i ty requirements, compet­it ive neutrality, charging on the basis of costs.

Figure 2.

Case 2: Simulation of Private Enterprise Behavior - Competition Figure

Possibility (a) —Optimum Output (Figure 4) .—This objective calls f o r a uniform market price, determined by assuming competition—a highly unrealistic working basis. Hence the pseudo-market price may coincide with the optimum level DB =OI (Poss ibi l ­i ty ' a ' ) , may be below optimum level (Possibil i ty ' b ' ) , or may be above the optimum price level (Possibil i ty ' c ' ) . Under Possibility (a) output is optimum OD, price OI and net revenue l A B .

Results and Objectives Achieved. —Optimum output, moderate government revenues, equalization of charges fo r a l l service units.

Objectives Not Achieved.—Public u t i l i ty requirements, competitive neutrality, cost charging.

Possibility (b)—Price Level Too Low (Figure 5) .—Price set too low at, say, level OK. Output is determined by intersection of assumed market price with marginal r e ­venue curve at point P; hence output i s supra-optimum ON. There may be a net p ro f i t or a net loss, depending on whether area KAF is greater or smaller than area FBP.

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PROFIT

Figure k. Figure 5.

Results and Objectives Achieved. —Equal charges, subsidization of some users, en­couragement of use of public services.

Doubtful. —Size of government revenues, public ut i l i ty requirements.

Objectives Not Achieved. —Optimum output, competitive neutrality, charging on the basis of costs.

Possibility (c)—Price Level Too High (Figure 6 ) . —Price set too high at, say7 level OH. Output determined by intersec-t ion of assumed market price with margin­al revenue curve at point G; hence output i s sub-optimum OE. Net revenue i s AFGH.

_6 Results may conceivably be s imilar to those of Case 1(b)—non-discriminating monopoly.

Results and Objectives Achieved. — Large government revenues, equalization of charges.

Objectives Not Achieved. —Optimum output, public u t i l i ty requirements, com­petitive neutrality, chargi i^ on the basis of costs.

Figure 6.

Case 3: Public Uti l i ty Approach—Equal Charging

Possibility (a) —Increasing Marginal (Figure 7 ) .

niis public u t i l i ty approach calls f o r a balancing of revenues and expenditures. This concept of "reasonable p ro f i t s " permitted to be made by the public u t i l i ty , is merely a modification and requires no special explanations. Price w i l l be set in such a way that prof i t s AKF earned on service units OE are exactly balanced by losses FPM sustained throughprovisionof "unremunerative services" EN.

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Results and Objectives Achieved. —Pub­lic u t i l i ty requirements, equalization of charges, encouragement of use of public services beyond output OD, subsidization of (presumably deserving) users of out­put quantities EN.

Objectives Not Achieved. —Optimum output, maximization of government rev­enues, cost charging, competitive neutral­i t y .

Possibility (b) —Decreasing Marginal Costs (Figure 8 ) . —The requirement of equal charging, coupled with decreasing marginal costs in the c r i t i ca l output range, leads to sub-optimum output OE. I t is a case which has received considerable attention in the theoretical l i terature. Revenues balance expenditures, with losses AFK cancelled out by prof i t s FPM.

Results and Objectives Achieved. —Public u t i l i ty requirements, equalization of charges, subsidization of some users.

Objectives Not Achieved. —Optimum output, maximization of government r e ­venues, cost charging, competitive neu­t ra l i ty .

PROFIT

Figure 7.

P R O F T

E D Figure 8.

Case 4: Public Ut i l i ty Approach-Dif ­ferential Charging

Possibility (a) —Optimum Output ( F i g ­ure 9).— The most logical way to achieve both optimum output and a balancing of revenues and expenditures is by charging exactly according to marginal costs. The so-called "incremental cost method" p r o ­poses this approach.

Figure 9.

Results and Objectives Achieved. —Optimum output, public ut i l i ty requirements, charging according to costs, competitive neutrality.

Objectives Not Achieved. —Maximization of government revenues, equalization of charges.

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Possibility (b) —Maximum Output (Figure 10). —The two objectives of maximum output (that is , s e r v i i ^ a l l users however small a charge they can pay) and balancing of revenues and expenditures can be achieved in a number of ways. An "equity" notion is introduced here by f ix ing charges " in proportion to benefits received" (that is , in proportion to "what the t r a f f i c w i l l bear") .

Solution. —Determine the proportionate relationship of magnitude of total revenues which could be collected under a perfectly dissimilar charging regime (that is , size of area OCBL) to total costs incurred when providing maximum output OL (that is , size of area O A F B M L ) . Let one assume that the ratio of total costs to total revenues is 4 to 5. Now f i x a l l charges at fou r - f i f t h s of the theoretically possible maximum level; this procedure provides the actual price curve H F L . Output is maximum OL, total revenues OHFL are equal to total costs OAFBML, prof i ts HAF on service units OE exactly balance losses F L M on service units EL; users of service units E L are subsidized.

Results and Objectives Achieved. —Maximum output, putlic u t i l i ty requirements, subsidization of users (that is , encourage­ment of maximum use of a public service), charging in proportion to benefits received, charging in proportion to "what the t ra f f ic w i l l bear."

Objectives Not Achieved. —Optimum output, charging on the basis of costs, competitive neutrality, maximization of government revenues.

Some Observations on Pricing Possibi l i -ities

PROFIT

What conclusions can be drawn f r o m the foregoing demonstration of the various possibilities fo r pr ic ing policies? In the f i r s t place there seems to be a great var ­iety of choice f o r the public authority. It should be emphasized in this connection that additional models and combinations of objectives could, of course, be readily

Figure 10. devised. Secondly, even i f the public authority conforms with the pr ime rules

established earl ier , in order to satisfy investment and output requirements, optimum output can be achieved in three different ways. Case 1(a) (Figure 2) , as well as Case 2( a) (Figure 4) and Case 4( a) (Figure 9) are equally satisfactory f r o m that point of view.

In order to ar r ive at a definite solution, the three possible cases have to be judged in the light of other c r i t e r i a . Case 1(a) yields maximum government revenues and might therefore be preferred f o r f i sca l reasons, provided there is not too much p o l i t i ­cal resistance to an all-out "charge what the public w i l l bear" regime. It appears that this i s the prevailing situation in the United Kingdom, where road transport i s an ex­t raordinar i ly lucrative source of government revenues; vet road users in Great Britain—and this i s just a very general observation not based on detailed study of con­ditions prevailing i n that country—appear to object more to the inefficiencies of the road plant and the obvious underinvestment in highways, than to the high level of motor fue l taxes and license fees.

Case 2(a) does not seem a practicable possibility, since i t would be a great coinci­dence indeed i f the pseudo-market price happened to be set at exactly the right level. How would a public authority, in practice, determine what the price level would have

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been i f there had been several competing providers of highway services? It i s known that there w i l l never be a number of competing to l l roads linking two towns, just as there w i l l never be different electric c i rcui ts , water systems and telephone connections in one house, installed by competing companies. Hence, i t w i l l be better if one real is­t ical ly bases his policies on the assumption of monopoly, rather than on a nebulous competitive ideal.

Case 4(a) , f ina l ly , appears to meet more objectives of public pricing policy than any other solution. I t is also the approach which is most frequently advocated in the United States; i t i s generally known as the "incremental cost method."

Benefit Charging, Value of Service, Average Cost Pricing

Very br ief ly some other pricing methods should be mentioned which occasionally come up in discussion. "Charging according to benefits received" is probably the best known of these. Unfortunately, the advocates of this approach frequently do not ex­plain what they mean by "benefits". Are benefits to be assessed in accordance with u t i l i ty measurements or a hedonistic calculus? W i l l the luxury-car owner pay more than the dr iver of an old f a r m truck? Does a truck load of timber accommodated on the highway represent greater highway benefits than a bus f i l l e d with sightseers? Does the r i ch man receive greater benefits f r o m highway use than the poor man and hence pay higher charges, or does i t work the other way? Can benefits conferred when a vehicle travels on a poor gravel road be compared to those of t ravel by the same vehicle on a modern expressway?

Obviously, as economic theory tells us and common sense confirms, no satisfactory answers can be given to these questions. Ut i l i ty , or benefits, cannot be measured directly as a sort of psychic or physical reali ty, independent of external observations. K, however, one w i l l assess benefits by the most convenient observable effect—namely by the amount of money users are prepared to give up in order to avail themselves of these benefits—then one w i l l be back to a perfectly dissimilar charging regime and Case 1(a) (Figure 2) applies without any modifications.

Occasionally the proposition is put forward that benefits are proportionate to the number of service units received by individual users. Highway services, under this approach, are supposed to be homogeneous benefit units as measured by ton-miles, vehicle-miles, passenger-miles, axle-miles, etc. , and would be sold by the highway authority at a standard price, in much the same way as loaves of bread are sold by the baker. A l l the objections which might be raised, to "homogeneity of service units", apply to this proposition. Proportionality of benefits to service units by itself does not provide any guidance f o r the f ix ing of the actual (uniform) pr ice level; therefore this version of the benefit approach is usually coupled with some other objective, such as '.'expenditures must equal revenues." Depending on the circumstances, the cases i l ­lustrated by Figures 3 to 8 apply. Rather surprisingly, the benefit method of pricing is sometimes confused with a pure cost approach.

Charging on the basis of the "value of the service" is also encountered in the f i e ld of transportation. I t i s a te rm which dates back to the earlier days of the railways and was really used as a substitute phrase f o r "charging what the t ra f f ic w i l l bear." It was and is regarded as the more e:Q)edient t e rm, since i t does not carry the same strong suggestion of discriminatory monopoly pr ic ing. Complex railway rate t a r i f f s and pseudo-scientific rate theories have been built around the "value of service" principle, with goods commanding high wholesale or re ta i l prices being charged higher railway t a r i f f s than less highly priced merchandises in otherwise identical circumstances. Charging on the basis of the value of the service can be likened to benefit charging; i t is covered by Case 1(a ) .

Finally, charging on the basis of average total costs is occasionally suggested. Case 3(a) (Figure 7) and Case 3(b) (Figure 8) i l lustrate average cost pr ic ing. In neither case w i l l optimum output be achieved by average cost p r i c i i ^ . Depending on the configuration of the marginal cost curve, excessive use of the highway plant (that is congestion) w i l l be encouraged when mai^inal costs are above average total costs (Figure 7) ; optimum use of the highway plant w i l l be discouraged when marginal costs are below average total costs (Figure 8 ) .

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The Public Service Approach

Taking an entirely different approach, one might also ask: why have any specific pr ic ing and taxation policies f o r highways at al l? Could one not regard the provision of highways as a public service, to be rendered f ree to a l l , and dispense with road user taxes and imposts on other beneficiaries altogether? This approach might very easily be just if ied in cases where i t is important to encourage road transport f o r development reasons or where the benefits conferred by roads and streets are widely and uniformly distributed throughout the entire economy. There exists no rationale—apart f r o m r e ­venue collection considerations—for specific highway pr ic ing policies and imposts in countries where a l l citizens are pedestrians and nobody owns a vehicle, or alternatively in countries where a l l persons are owners of automobiles.

The F i r s t Progress Report considers the public service approach in the following way: "The proposition that there should be no road-user taxes, as such, i s worth ex­amining, at least as a point of departure. Considered by itself, general tax support of highways might not be inherently unjust, even under modem conditions. The use of the automobile is almost universal, except in large ci t ies. As f o r commercial vehicles, freight trucks and combinations distribute and deliver the food, clothing, building mate­r i a l , household goods, and general merchandise of the Nation. The benefits and savings their operators derive f r o m highway improvements are distributed in large part to their customers; f o r i f this were not so their business would not increase. The same is true of buses within their more l imited sphere of operation. Thus, the provision, out of general revenues, of roads adequate to support the heavier weights of commercial ve­hicles would not of i tself, in the absence of competitive conditions, severely violate principles of equity." (pp. 10-11). In terms of the present diagrammatical represen­tation, the public service approach would lead to maximum output OL (Figure 10), with almost aU benefits presumed to be social benefits and social costs presumed to be very small . There would be no government revenues accruing f r o m the highway function and no "rationing" of highway services by means of user imposts and other levies would take place.

The discussion throughout has emphasized the many possibilities which exist f o r pricing policies. The various choices which confront a public highway authority have by no means a l l been described, but the ones dealt with in this chapter may serve as representative cases. There can be no conclusion that one approach is " r ight" in a l l situations and that another method has only defects and no meri ts . A l l the economist can do is to point out the various ways in which different policy objectives can be achieved most efficiently.

REFERENCES

1. Keynes, John Maynard., "The General Theory of Employment Interest and Money." Harcourt, Brace and Co., New York, 403pp. (1936).

2. Milne, A . M . , "The Economics of Inland Transport ." Sir Isaac Pitman & Sons, L t d . , London, (1955).

3. i b i d . , p . 168. 4. Owen, Wil f red , and Dearing, Charles L . , " T o l l Roads and the Problem of High­

way Modernization." The Brookings Institution, Washington, D. C. (1951). 5. Dearing, Charles L . , " T o l l Road Rates and Highway P r i c ing . " The American

Economic Review, Vo l . X L V I I , No. 2, pp. 441-452 (May 1957). 6. Duzan, H . C . , "Vehicular Charges on Highway Toll Fac i l i t i e s . " Proceedings,

H^hway Research Board, pp. 45-67 (1953). 7. Kuhn, T i l l o E . , "The Economics of Road Transport ." Ph.D. Thesis approved

by McGi l l University, published by Canadian Good Roads Association, Ottawa, Canada, 297 pp. (1957).

8. i b i d . , pp. 14-17, Figure 3. 9. van Glinstra-Bleeker, R . J . P . , "Some Economic Aspects of Road Development."

P r o c , I n t e r n . Road Fed. , World Meeting, Rome, pp. 47-61 (1955) 10. Galbraith, J . K . , "The Affluent Society." Hamish Hamilton, 288 pp. (1958).

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11. United States Government, "F i r s t Progress Report of the Highway Cost Alloca­tion Study." U.S. Government Printing Office, Washington, D.C. (1957).

12. Dearing, C . L . , "How We Pay For Our Highways." (Sept., 1946). 13. Pegrum, Dudley F . , "Investment in the Railroad and Other Transportation

Industries Under Regulation." The American Economic Review, Vo l . X L V I I , No. 2, p . 427 (May 1957) .

14. L i t t l e , I . M . D . , "A Critique of Welfare Economics." Clarendon Press, Oxford, pp. 205-6 (1950).

15. Winch, David M . , "The Economics of Highway Planning." Ph.D. Thesis approved by the London School of Economics and Political Science, London University (1957).

16. Ontario Department of Highways, "A Plan f o r Ontario Highways." Toronto, ( D e c , 1956).

17. Winch, David M . , "op. c i t . " , pp. 28-43. 18. i b i d . , p . 32. 19. i b i d . , p . 35. 20. i b i d . , p . 36. 21. Beckman, Mart in , McGuire, C . B . , and Winsten, Christopher., "Studies in the

Economics of Transportation." Published f o r the Cowles Commission fo r Research in Economics by Yale University Press, New Haven (1956).

22. Winch, David M . , "op. c i t . " , p . 43

General Discussion J A M E S C. N E L S O N , P r o f e s s o r of Economics , Washington State College

# F A R M O R E in tens ive read ing and ana lys i s than has been poss ib le i n the t i m e a v a i l ­able i s essent ia l to f u l l and f i n a l evaluat ion of the papers p r e v i o u s l y presen ted . H i e r e -f o r e , t h i s p resen ta t ion i s l i m i t e d to d i scuss ion of gene ra l p o i n t s .

The f i r s t po in t to be s t ressed i s the wide a rea of agreement , e x p l i c i t o r i m p i c i t , i n the seve ra l papers on the economic p ropos i t i ons that cons t ruc t ion , maintenance, and ope ra t ion of h ighways r e q u i r e scarce r e sou rces tha t cou ld be u t i l i z e d i n o ther types of p roduc t ion , e i the r i n o ther t r a n s p o r t o r i n o ther f i e l d s ; that the values of such r e ­sources i n o ther uses c o m p r i s e the oppor tun i ty costs of t h e i r devot ion to highway use; and that a l l such oppor tun i ty cos ts mus t be taken in to account i n highway inves tment decis ions and pos s ib ly i n p r i c i n g dec i s ions .

I n p l ac ing highways i n an economic se t t ing . P r o f e s s o r Brownlee has a d m i r a b l y stated, i n s i m p l e t e r m s , the condi t ion that mus t be f u l f i l l e d i n o r d e r f o r highway i n ­ves tment and p r i c i n g to be o p t i m a l i n an economic sense. Thus , compar i sons of h i g h ­way s e rv i ce p r i c e s and cos ts can show wh ich highway needs should be s a t i s f i e d and which should not i f the p r i c e s a re "good approx ima t ions as to what th ings a r e w o r t h " and the cos t s " y i e l d accura te es t imates of what mus t be s a c r i f i c e d . " V i e w i n g the h i g h ­way f u n c t i o n i n t e r m s of the economy as a whole , r a t h e r than as an en t i ty having no consequences f o r r e sou rce a l loca t ions i n o ther a reas , Brownlee i m p l i e s that f a r m o r e cons ide ra t ion than i n the past mus t be g iven to the r a t e s of r e t u r n w h i c h cap i t a l can ea rn i n o ther employments and to impu ted p r o p e r t y taxes on highways i f compar i sons of p r i c e s and cos t s a r e t o y i e l d f u l l y economic highway inves tmen t s . Wi thout adding i n those cost components—that i s , i n t e r e s t at the oppor tun i ty r a t e r a t h e r than the gov­e rnment ra te , and impu ted p r o p e r t y taxes—the to t a l cos ts to be j u s t i f i e d by p r i c e a b l e benef i t s a r e unders ta ted and a tendency ex i s t s to ove r inves t i n highways m o r e o r less cont inuous ly .

A second po in t i s the gene ra l r e cogn i t i on i n these papers tha t a l though t h e r e a r e i n d i r e c t benef i t s to be cons idered , i n mos t cases the highway u s e r s should pay highway cos t s . B rown lee makes t h i s po in t e x p l i c i t l y i n suppor t ing "the content ion that the bene­f i t s f r o m inves tment i n h ighways have p r o p e r t i e s such that a highway inves tment can be evaluated i n the same manner as can any inves tment designed to produce goods and s e r v i c e s that a r e t o be s o l d . " Al though the s tudies by Baker and h i s associates w e r e intended as p u r e l y engineer ing s tudies , i t i s to be noted that compar i sons w e r e made of the cost r e s p o n s i b i l i t i e s f o r v a r i o u s highway groups and the taxes pa id , w i t h the i n ­t e r e s t i n g conc lus ion that the " e f f e c t of the revenue d e r i v e d f r o m the a x l e - m i l e t a x . . . i s to make cost r e s p o n s i b i l i t y m o r e cons is tent ly equal to taxes p a i d ( 1 ) . " K a f o g l i s g ives a t h e o r e t i c a l case f o r a nonuser share i n j o i n t demand p o s s i b i l i t i e s , bu t s t resses tha t where the soc i a l l y des i r ab le amount of h ighway s e r v i c e c l e a r s the m a r k e t at a cos t -de ­t e r m i n e d p r i c e , such a share i s not needed and w i n d f a l l s to nonusers can become a source of genera l tax revenues . He also f i n d s that as "highways a re b u i l t f o r ac tual o r po ten t i a l highway use and l i t t l e m o r e . . . the p h y s i c a l by -p roduc t s of highway deve lop­ment do not p r o v i d e an i m p o r t a n t bas i s f o r a nonuser s h a r e . " Where h ighways a r e t r u l y needed m o r e than o ther th ings , there i s l i t t l e reason to be l ieve that the e f f ec t i ve demand at app rop r i a t e use r f ees , t o l l s , o r r o a d taxes ( w h e r e d i f f e r e n t i a l u se r fees a re unworkable ) w i l l not y i e l d a v o l u m e of p r i ceab l e benef i t s equal to the t o t a l costs i n ­v o l v e d i n adding to highway supply ( w i t h poss ib le exceptions f o r undeveloped a r e a s . ) F i n a l l y , Kuhn s tates as a p r i n c i p l e tha t "publ ic p r o j e c t s should compete , as i t w e r e , on equal t e r m s w i t h p r i v a t e ones and l o g i c a l p r i o r i t i e s f o r a l l of t hem should be based on the expected e f f i c i e n c i e s of cap i t a l f o r the v a r i o u s v e n t u r e s . "

Kuhn ' s i n t e r e s t i n g paper deals i n some d e t a i l w i t h economic c r i t e r i a f o r highway inves tmen t . Recommending a b roader p lanning h o r i z o n than f o r p r i v a t e e n t r e p r e n e u r i a l inves tmen t and the wides t cons ide ra t i on of ex t e rna l economies ( i n d i r e c t benef i t s ) and ex t e rna l d i seconomies ( s o c i a l c o s t s ) , Kuhn sets f o r t h the ideal as "the m a x i m i z a t i o n of soc i a l benef i t s and the m i n i m i z a t i o n of soc i a l c o s t s . "

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However a t t r a c t i v e i n an abs t rac t sense, the re a re numerous d i f f i c u l t i e s w i t h such b road c r i t e r i a as guides to economic highway inves tment . F i r s t , al though the d i f f i ­cu l t i e s of measur ing s o c i a l benef i t s and costs not cons idered i n the m a r k e t a r e m e n ­t ioned , no f o r m u l a i s g iven f o r t h e i r concre te eva lua t ion . Second, some highway bene­f i t s ment ioned f o r cons ide ra t ion , such as t r a n q ) o r t a t i o n cos t , p r o d u c t i o n cos t and d i s ­t r i b u t i o n cost savings a c c r u i n g to the en t i r e economy, a r e no d i f f e r e n t than s i m i l a r genera l gains to the economy f r o m an i m p r o v e m e n t i n the a r t of r a i l r o a d i n g o r i n the manufac tu r ing of s t ee l . In any case, double counting may be invo lved i f savings to u s e r s a r e counted as benef i t s and i f they a re again counted i n t e r m s of e f fec t s on the e n t i r e economy. I T i i r d , K i h n appears to s t r e s s the d i f f i c u l t i e s o f the m a r k e t mechan­i s m i n d e t e r m i n i n g the o p t i m u m highway inves tment wi thout subs t i tu t ing anything as workab le as the m a r k e t , w i t h a l l i t s defects , has been i n t o l l r o a d inves tment and i n many areas of " f r e e " road inves tment on the bas i s of u se r f e e revenue, t r a f f i c , and o ther i n d i c i a of e f f ec t i ve demand. Kuhn admi t s that under h i s c r i t e r i a "a l a r g e p r o ­p o r t i o n of government out lay , because of the f a m i l i a r d i f f i c u l t i e s of measurement , w i l l not be subject to the economic cos t /ne t r e t u r n ca lcu lus and w i l l thus p r e s u m a b l y be de ­t e r m i n e d by c o l l e c t i v e p o l i t i c a l j u d g m e n t . " In the Uni ted States many f a i l u r e s to a t t a in o p t i m a l highway inves tment , i n v o l v i n g both over inves tmen t and under inves tment , can be a t t r i b u t e d p r e c i s e l y to the vaga r i e s of such c o l l e c t i v e p o l i t i c a l judgment . Perhaps m o r e e f f o r t should be g iven to the task of i m p r o v i i ^ the m a r k e t u i w h i c h highway s e r ­v i c e s a r e produced and so ld , i nc lud ing a t tent ion to t o l l s as se lec t ive supplements to u se r fees , o f f - a n d - o n peak p r i c i n g to encourage o r discourage u t i l i z a t i o n and to lessen tendencies t o w a r d ove r inves tmen t , ad jus tment of u s e r f ee schedules to r e f l e c t use m o r e f u l l y , and d i f f e r e n t i a t i o n i n u s e r fees acco rd ing to cost and qua l i t y v a r i a t i o n s .

Ano the r genera l po in t w o r t h emphasis i s that these excel lent papers r e v e a l the c lose and dove ta i l ing r e l a t ionsh ips between engineers and economis t s so f a r as the highway f u n c t i o n i s concerned . Economis t s mus t depend on engineers f o r knowledge of des ign, maintenance, and opera t ing p r a c t i c e s and the f a c t s needed f o r m a k i n g e x p l i c i t the a s ­sumpt ions basic to the app l i ca t ion o f economic ana lys i s to h ighway inves tment and p r i c ­ing p r o b l e m s . Engineers , at least i n mos t cases, mus t depend on the economis ts f o r the p r i n c i p l e s of r e source a l loca t ion and use tha t c o m p r i s e the economic way of t h i n k ­i n g . Engineers cannot avo id economic questions and economis t s t r y i n g to apply eco­nomic p r i n c i p l e s to highways cannot avo id engineer ing quest ions . But because i t i s i m ­p r a c t i c a l to expect engineers to be f u l l - s c a l e economis ts and economis t s to be p r o f e s ­s iona l engineers , what i s u r g e n t l y needed i s the w i l l i ngnes s of both engineers and eco­n o m i s t s to assume the r e s p o n s i b i l i t y of a s s i s t i ng m e m b e r s of the o ther d i s c i p l i n e to comprehend the t echn ica l knowledge and p r i n c i p l e s s u f f i c i e n t l y w e l l f o r each group to do i t s p r i n c i p a l job be t t e r and f o r the j o i n t p roduc t of the two p ro fe s s ions to ass i s t state l e g i s l a t u r e s and the Congress to es tabl i sh sound highway and genera l t r a n s p o r t p o l i c i e s .

The m u t u a l dependence of engineers and economis ts on one another can be i l l u s t r a t e d f r o m the s t i m u l a t i n g conceptual paper by K a f o g l i s . In t r e a t i n g the p r o b l e m of es tab­l i s h i n g an economic use r p r i c e s t r u c t u r e , he assumes that "geomet r i c design imposes on ly c o m m o n c o s t , " whereas "pavement th ickness . . . imposes specia l c o s t . " A f t e r mak ing t h i s d i v i s i o n of design costs in to those ( g e o m e t r i c costs) f o r v ^ i c h a l l veh i c l e s a re respons ib le and those (we igh t costs) f o r w h i c h on ly the veh ic l e s w i t h h e a v i e r - t h a n -basic veh ic l e axle loads a re separate ly respons ib le , he then suggests that engineer ing studies of highway capaci ty have es tabl ished the v o l u m e re l a t ionsh ips re levan t to the g e o m e t r i c des ign . However , he s tates that " v o l u m e o r quant i ty r e l a t i onsh ips f o r pave ­ment th ickness a re not as w e l l es tabl ished as those f o r geomet r i c d e s i g n . " He notes that "the pavement t h i c k n e s s . . . m a y be a f f ec t ed by the number and f r equency of r e p e t i ­t ions of a p a r t i c u l a r ax le l o a d , " but concludes that "pavement design does not cons ider t h i s r e l a t ionsh ip i n a manner such that a de f in i t e r e l a t ionsh ip between number of r e ­pe t i t i ons and pavement th ickness can be d e t e r m i n e d . "

Never the less , two r a t h e r s i gn i f i c an t in fe rences w e r e d rawn f o r m a r g i n a l cost p r i c ­i n g . The f i r s t i s that no geomet r i c costs need be cons idered as special l o n g - t e r m m a r ­g i n a l cos t s f o r the heavy and l a r g e v e h i c l e s . The second i s that the weight costs that a r e separable f o r the heavy veh ic l e s do not impose s h o r t - r u n m a r g i n a l cos ts w i t h use by such veh ic l e s because " h i g h - v o l u m e roads a re designed f o r an i n f i n i t e number of r epe t i t ions o f a l e g a l l y p e r m i s s i b l e m a x i m u m axle l o a d . "

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The p r i c i n g i m p l i c a t i o n s of these cos t behavior genera l i za t ions w h i c h K a f o g l i s has d r a w n f r o m engineer ing f a c t a r e r a t h e r sweeping. I f pavements on p r i m a r y highways can stand " i n f i n i t e " r epe t i t i ons of the m a x i m u m ax le load , then "the m a r g i n a l cost of pavement i s ze ro because the add i t ion of one m o r e v e h i c l e does not increase the t o t a l cos t of p a v e m e n t . " Such cost condi t ions wou ld j u s t i f y l ow highway se rv i ce p r i c e s f o r heavy veh ic l e s to encourage use and the r i s k i n g of revenue " losses" equal to spec ia l pavement cos t . However , r ecogn iz ing that spec ia l pavement cost must be r e c o v e r e d i f the highway pavement s e r v i c e i s to be cont inued, l u m p sum charges such as g r a d u ­ated r e g i s t r a t i o n fees wi thou t a mi l eage o r use component a re suggested as a p p r o p r i ­ate pavement charges . On the o ther hand, K a f o g l i s s tates that should i t be c o n f i r m e d that "pavement cost i s a continuous f u n c t i o n of number of r epe t i t i ons , an add i t iona l v e ­h i c l e w i l l impose add i t iona l pavement cos t and a p r i c e based on use should be e m ­p l o y e d . "

Obvious ly , w i t h such w i d e l y and s i g n i f i c a n t l y d i f f e r e n t m a r g i n a l cost i nc r emen t s r e s u l t i n g i n the sho r t r u n depending on whether pavements a r e designed f o r i n f i n i t e r e ­pe t i t i ons o r acco rd ing to number of r epe t i t i ons of spec ia l ax le loads, i t i s of c r i t i c a l impor t ance that t h i s engineer ing quest ion be solved as r a p i d l y as pos s ib l e . So long as such i m p o r t a n t f u n c t i o n a l r e l a t ionsh ips a r e not known o r a re p r a c t i c a l l y imascer ta inable by economis ts , they cannot w i t h conf idence p r e s c r i b e economic highway s e r v i c e p r i c e s even i f the r u l e that such p r i c e s should be equated w i t h m a r g i n a l costs i s adopted as the genera l economic gu ide l ine . However , even i f i t w e r e c o n f i r m e d that engineer ing de­s ign of pavements i s u n i f o r m l y on the bas i s o f i n f i n i t e r epe t i t i ons of the m a x i m u m axle load , the quest ion would s t i l l a r i s e as to the s h o r t - n m m a r g i n a l cos ts of v e h i c l e s hav­i n g ax le loads above the designed m a x i m u m load . I t i s h igh ly doub t fu l that they could be r ega rded as equal ly at a z e r o l e v e l . A n d the quest ion of l o n g - r u n m a r g i n a l cos ts of pavements mus t be f aced , s ince heavy a x l e - l o a d t r a f f i c i s i nc reas ing , highway c o n ­s t r u c t i o n (a s acknowledged by K a f o g l i s ) i s a continuous p rocess , vas t sums w i l l be i n ­ves ted i n the f u t u r e i n supply ing the s t reng th essent ia l f o r bea r i ng heavy ax le loads, l ega l o r nonlegal , and the i n c r e m e n t s of inves tment cost f o r t h i s purpose w i l l appar ­ent ly v a r y acco rd ing to the magnitude of the ax le load and the r e l a t i v e r epe t i t i ons of the d i f f e r e n t nonbasic v e h i c l e ax le loads .

The assumpt ion of K a f o g l i s tha t a l l geome t r i c costs a re common , s ince highway capac i ty i s c r ea t ed on behalf of a l l veh i c l e s , a lso appears to r e q u i r e add i t iona l e n g i ­nee r ing c o n f i r m a t i o n . I n c r e m e n t a l cost s tudies i n the past have assumed, on the bas is of exper t engineer ing op in ion and design p r a c t i c e s , tha t some lane and shoulder wid th , some c u r v a t u r e r e q u i r e m e n t s , and some grade reduc t ions o r pass ing lanes on steep h i l l s have been r e q u i r e d because of the s ize and power c h a r a c t e r i s t i c s of l a r g e v e h i c l e s . I f these e lements a re not essen t ia l f o r the basic veh ic l e s , then the l o n g - t e r m inves t ­ment cos ts i n v o l v e d mus t be a t t r i bu t ab l e to the l a r g e r veh ic l e s and those wi thout power to take h i l l s at average l i g h t - v e h i c l e speeds. Al though i t wou ld be des i rab le to s i m p l i f y ca l cu la t ion of the spec ia l inves tment and use costs f o r the l a r g e and heavy veh i c l e s , t h i s should not be done to the po in t that spec ia l -veh ic l e and bas i c -veh i c l e cos t s a r e l umped together f o r convenience.

I n d e s c r i b i n g the p r o b l e m s of i n i t i a t i n g studies o f h ighway cos t r e l a t ionsh ips w i t h v e h i c l e s ize such as those done at Ohio State, Baker concludes that the " t h e o r e t i c a l " approach of u t i l i z i n g only r a t i o n a l express ions r e l a t i n g cost w i t h v e h i c l e s ize " i s not a p r a c t i c a l p o s s i b i l i t y because of the many func t ions wh ich have not been es tabl ished on a r a t i o n a l b a s e . " He then assumes tha t any so lu t ion achieved d u r i n g the next f e w yea r s w i l l r e q u i r e e m p i r i c a l techniques , and v i e w s c u r r e n t design techniques as the best source of d i f f e r e n t i a l cost r e l a t i o n s . Even on t h i s bas i s , i t appears that de ta i l ed s tud ­ies of cost , such as the Ohio State r e p o r t , have t h r o w n much t echn ica l l i g h t upon d i f ­f e r e n t i a l cos t s . Never the less , as i t i s not made ope ra t iona l ly c l e a r how i m p o r t a n t e lements of highway cost v a r y w i t h veh ic l e d imens ions and highway use, m o r e r e sea rch was r ecommended .

The p r a c t i c a l quest ion can be r a i s e d : W i l l m u l t i p l y i n g t echn ica l studies ever r e s u l t i n s u f f i c i e n t l y c l e a r and r e l i a b l e d i f f e r e n t i a l cost r e l a t i onsh ips that h ighway i m p r o v e ­ment and p r i c i n g dec is ions can be taken by the p o l i c y m a k e r s w i t h f u l l r e f e r ence to t h e i r economic s ign i f i cance under m a r g i n a l cos t p r i c i n g o r some a l t e rna t i ve scheme

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of economic p r i c i n g ? One p r a c t i c a l answer to t h i s quest ion ca l l s f o r i n t e r d i s c i p l i n a r y teams of engineers and economis ts to w o r k together to increase mu tua l unders tanding and to de t e rmine the best app rox ima t ions of cost func t ions that a re pos s ib l e . W i t h a l l the h ighway r e s e a r c h app rop r i a t i ons c u r r e n t l y au thor ized , i t w o u l d seem sensible to au thor ize exper imen ta t ion along those l i n e s .

A f i n a l genera l po in t concerns the economis t ' s idea l that highway se rv i ce p r i c e s should equate w i t h m a r g i n a l cos t . In addi t ion to the po in t a l ready made that much cost and t echn ica l i n f o r m a t i o n about highways i s not i n such f o r m as to p e r m i t a sce r t a in ing re levan t m a r g i n a l cost , i t should be recognized that not a l l economis ts postulate the eqiiat ion of p r i c e w i t h m a r g i n a l cos t as idea l p r i c i n g f o r e f f i c i e n t r e source a l loca t ion( 2). Depending on the assumpt ions made w i t h respec t to cost behavior and the p e r i o d of t i m e re levant to the quest ion at i ssue , e i the r p r i c e equal i ty w i t h m a r g i n a l cost o r w i t h a v e r s e cost can s a t i s f y idea l condi t ions . Even where the sho r t r u n i s the pe r t i nen t p e r i o d f o r p r i c i n g and grea t excess capaci ty ex i s t s , as on many secondary roads , h o l d ­ing p r i c e s to m a r g i n a l costs when below average o r p r o g r a m cos ts , as suggested by K a f o g l i s , may be po in t l e s s i f , as a lso was assumed, the demand i s i n f i n i t e l y o r h igh ly i n e l a s t i c . In t h i s case, o ther than f o r a d m i n i s t r a t i v e reasons, the highway use r p r i c e m i g h t w e l l be es tabl ished at a f i g u r e cons iderab ly h igher than m a r g i n a l cost wi thout depress ing highway use . A n d cons ide r ing the f a c t that t r a f f i c congest ion i s widespread and q u i c k l y develops even on new and i m p r o v e d f a c i l i t i e s , at least at peak pe r iods , s h o r t - r u n m a r g i n a l cost p r i c i i ^ may be m o r e feas ib le i n t e m p o r a r i l y l i m i t i n g highway demand, b r i n g i n g about r e r o u t i n g s ove r less congested highways, and poss ib ly i n l e s ­sening the u l t i m a t e inves tment th rough encouraging be t te r use of ex i s t ing f a c i l i t i e s . However , i n cases where t o l l s have been set too h igh , g rea t e r u t i l i z a t i o n of t o l l roads can be induced, as the Ohio exper ience apparent ly ind ica tes , by l o w e r i n g t o l l s , p o s s i b ­l y to equal i ty w i t h s h o r t - r u n m a r g i n a l cost .

I n conc lus ion , the papers under d i scuss ion g ive f o o d f o r much thought and d i scus s ­ion by both engineers and economis t s . Just as engineer ing f a c t s concern ing c r i t i c a l highway cost f unc t ions a re h a r d to come by , the economic way of t h i n k i n g i n a f u n c t i o n as complex as highways i s d i f f i c u l t t o p e r c e i v e , except a b s t r a c t l y . Whatever i s u l t i ­ma te ly done concern ing benef i t s to those o ther than d i r e c t u se r s i n t e s t i ng highway i n ­ves tment and i n d e t e r m i n i n g p r i c e s , i t seems that what the economis ts a r e saying i s that a l l cos ts , i nc lud ing oppor tun i ty cos ts , mus t be counted. I n add i t ion , they a r e c o n ­tending that highway costs mus t u l t i m a t e l y be expressed i n t e r m s re levant to economic reasoning i f o p t i m a l highway inves tment and u t i l i z a t i o n a r e to be s t i m u l a t e d . F u r t h e r ­m o r e , i t seems c l e a r that m o r e e f f o r t i s des i r ab le to cast highway benef i t s in to demand schedules and to de t e rmine the e f f e c t i v e demand f o r highway se rv i ce s to the extent p r a c t i c a b l e .

R E F E R E N C E S

1 . Bake r , R . F . , C h i e r u z z i , R . , and B le t zacke r , R . W . , "Highway Costs and T h e i r Rela t ionship to V e h i c l e S i z e . " Eng . E x p e r . Sta . , B u l l . 168, p . 228, Ohio State U n i v e r s i t y , ( M a r . 1958) .

2 . H a l d i , J . , " P r i c i i ^ Behav io r : Economic Theo ry and Business P r a c t i c e . " Cur r en t Econ . Comment , 20:55-56 ( N o v . 1958) .

B E R T R A M H . L I N D M A N , Consul t ing Engineer , Washington, D . C .

# T H E PAPERS contained here have presen ted h igh ly s t i m u l a t i n g and v a r i e d ideas wh ich should con t r ibu te to i m p r o v e d highway inves tment and f i n a n c i n g . However , t he r e a re th ree t roub le some aspects of the app l ica t ion of the p r i c i n g theory to highway f inance w h i c h need some comment .

F i r s t , one i s f o r c e d to wonder what the r e s u l t s would be i f the p r i c i i ^ t h e o r y w e r e appl ied to the i m m e d i a t e highway f inanc ing i ssue b e f o r e the Congress; namely , the

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f inanc ing of the Nat iona l System of In te r s t a te and Defense Highways . Would i t be p r o p ­e r to r e q u i r e the highway u s e r s to d e f r a y the en t i r e cost of t h i s sys t em when f i v e t r a n s ­cont inenta l rou tes , f o r example , were not j u s t i f i e d by use of the p r i c i n g theory of eco­n o m i c s and, i n the w r i t e r ' s op in ion , a l l f i v e cannot be so j u s t i f i e d ?

Second, under the p r i c i n g t heo ry the cost of a highway would inc lude an in t e r e s t charge , o r a r a t e of r e t u r n , on the inves tmen t . Highways i n the Uni ted States a r e be ­ing f i nanced p r edominan t ly on a pay-as -you-go bas is , t h e r e f o r e highway u se r s and o ther payers of specia l h ighway taxes i n e f fec t p r o v i d e highway cap i t a l i n advance of h ighway c o n s t r u c t i o n . Consequently, i t w o u l d appear to be u n f a i r to impose upon them the k i n d of i n t e r e s t imposed when b o r r o w e d funds a re being used .

T h i r d , i n the meet ing of the Commi t t ee on Highway Costs the statement was made tha t a p o l i t i c a l r e a l i t y i s the necess i ty of t ak ing c a r e of the p r o b l e m of f i nanc ing l o c a l and secondary roads be fo re a t tempt ing to solve the p r o b l e m of f inanc ing state h ighways . I n v i e w of t h i s p o l i t i c a l r e a l i t y , one wonders how the p r i c i n g theory can be appl ied to the l o c a l and secondary road p r o b l e m s .

The comment that s eve ra l routes of the In te r s t a te System cannot be j u s t i f i e d by ap­p l i c a t i o n of the economic p r i c i n g t heo ry and B r o w n l e e ' s r e p l y to the e f fec t tha t highway u se r s should not be expected to pay f o r economica l ly u n j u s t i f i e d h ighways , may have c rea ted the i m p r e s s i o n that the w r i t e r i s c r i t i c a l of the In te r s t a te Sys tem. A c t u a l l y h i s v i e w i s that the In te r s t a te System i s w e l l designed to meet the r e a l i t i e s of the c u r ­r e n t p o l i t i c a l s t r u c t u r e and the r equ i r emen t s of na t iona l s e c u r i t y . W i t h r e g a r d to the l a t t e r , r ecogn i t ion was g iven the f a c t tha t the Uni ted States i s f aced w i t h a se r ious m i l i t a r y th rea t and needs a sys t em to encourage decen t ra l i za t ion of the m a j o r m e t r o ­p o l i t a n c i t i e s , to d i s t r i b u t e the popula t ion and i n d u s t r y m o r e w i d e l y , and to p r o v i d e a l t e rna te rou tes i n the event enemy a t tacks should cause mass ive de s t ruc t i on .

HRB:0R-262

r p H E NATIONAL ACADEMY OF SCIENCES—NATIONAL RESEARCH COUN-I CIL is a private, nonprofit organization of scientists, dedicated to the

furtherance of science and to its use for the general welfare. The ACADEMY itself was established in 1863 under a congressional charter signed by President Lincoln. Empowered to provide for all activities ap­propriate to academies of science, it was also required by its charter to act as an adviser to the federal government in scientific matters. This provision accounts for the close ties that have always existed between the ACADEMY and the government, although the ACADEMY is not a govern­mental agency.

The NATIONAL RESEARCH COUNCIL was established by the ACADEMY in 1916, at the request of President Wilson, to enable scientists generally to associate their efforts with those of the limited membership of the ACADEMY in service to the nation, to society, and to science at home and abroad. Members of the NATIONAL RESEARCH COUNCIL receive their appointments from the president of the ACADEMY. They include representa­tives nominated by the major scientific and technical societies, repre­sentatives of the federal government, and a number of members at large. In addition, several thousand scientists and engineers take part in the activities of the research council through membership on its various boards and committees.

Receiving funds from both public and private sources, by contribution, grant, or contract, the ACADEMY and its RESEARCH COUNCIL thus work to stimulate research and its applications, to survey the broad possibilities of science, to promote effective utilization of the scientific and technical resources of the country, to serve the government, and to further the general interests of science.

The HIGHWAY RESEARCH BOARD was organized November 11, 1920, as an agency of the Division of Engineering and Industrial Research, one of the eight functional divisions of the NATIONAL RESEARCH COUNCIL. The BOARD is a cooperative organization of the highway technologists of America operating under the auspices of the ACADEMY-CoUNCiL and with the support of the several highway departments, the Bureau of Public Roads, and many other organizations interested in the development of highway transportation. The purposes of the BOARD are to encourage research and to provide a national clearinghouse and correlation service for research activities and information on highway administration and technology.