Post on 22-Feb-2018
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THE ANATOMY OF MARKET FAILURE
By FRANCIS M. BATOB*
Introduction, 851. I. The conditions of market efficiency, 868. II.
Neoclasdcal external economies: a digression, 866. III. Statical externalities:
an ordering, 868. IV. Comments, 871. V. Efficiency, marketa and choice
of institutions, 877.
What is it we mean by market failure ? TypicaUy, at least in
allocation theoiy, we mean the failure of a more or less idealized
system of price-market institutions to sustain desirable activities
or to estop imdesirable activities.* The desirability of an activity,
in turn, is evaluated relative to the solution values of some expiidt
or implied maximum-welfare problem.
It is the central theorem of modem welfare economics that under
certain strong assumptions about technology, tastes, and producers'
motivations the equUibrium conditions which characterize a system
of competitive markets will exactiy correspond to the requirements of
Paretian efficiency.* Further, if competitivdy imputed incomes are
continuoudy redistributed in costiess lump-sum fashion so as to
achieve the income-distribution implied by a sodal welfare function,
then the competitive market solution will correspond to the one
electronically calculated Pareto-efficient solution which maximizes,
subject only to tastes, technology and initial endowments, that par-
ticular welfare function.*
* Center for International Studies and Department of Economics, Masssr
chusetts Instituto of Technology.
I am mudi indebted to R. S. Eckaus and R. M. Solow for detailed conunent
anddis
1 Activities broadly defined, to cover consumption as well as production.
2
I.e., to the conditions which define the attainable frontier of maximal
utility combinations with given preference functions, resource endowments and
technology. A community is on its Faretian frontier if it is imposmble to make
anyone better off (in terms of his own ordinal preference function) without mak-
ing someone else worse off. Associated with the utility possibility frontier, in
tum, is a production possibility frontier denoting maxinial alternative output
combinations. (Cf. my Simple Analytics of Welfare Maximisation, American
Economie
Reeiew XLVII (Mar. 1957), 22-50, and references therdn.)
8. In other
warda
given the right lump-sum taxes, markets will mateh
the aUocation called for by the point of tangenqr of the rdevant TT-function with
the utiliiy-possibiUly frontier, i.e., by the bliss point. The TT-function need
not, of course, be explicit it could be implicit in the political powei configuiHr
tkm which characterises a community. On the other hand, it cannot be just any
land of function. It has to have some special characteristics which refiect a
number of ethic-loaded restrictions, e.g., that individuals' preference functions
are to count, and to count positively (cf.,
HM.
and Section V bdow).
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Many things in the real world violate such coiiespondence:
imperfect information, inertia and resistance to change, the infeasi-
bility of costless lum p^u m ta xes, businessmen's desire for a quiet
life,
uncertainty an d inconsistent expectation s, the vagariesd aggre-
gate demand, etc. W ith mo st of these I am not here concem ed: they
ha ve to do w ith the efficiency of real life ma rket institu tions
operated by real life people in a nonstationary world of unc ertainty,
iT'scalculation, etc.
What foUows is an attempt, rather, to explore and order those
pheno men a w hich cause eve n errorless profit- and preference-maxim iz-
ing calculation in a stationary context of perfect (though limited)
information an d foresight to fail to sustain Pareto-efficient aUocation.
I am concemed, in other words, with the decentralizing efficiency of
that regime of signals, rules and built-'in sanctions which defines a
price-market system.*
SpecificaUy, Section I sets out the necessary conditions for effi-
ciency of decentralized price-profit calculations both in a laissez-
faire and in a socialist setting of Lange-Lem er d v il servants.
Section II is a brief digression on an often discussed mode of faUure
in these cond itions: neoclassical external econom ies. It is concluded
tha t the m od em formulation of the doctrine, in terms of direct inter-
action , begs more questions than it answers; further, tha t the usual
em phasis on divorce of scarcity from effective ownership is m is-
placed. Section III , then , suggests a comprehensive ordering of type s
of market failure, with generalized indivisibility, pubUc goods, and,
last and least, nonapprop iiabiUty as the villains of the piece. Sectio n
IV con sists of some comm ents on the M eade and Scitov sky daasifiea-
tions of external economies; on tKe analytical link between indivisi-
bility and pubUc good s; on the significance of exclusion ; on oigan -
izational arrangements designed to c set extemaUty; and on blends
of the various typ es of market failure. Section V con du des w ith
som e cautionary no tes on the relevance of market-efficiency for choice
of institutions.
4.
In most of what follows, I shall assume that individual preferences,
though not necessarily sensitive cmly to own-consumption, are representable by
strictiy convex indifference surfaces (i.e., by an ordering (one for eaeh individual)
such that all points on a sttaight line connecting two equivalent pdnts x and
y
are preferred to
x
(hence to
y .
Bu t convexity is too restrictive. It exdud es
not only such duu acteristics of man's psyche as violato the usual regularities
these I do want to exclude but also such physical and topographical facts
as lumpy consumption-goods. Rather than attemp t a specification of preferences
with convex-like properties w h n e ch dc e must b e made among disorato bundles,
I dodge the problem by attributing lumpiness only to inputs (including, however,
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THE ANATOMY O F MARKET FAILURE
353
I . T H E CONDITIONS OF M AR K ET EITPTCIENCT
The central theorem of modem welfare economics, the so-caUed
duality theorem,asserts a correspondence betw een P are to efficiency
and market performance. It s ana lytical essence lies in the remark-
able fact that with all-round convexity, independence of tastes, etc.,
the technocratically formulated, institutionally neutral, Paretian
maximum-of-welfare problem has embedded within it a set of con-
stan ts: duals, Lagnm gean multipliers, shadow-prices, which hav e
all the analytical characteristics of prices, wages, rents, interest
rates.* Correspondence betwee n Pareto-efficiency and ma rket per-
formance implies, at th e least, th at decentralized decisions in response
to these prices by atom istic profit- and satisfaction-maximizers
sustain just that constellation of inputs, outputs and commodity-
distribution, that the maximum of the specified social welfare func-
tion calls for. It imp lies, in other words, th at decentralized m arket
calculations correctiy accoun t for aU economic costs and benefits
to which the rdevant W-function is sensitive.'
D u ali ty can fail in m any w ay s. SpecificaUy, and in a statical and
laissez-faire contex t:^
(1) D ua lity wiU fail unless the Pareto-efficient (a) in pu t-outp ut
points (production) and (b) associated commodity distribution points
(exchange) which associate with the maxim um of the welfare fun ction
in hand are characterized by a com plete set of marginal-rate-of-
substitution
MRS)
equalities (or limiting inequa lities) which, in
5. Th e theorem holds for the statical steady-statofiow mo dd of the W alrasian
sort where the solution values are station aiy time-rates; it holds, also, for dynam i-
cal system s involving cap ital formation Upven, still, convexity throuBluMit). For
these last, the solution values are time paths of inputs, outputo, prices, eto. (A
set of pointo is convex if, and only if, the strsight lines connecting all posdUe
pairs do not anywhere pass outside the set. Th e set of feadble outp ut points
bounded by a production posdbility curve is convex, for instance, if the curve
itself is concave-to-the-origin or a straight line. On all this, see Section V of
ffimple Analytics,
Und.)
6.
Given, again, optimal himp-sum redistribution of as-imputed incomes.
While I make use of the luinp-sum transfer device throui^iout this paper to
abstnwt from the income distribution problem and permit exdudve attention to
Fareto efficiency, it is w dl to noto that this involves a measure of deight-of-hand.
N o decentralised price-market typ e game can reveal the pa ttem of taxes and
transfers tha t would nuudmise a particular welfare function. Central calcula-
tion im plid t if not escplidt is unavoidable. Moreover, since_ distribution
(hence correct redistribution) of numersire^comes interdepends witii allocation
in production and exchange, the supposedly automatic, nonpolitical character of
market mediation is a myth on the strictest neoda sdcal assumptions. Th is is
not to say, even on our stratospheric levds of abstntction, that markets are
useless. Where i h ^ do computo well we are saved aa awful lot of calculation.
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tu m , yield a set of price-like constants. Where no such constan ts
exist, reference wiU be tofailure of existence.
(2) Should such an associated set of Lagrangean parameters
exist, duaUty would neverthdess faU, specifically in production, unless
the bliss configuration of inputs and outputs, evaluated in terms of
these price parameters, wiU y id d : (a) a local profit-maximum position
for each producer, rather than , as po ssible, a profitTniniTnnm;(b) no n-
negative profits for all producers from whom production is required;
(c) m aximu m profits-in-the-large for each producer. Failure on
counts (a) and (c) wiU be labeled failure bysignal that on count (b)
failure by incentive.^
(3) }ven if aU efficient production configurations, or the one
which maximizes a particular welfare-function, coincide with points
of maximum and non-negative producers' profits, market mediation
m ay fail in produ ction. If prices are determ ined by m arket forces,
they will not correspond to a Paretian maximum unless self-policing
perfect com petition obtains in aU mark ets. Self-policing com petition
requires very m an y producers in every m arke t.' If, the n, for
whatever reason, some markets are saturated by a few firms of
effident scale, the fuU welfare-maximum so lution of inpu ts, outpu ts
and prices wiU no t be sustained. There wiU be faUure by structure.
(4) F inally , even if aU ab ov e is satisfied, ma rket performance
could still faU, and fail in a statical sense, due to arbitrary legal and
organizational imp erfections, or feasib ility lim itation s on keeping
book, su di as leave some inputs or outpu ts hidden, or predu de
their expUcit allocation or capture by market processes (e.g., the
restriction, unless I go into basebaU, on the sale of the capitalized
valu e of m y lifetime service s). FaUure isb y enforcem ent.
8. We could consider, instead, the configuration which associates with the
initial pattern of ownership of endowm ent. Or we could play it safe and extend
the conditions to cover each and eve iy Fareto effident configuration. Bu t this
would be overly strict, since many efficient dtuations bave no rdevance dther to
any interesting IT-functions or in terms of the initial distribution of scardties.
It may bie worth noting, incidentally, tha t enstence, as used above^ is
not the same as existence in the sense of, e.g., An ow and Debreu (in Existence
ofanEquilibrium for a Competitive Economy, Econometrica,Vol. 22 (July 1054),
pp.
266-00). They use the term to denoto the completo set of conditions which
defines competitive equilibrium, and this indudes, in addition to all that is
implied by (1) above, conditions akin to my conditions (2), and some analogous
conditions co consumers.
0. Th is is slightly midesd ing: a s we shall see, failureoncount c)leads both
to MgnuWngand to incentive troubles. Anyway, the lahd s are only for expodtoty
convenience.
1.
Or at least the potentiality of veiy many producers, ready and able to
enter the fray instantaneously. Th is may be sufficient in the constant-cost
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THE ANATOMY
O
MARKET FAILURE
355
All the above are germane to duality in its usual sense, to tbe
statical Ptueto-efficiency of laissez-faire markets witb genuine pixxfit-
and satisfaction-seekers.* Con ditions (1), (2) and (4) are relevant,
also,
to th e decentralizing efficiency of a L ange-Lem er ty pe organiza-
tional schem e. In its capitalist version, w ith profit-motivated
operation of privately-owned means of production where it is simply
an anti-monopoly device to assure parametric take-prices-as-given
behavior, conditions (1), (2) and (4) are all necessaiy for efficiency.
Of course condition (3): self-policing competition, no longer matters.
In its tm e socialist version, a Lange-Lemer f ^ t e m can afford to
fail also by incen tive, (2b ). Socialist civU servan ts, under injunc-
tion to maximize profit (in the small) in terms of fixed centrally-
quoted prices, care or should care not at aU about absolute profit-
ability. B y assum ption the scheme can dispense wit h the built-in
incentive of po sitive profit: the lure of bureaucratic adva ncem ent, the
image of Siberia, or the old school tie presumably substitute for the
urge to get rich. B ut if prices and the injunction to maximize profit
are to be used to decentralize, condition (1): existence, and (2a) and
(2c):
correct and unam biguou s signals, remain crucial.* S o do es
condition (4): the solution of quantities and prices need not be
profitable and sdf-enforcing, b ut it does hav e to be enforceable. If
the nectar in apple blossoms is scarce and carries a podtive shadow
price, it must be possible to make eveiy beekeeper pay for his
It warrants repetition that this has to do with whether a decen-
tralized price-market game wiU or will not
sustain
a Pareto-efficient
configuration. Th e word sustain is critical. There exists a ho st of
further considerationis which bear on dynamical questions of adjust-
m ent , of how the system get s there. (E.g ., wiU some natural
price-market type computational routine of price-quantity responses
with a meaningful institutional counterpart tend to track the sdu-
tion?) Th ese are no t here at issue. W e shaU be conc em ed only wit h
the prior problem of wh ether a price-market sy stem which finds itself
2. Th e mathematically minded will object tha t \3 and (4), at least, do not
rea l^ violato duality in its strict mathematical sense; the dual minimum prob-
lem still yields Lagrangean constants. True, yet I think it suggestive to use
dualily mther more loosely as a labd for the general wdfare theorem, particu-
larly as this does not lead, in this context, to any ambiguity.
8. It is tempting, bu t wrong, to suggest that in a true Lange-Lemer world
totals do not m atter and only margins count. It is true that the non-negativeness
of profits is immaterial. Where there is any sharing of diadow-price sets by tw o
or more production points, however, totals necessarily become a part of the
signaling system and if 2(c) does not hd d t h ^ may lead down the garden path.
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a t the m aximum -welfare poin t wUl or wUl no t tend to remain there.*
Th e rd ev an t literature is rich but confusing. It abounds in
mutually reinforcing and overlapping descriptions and explanations
of market faUure: external economies, indivisibUity, nonappropri-
ability, direct interaction, public goods, atmosphere, etc. In a sense,
our problem is simply to sort ou t the relations amo ng these. In doing
so, it is appropriate and useful to begin with a brief review of the
neoclassical doctrine of external economies and of its modem formula-
tion in terms of direct intera ction .
II . NEOCLASSICAL EXT ERN AL ECONO MIES: A DIOBEBSION
By Way cf Some H istory
Mardiall, as has
dtea
been pointed out,
jarapaaed
the external
economy argument to explain, without resort to dynamics, the phe-
nomenon of a nega tively sloped ( forward falling ) long -mn indu stry
supply curve in terms consistent with a horizontal or rising marginal
cost curve
M C)
in the representative firm. Th e device perm its
in logic, if not in fact long-run competitive equilibrium of many
firms within an in du stiy, each producing at its profit-maximum price-
equal-to-a-rising-ilf C position, without foredosing the possibility of a
falling supply price with rising industry output.*
Th e mechanism is simple. It is postulated tha t an expansion in
the output of the industry as a whole brings into play econcmiies
which cause a dow nward shift of the cos t curves of aU the comp
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THE ANATOMY OF MARKET FAILURE 357
firms. Th ese econom ies, how ever, are no t subject to exploitation b y
any one of the myriad of tiny atomized firms. Their own M C curves,
at p =
M C,
rise both before and after the shift, due, presumably, to
intemal diseconomies associated with the entrepreneurial function
which defines the firm. Even the modem formulation is not entirdy
witho ut am biguity institutional amb iguity is intrinsic to th e device
of parametrization: how many firms does it take for the demand
curve of each to b e perfectiy horizontal? bu t it does provide a
means for saving the comp etitive m od d, of ducking the mon opoly
problem.
M arshaU, and also Professor Pig ou , preferred, as it were, th e
other ho m of wh at they perhaps saw as a dilemma. Th e external
economy device, whUe saving competition, implies a flaw in the effi-
cacy of the invisible han d in guiding production.* Price equal to
M C is saved, but wrong. Market forces, they aigued, wiU not give
enough output by industries enjoying external economies and wiU
cause industries with rising supp ly curves to overexpand. H ence th e
MarshaU-Pigou prescription: to harmonize private production deci-
sions with pubUc welfare, tax t he latter se t of industries and subsidize
the fonner.
It took th e better part of thirty years, and the cumu lative powers
of AUyn Young, and Messrs. Robertson, Knight, Sraffa, and Viner,
to unravd the threads of truth and error which mn through the
M arshall-Pigou argum ent.' Th e cmcial distinction, which provides
the k ey to it aU,.is between w hat Viner labd ed tec hnd ogical external
economies, on the one hand, and pecuniary external economies on the
other. Th e latter, if dominan t, cause the long-run supp ly curve of
an industry, say A, to decline because the price of an input, B, falls
in response to an increase in A 's dema nd for it. Th e tech nd ogica l
variety , on th e other hand, thou gh also a reversible function of indus-
try output, consists in organizational or other improvements in effi-
ciency which do not show up in input prices.*
6. Tha t there are difficulties also with income distribution was by tha t time
generally recognised.
7. The stntegic articles, with the exception of Young's ( Figou's WtaUh
and W Ojate,
this /ourno /, X X V II (1018), 672-86 ), as wdl as Ellis and FeUner's
1048 treatment, have all been reprinted in American Economic Association,
RmUrn^tn Price Theory,ed. Stigler&Boulding. For an excdlent modem dis-
cussion, see R. L. Bidiop, conomic Theory(to appear).
8. Note, however, that there need be nothing about an organisational
improvement to make it obvious in advance whether it will tum ou t to be techno-
logical or, thro ui^ intconalisation, pecuniaiy. Many trade assoda tion typ e
services which are justified by the scale of an industiy could as wdl be provided
commercially, and vice versa.
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As regards pecuniaiy external economies, Robertson and Sraffa
made it clear that in a sense both the MarshaU-Pigou condusions
were wrong. For one thing , no subsid y is caUed for. Th e implied
gains in efficiency are adequately signaled by the input price, and
profit-maximizing output levds by the A-firms are sociaUy efficient.
Second, monopoly troubles may be with us, via, as it were, the back
door. For wh at causes the price of to drop in response to increased
demand? W e are back where we started : a declining long-run supply
curve.
In the end, then, if
intemal
technological economies of scale are
ruled out, we are left with only
tedaiological
external econom ies. AU
pecuniaiy external economies must be due to technological economies
somewhere in the system .' It is tm e and this is wh at remains of
the original MarshaU-Pigou proposition th at tech nological exter-
naUties are not correctly accounted for by prices, that they violate
the effidency of decentralized market calculation.
The Modem Formulation^
In its m odern version, the n otion of external economies exter-
nal econ(Hnies proper that i s: Viner's techn do gical variety bd on gs
to a more general doctrine of direct intera ction. Suc h interaction ,
wh ether it involv es producer-producer, consumer-consum er, producer-
consumer, or emplQyermployee relations, consists in interdepend-
ences tha t are external t o the price system, h ence unaccounted for by
market valuation s. AnalyticaUy, it implies the nonindependence of
various preference and production function s. It s effect is to cause
divergence between private and social cost-benefit calculation.
That this is so, is easUy demonstrated by means of a simplified
variant of a production m od d suggested by J. E. Meade.* Assum e
a world of all-round perfect competition where a single purchasable
and indastically supplied input, labor
L),
is used to produce tw o
homogeneous and divisible goods, apples A) and honey H), a t
nonincreasing retums to scale. B ut while the outp ut of A is depend-
ent only
aa Lji :A = A LA),
hon ey production is sensitive also to
the level of apple output:
H = H LH,A LA)).
(Professor M ead e
0. Fecun iaiy diseconomies, in contrast, need have no technological coun ter-
part. Finite-elastic supplies of unproduced inpu ts are a sufficient cause. Recall,
indd enta lly, th at only narrowly statical reverdble phenomenaare adm isdble here.
1. While this section makes some dight use of elementary calculus, the
reader uninterested in technicalities may avnd, without loss of continuity, all
but some dmple notation.
2 .
conomic
Journal,LX II (Mar. 1052 ). Meade uses a two factor modd
and, while he does not explidtiy solve the Faretian maximum problem, shows
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THE ANATOMY OF MARKET FAILURE 359
makes pleasurable the thought of apple blossoms making for honey
abundance.)*
By solving the usual constrained maximum problem for the
production-possibility curve, it can be shown that Paretian produc-
tion efficiency implies
dA , dH dA
,
...
where
PH, PA,
and
w
represent the prices, respectively, of honey,
app les and labor.* Eq uation (1) is famUiar enough and c onsistent
with profit max imizing. Ea ch com petitive honey producer wUl do
for profit what he must for efficiency: hire labor until the value of its
social as weU as priva te mftrgini^l produc t equ als the wage rate. N o t
3H
so the apple producers; unless
T = 0
unless the cross effect of
oA
apples on hon ey is zero their profit-maximizing production deci-
sions wUl be nonefficient. SpecificaUy, if app les ha ve a po sitive exter -
nal effect on honey output, market-determined L^ wiU be less than
is soc ially desirable.*
A different w ay to see this is to exam ine the relations of private to
social marginal cost. Th e marginal m oney cost of apples to the com -
8. Both functions reassumed homogeneous of d ep ee one. Moreover, apple
blossoms (or the nectar therein) are exhaustible, nti on ab le privato good s:
more nectar to one bee means less to anotber. On the need for tiiis assumption,
sse Section I I M bdow.
4. Assuming intemal tangend es ndall-rouud convexity (the last is im plid t
in constant retums to L: the A-effect on
H
reinforces convexity), as well as non-
satiation and nonredundam ^(L ^ L^ + Lg), the maximisation ofp^A + PgH,
subject to the production functions and the supply of labor, is equivalent
to finding a critical vulue for the Lagrangean expresdon,
F
p^A (Ii^) +
PgHlLg A(Lj)] + v(L - LA - Lg). To do so, differentiato Fwith respect
to
L
an d
L y,
treating
p^, Pg
and w as arbitrary constants and set the resulting
first order partial derivative s equal to sero. This will giv e exactiy (1) and (2).
(Needless to say, the value weights can be varied at will, or taken as given.)
5. To see this, lewrito (2) to read
:;=-
,. ^ and match it against
aii on
theprofitrmaximidngrule,
^ -
Clearly, 3 - : ^ 0
at p OA >
/ d A \ < : /_ d A\
V V dL ^/S od
odal
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ECONOMICS
p e t i t i v e a p p l e p r o d u c e r i s . . . . ,; t h a t 0,the tme
margiTial
social
cost
ofan
extra
oA
apple,intermsof honey foregone,isless than
the
m arket-indicated
private cost.
It is
less precisely
bythe
amount
of
positive feed-
back
on
honey output
due the
extra apple.
By combining
1) and 2),
diminatingw
and
dividing through
dA
by PB
and T T - we get the
cond ition
for
Pareto efficiency in terms of
dL
private JlfC's:
dH dLg
_ PA dH
dA dLA
PH dA
Clearly, price equaltoprivate marginal cost wiUnotdo. Further,if
prices are market-determined, the y wiU diverge from tm e,
social
mar-
ginal cost.
Any number
of
variations
on the
m od d suggest themselves.
As
Meade pointed out, interactions can
be
mu tual and need
not be
asso-
ciated with
the
outputs. Even
in the
above case,
it
is perhaps more
suggestive
to
think
of
L^
as
producing some social value-product both
in
the
industiy and
the
H industry.
In the
most general formula-
tion, one
can
simply think
of
each p roduction function
as
containing
aU liie other variables
of the
system, some perhaps with zero weight.
Moreover,
by
introducing
two or
more nonproduced inputs
one can,
as M eade d oes, work ou t the consequences for income d istribution and
input proportions.*
6.
The
question
of
whether technological external economies involve shifts
of eadi other's production functions, or mutually induced movements along such
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THE ANATOMY OF MARKET FAILURE
361
Some Queries
The modem formulation of the doctrine of external economies,
in terms of direct interaction, is not only intemaUy consistent: it also
yields insight. Y et one m ay weU retain abou t it som e dissatisfaction.
Th ere is no dou bt th at th e Robertson-SraffarViner distinction betw een
the technological and the pecuniary sort gets to the nub of what is
the matter wit h th e original M arshallian analysis. It cuts right
through the confusion which led MarshaU and Pigou to conclude
that the price mechanism is faulty in situations where in tmth it is
at its best: in aUocating inputs in less than infinitdy elastic supply
betw een altem lttive produ ctive uses. It also facOitates unam biguous
formu lation of the more difficult faUing sup ply price case. B u t in
a sense it only begs the fundamental question: what is it that gives
rise to direct inter actio n, to short circuit, as it wer e, of th e signaUng
system?
M ost m od em writers have le t ma tters rest with the EUis-FeUner
ty pe explanation : the divorce of scarcity from effective own ership.'
D oe s nonapp ropriability then explain all direct interaction? In a
sense it does, yet by directing attention to institutional and feasibility
considerations wh ich ma ke it impracticable for real life m arket-
institutio ns to mim ic a price-profit-preference com puta tion, it d iverts
atte ntio n from some deeper issues. Surely the word ownership
serves to iUuminate but poorly the phenomenon of a temperance
leaguer's reaction to a hard-drinking neighbor's (sound insulated and
solitary) Satu rday n ight, or the reason wh y a price system , if efficient,
wUl no t permit fuU comp ensation, in an age of dec tron ic scramblers,
for an advertisemen t-less radio program, or for the services of a
bridge.*
function as to give a xes only to inputs and outp uts tha t are purchased and sold,
or a t least controlled, and the effects of everything else impinging on production
(e.g., of humidity, apple blossoms, eto.) are built into the curvature cf the func-
tion,
then it follows that externalities will condst in shifts of some functions in
response to movem ents along others. On the other hand, if, a s in our apple-
hon ey case, it seems useful to think of the production function for 0 as having
an A-aida then, dearly, induced movement along the function is a signal of
extemality.
7.
Op. cU.
8. Moreover, in th e one sense in which nonappropriability fits all cases of
direct interaction, it explains none. If
a
it denotes is the failure of a price-market
game properly to account for (to appropriato) all rdevant costs and benefits,
tben it is simply a qrnonym for market failure (for generalised extemality)i uid
cannot be used to explain what causes any particular instance of such fsilure. I
use i t in a much narrower sense, to mean the inability of a producer of_ a good or
service phydcally to exclude users, or to control the rationing of bis produce
among them. In my sense not only bridges but also, say, tolevidon programs are
fully appropriable: it is always posdble to use scramblere.
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It m ay b e argued, of course, tha t at least the tw o latter examples
are out of order, that radio programs and bridges do not involve
d irect, i.e., non-price, interaction. B ut is this really so? D oes no t
the introduction of a new program directly affect my and your con-
sumption possibilities, in ways other than by a change in relative
prices? D oe s not a bridge, or a road, hav e a direct effect on the pro-
duction possibilities of neighboring producers, in precisely the sen se in
which apples affect the possibilities of beekeepers?'
True, perhaps bridges and roads are unfair: they violate the neo-
classical assumption of perfect divisibility and nonincreasing retums
to scale. B ut they surely do involve non-price interaction. In fact,
lumpiness and increasing retums are perhaps the most important
causes of such interaction. Are they t o be denied statu s as external-
ities? M ore generaUy, ure we to exclude from the class of exte m alitie s
any direct interaction not due to difficulties w ith effective owner-
ship, an y faUures other than by enforcement ?
It w ould be, of course, perfectly legitimate to d o so tastes are
various. B ut I think it more natural and useful to broaden rather
than restrict, to let externality denote any situation where some
Paretian costs and benefits remain
external to
decentralized cost-
revenue calculations in terms of prices.' If, ho weve r, we do so, then
clearly non approp riability' wiU no t do au a com plete explana tion. It s
concem with the inability of decentralized markets to sustain the
sdution-prices and quantities called for by
a
price-profit-preference
type calculation, as computed by a team of mathematicians working
with IBM machines, tends to mask the possibUity that such machine-
0. l t is posdble, of courae, to intorpret these examples sinvolving very large
changes in price: from infinity to zero. Bu t it does not help to do so. The shared
characteristic of bridges and programs is tha t therei no price which will efficiently
mediato both supply and demand.
I have pussled over ways of limiting the notion of direct intoraction to
something lesa than all inatanceg where tbere ia wme intoraction not adtiquatoly
signaled by price. Robert Solow has suggested to me tha t tbis might be done by
distinguishing situationH where something ia not subject to a market tost at all
from instanceiji where no single price constitutes
H
correct teat for both ddea of a
transaction (e.g., where the correct ration price for the aervicea of an expensive
facility ia sero). I am inclined, rather, to drop the attom pt to uae direct intor-
action as an explanation of market failure; it ia beat uaed, if a t all, yet another
aynonym for such failure.
1.
Recall that it ia the exiatence of such extornality, of reddue, at the
blias-point, of Pigouvian unoompenaated aervicea and inddental uncharged
disservices tha t definea market failure. It may be objected that to generalize
the extemality notion in thia way is to rob it of all but deacriptive aignificance.
Bu t surely tbere ia not much to rob ; even in ita atrictost neodasd cal formulation
it begs more than it anawera. In its generalised aenae it at leoat has the virtue
of suggesting the right questions.
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THE ANATOM Y OF MARKET FAILURE
363
calculated solution
Q'S
m ay weU be nonefficient.* I t explains failure
by enforcement, bu t leave s hidden the empirically more impo rtant
phenom ena wh ich cause failure by nonexistence, signal, and
incentive. S ection III is designed to bring these deeper causes of
generalized extemaUty into the foreground.
III . STATICAL EXTER NALITIES : A N OBDEBINO
If nonappropriability is, by
itself
too fiimsy a b ase for a doctrine
of generalized (statical) externality, what broader foundation is there?
Section I's hierarchy of possible modes of market failure suggests a
fivefold classification. If, how ever, one looks for an organizing prin-
ciple not to modes of failure but to causes, there appear to be three
polar types: (1) Ownership Extemalities, (2) Technical Extemalities,*
and (3) Public Good Extem alities. These are not mu tually exclusive:
most extem ality phenomena are in fact blends. Y et there emerges a
sufficient three-comered clustering to warrant consolidation.*
Type 1): Own ership Extemalities
Imagine a world which exhibits generalized technological and
taste convexity, where the electronically calculated solution of a
Paretian maximum-of-welfare problem yields not only a unique set
of inputs, outputs and commodity-distribution, but where initial
endo wm ents plus lump-sum transfers render income distribution o pti-
mal in terms of the comm unity' s social welfare function. Assum e,
further, that everything that matters is divisible, conventionally
rationab le, and either av ailable in inelastic tota l supply,* or producible
at constant retums to scale; also that tastes are sensitive only to
own-consumption. W e know, then, from the duality theorem, t ha t
8. Or that tbe algorism may break down for lack of a condstent set of p's.
4.
I should much prefer technological, but rince tbia would necessarily
confuse
my Typa
(2) with Frofeaaor Viner'a technolcicical Ifixedon technical. .
5. In effect, we end up with a five-by-th ree ordering of types of failure :
five modes vs . three cauaea. Its relation to Meade's catogoriea (op.cit.)
and to Tibor Sdtovsky's claadfication (in 'Two Concepts of Extomal Econ-
omies, Journa l ttf Political Econom y,LXII, April 1054) is discussed in Section IV
bd ow . I have had tbe benefit of reading, alao, William FeUner's Individual
Investment Frojects in Growing Economies,
nvestment Criteria and Economic
Growth
(Froceedinga of a Conference, C entor for International S tudies, Massa-
chusetts Inatituto of Technology, 1955) and an unpublinhed paper by Svend
Laursen, Extemal E^ionomiea and Econonuc Growth.
6. The supply of such nonproduced acard ties need not, of courae, rem ain
constant. On the other band, thdr ownership distribution m ust not be ao con-
centrated aa to preclude com petitive rationing. There muat exist no indivis-
ible lake full of fish, etc., such aa might lie subject to monopolisation, but tbou-
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QUARTERLY JOURNAL OF ECONOM ICS
the bliss point implies a unique' set of prices, wages and rents, such
as would cause atomistic profit- and preference-maximizers to do
exa ctiy w hat is necessary for bliss. In particular, aU required produc-
tion points give maximum and non-negative producer's profits.
Th is is an Adam Sm ith dream world. Y et it is possible that due
to more or less arbitrary and accidental circumstances of institutions,
laws, customs, or feasibility, competitive markets would not be
Pareto-efficient. Ta ke, for instance, the Mead e exam ple of app les
and honey. Apple blossoms are produced at constant retums tu
scale and are (we assumed) an ordinary, private, exhaustible good:
the m ore nectar for one bee, the less for another. It is easy to show
that if apple blossoms have a positive effect on honey production (and
abstracting from possible satiation and redundancy) a maximum-of-
welfare solution, or any Pareto-efficient solution, wiU associate with
apple blossom s a po sitive Lagrangean shadow-price. If, then , apple
producers are unable to protect their equity in apple-nectar and
markets do not impute to apple blossoms tJieir correct shadow value,
profit-maximizing decisions wiU fail correctly to allocate resources
(e.g.,
L)
at the margin. The re will be failure by enforcement.
This is what I would call an ownershipextern ality. It is esseii-
tiaUy M eade's unpaid factor case. Non appropriation, divorce of
scarcity from effective ownership, is
the
binding consideration. Cer-
tain goods (or bads ) with determ inate non-zero shado w-values
are simply not attributed . It is irrelevant here whether this is
because the lake where people fish happens to be in the public dom ain,
or because keeping book on who produces, and who gets wh at,
may be impossible, clumsy, or costly in terms of resources.* For
whatever legal or feasibility reasons, certain variables which have
positive or negative shadow value are not assigned axes. Th e
beekeeper thinks only in terms of labor, the orchard-owner only in
terms of apples.
The important point is that the difficulties reside in institutional
arrangem ents, the feasibUity of keeping tab , etc. Th e scarcities at
issue are rationable and finely divisible and there are no difficulties
with total conditions : at the bliss-configuration every ac tiv ity
would pay foritself Apple nectar has a positive shadow price, which
7. Or, where there are cornera, only inesaentially indeterminato.
8. Set up a variant of tbe A pple-Honey model of Fart II, introducing apple
blossoms, B, explicitly. Add a production function, B
i?(&^), and aubatituto
B Lji) for A L^) as the second input in honey production. The solution will
give out a positive Lagrangean shadow price for
B,
and profit-maximising pro-
A
and
B,
will puah L^ to the so dally dedrabiemargin.
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THE ANATOM Y OF MARKET FAILURE
365
would, if only payment were enforceable, cause nectar production in
precisely the right amount and even distribution would be correctly
rationed. T he difficulty is due exc lusive ly to the difficulty of keep ing
accounts on the nectar-take of Capulet bees as against Montague
bees.'
Many of the few examples of interproducer extemal economies
of the reversible technological var iety are of this typ e: shared
dep osits of fish, water, etc.* M uch more important, so are certain
irreversible dynam ical exam ples associated with investm ent. For
instance, many of Pigou's first category of extemalities: those that
arise in connection with owner-tenant relationships where durable
investments are involved, have a primarily organizational quality.*
Perhaps the most important instance is the training of nonslave labor
to skills as distinct from education in a broader sense (which par-
take s more of T yp e ( 3)) . In the end, however, and in particular if
restricted to reversible statical cases, it is not easy to think of many
significant ownership exte m alities pure and simple. Y et it turn s
out that only this type of extemaUty is really due to nonappro-
priabUity.
Type 9): Tedm ical Extem alities
Assume, aga in, tha t all goods and services are rationable, exhaust-
ible, scarcities, that individual ordinal indifference maps are convex
and sensitive only to own-consumption and that there exist no
ownership defects of Ty pe (1). If, then , th e technology exhib its
indivisibility or smooth increasing retums to scale in the rdevant
range of output, these give rise to a second and much more important
typ e of market failure: technical extemaUty. *
1.
More generally, it could as wdl be due to difficulty in knowing who
produced the benefit oil wd la drawing on the same pool are an example.
Th e owner cannot protect his own; in fact it is difficult to know wh at one m eans
by his own . Moreover, in the case of diseconomies, at least, it ma y be tha t
both the source and the redpien t of the bad are identified: one factory pro-
dudng soot and notbing but one laundiy in tbe neigbborbood, yet it is difficult
to see how a price can be brought to bear on the dtu ation. Fresumably t he
laundry can pay for negative un its of smoke.
2.
Though individb ility elements entor into some of these. W hy can't
somebody own p u t of a lakeful of fish?
8. When not dmply due, in a world of uncertainty, to incondstent expec-
tations.
4 .
Again, this snot the same as Viner'a technological. No to, indde ntally,
that the above formulation unabashedly begs tbe question of wbether smooth
increadng returns to scale could or could not azise without individbility some-
where. Th e issue is entirely definitional: it is conceptually impo sdble to dis-
prove dt her view by reference to empirical evidence. (Cf. Simple An alytics,
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The essential analytical consequence of indivisibiUty,* whether
in inputs, outputs or processes, as wdl as of smooth increasing retums
to scale, is to render the set of feasible points in production (input-
output space) nonconvex. A connecting straight line between some
pairs of feasible points will pass outside the feasible set. Non-
convexity, in tum, has a devastating effect on duaUty.*
In situations of pure technical extemality there does, of course,
stiU exist a maximal production possibility frontier FF); and with
a Samuelson-type social indifference map SS) i.e., a map cor^
rected for income distribution which provides a ranking for the
community as a whde of aU conceivable output combinations' it
is possible, in concept, to define a bliss point(s).* Also, where indi-
visibility is exhibited by outputs, and only outputs, or, stronger,
where smoothly increasing retums to scale is the only variety of
nonconvexity isoquants for one, are properly convex the locus
of efficient output combinations can be defined in terms of conditions
on marginal-rates-of-input-substitution.* Moreover, bliss could pos-
sibly occur at a point where
SS
is intemaUy tangent to
FF,
perhaps
to a convexFF. But even in the least pathological, most neodassi-
Tbe pioneer work on decreasing cost dtuations is Jules Dupuit's remarkable
1844 essay,
On the
Measurement
of
Utility
of
Fublic Works, trandated
in
International Economic
Papers
No . 2, ed. A. T. Feacock,etal. Harold H otdling 's
The General WdfareinRelationtoFroblemsofTasiation andofRailway and
Utility Rates, inthe Ju ly 1088 issueof
E conometriea
istbe originating mod em
formulation.
Cf.,
also, references
to
work by
R.
Frisch, J. E . M eade, W. A. Lewis
and othersin Nancy Ruggles' excdlent survqr artidesonnuuginal cost pricing
Reviewef
Ecmumic
Studies XVII (10^^50), 20-46,and 107-20).
5. Individbilitymeanslumpiness inscale andnot tbekindof individbility-
in-timewe call durability. (Durability, as such, doesnot violato conveidty.)
Lumpinesshas
t
do with th e imp osdbilitytovaiy continuoudy, e.g., the capadty
service-yidd per unit timeofsuch thinggasbridges.
6. The best knownand perhaps most important variety of nonconvexity
occurs where isoquants are properly convex,butretumstosode are increasing,
bence the fullset offeadble input^output pointsisnonconvex. (Inatwainput,
one-output dtuation, dices
by
(vertical) planes through the origin perpendicuUr
to
the input phme will cut the production surface in such
a
way as
to
give
a
non-
convex boundaiy.) A production punt lyingin an increadng retu ms region
ofaproduction function implies that(1)the associated average cost curve AC)
is downward slopingat that levd of output; (2) theassociated marginal cost
curve MO, whLe
it may be
rising, could
as wdl be
falling and wiU certainly
lie bdo w AC;and(8)the production posdbility curveoftbe community maybe
nonconvex. Onallthis,see FartV of Simple An alytics, loc.
cU .
7. Cf. F. A.Sam udson, ScKdal Indifference Cu rves, tiiis Journal LXX
(Feb. 1056), 1-22. Sucha function presumes that numeratra-incomesare con-
tinuoudy redistributedso as tomaximiseinutility space overthecom munity's
operative aodal welfare function.
8. Thisissaying very Iittie,ofcourse, excepton thelevelofmet^>hydcs.
0. Inequalities duetokinks and comers areasgoodasequalities w h eall
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THE ANATOMY OF MARKET FAILURE 367
caUy weU-behaved case, where there exists a mean ingfully defined set
of shadow prices associated with the bUss point, genuindy profit-
seeking com petitive producers, responding to t ha t set of prices, wou ld
fail to sustain optima l production. A t best, eve n if at the bliss-
configuration allM CB are rising, some producers would ha ve t o m ake
continuing losses, hence wou ld go out of business; mark et calculations
would necessarily faU by incen tive. If, in tu m , prices are no t
centrally quoted but permitted to set themsdves, monopoly behavior
wiU result. Th ere will be faUure by stm ctu re .
Further, bliss may require production at levels of output where
losses are no t only positive, b ut a t a constrained maximum;*p = MC
m ay be correct, though M C at tha t point
s
falling . Ifso,the embedded
Lflgrangean constants may stiU retain meaning as marginal rates of
transformation, bu t th ey wiU faU to sustain efficient production eve n
by Lange-Lemer civil servants who care only about m argins and n ot
abo ut absolute tota ls. There wiU be failure by signal : producers
under injunction to maximize profit (in the small) will not remain
where they ought to be.
If, moreover, we drop the assumption of smooth increasing
retums to scale and permit indivisibilities such as ^ve scaUop-like
effects and kinks in cost curves and in the production-possibiUty
curve, things ge t even more compUcated. Bliss could require produc-
tion at points of positive but locaUy minimum profit, where
M C
exceeds
AC
bu t is faUing. W orse, eve n if bliss should occur at p oints
where production functions are locaUy convex and M C (greater than
AC is rising, prequoted prices may still not sustain the solution
unless production functions are in fact convex throughout. T h o u ^
positive and at a local maximum , profits m ay not be a tth dr m ax im um -
nuudmorum: other hills w ith higher peaks ma y indu ce producers with
vision at a distance to rush aw ay from bliss. Altern atively, if prices
are not administered, competition may not be self-policing and
mark ets could fail by stmcture. *
1. Subject to the requirement that total cost for that levd of output be a
minimum, i.e., that each producer be on his least-cost expansion path.
2 .
Where du up individb ility gives a nonconvex production posdbility curve
witb comere and kinks, duality may fail even if there exists a price vector in
terms of wbich decentralised producer-calculations would sustain the bliss-point
outpu t mix. Th e existence of such a vector does not assure tha t it will coindd e
with tb e price-vector wbicb would effidentiy ration tba t bill of goods among
consumers. Th e point is tha t there may not exist a
single
set of prices whidi
will at th e same tim e keep both consumers and producers from rushing aw ay from
where they ought to be. Th e pricea which will effectively mediato production
may cause consumers' calculations to go wrong and vice versa.
It should be noted, indden tally, th at none of the above takes space anddis-
tance condderations into accoun t. For aome interesting effects of plant-ind ivid-
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QUARTERLY JOURNAL OF ECONOM ICS
On the other hand, given our assum ptions, the Paretian contract
locus of maximal (ordinal) utility combinations which is associated
with any one particular output point is defined, as in the trouble-
free neoclassical modd, by the usual subjective, taste-determined,
marginal-rate-of-substitution equalities (or, at comers, inequalities).
These
M RS
equaUties, in tu m , im ply a set of shadow -prices which,
if centraUy quoted, would efficientiy ration among consumers the
associated (fixed) totals of goo ds. In the sphere of excha nge, then,
a decentralized price system works without fiaw.
In what sense do these Ty pe (2) situations exhibit extemaUty ?
In the (generalized) sense that some social costs and benefits remain
extem al to decentralized profitability calculations. W ith T y p e ( l )
extem aU ties, tho ugh it is no t feasible t o poUce the b liss valu es of aU
quantities and prices, there exists embedded in the solution a set of
prices whose use for purposes of decentraUzed signaUng would su stain,
if only appropriation or exdusion were feasible, both itsdf and the
maximum welfare configuration of inputs, outputs, and distribution.
Th is is not the case here. In Ty pe (1) situations, at the bliss point
there is complete correspondence between social and private pay-off
both at the margin and in totals.* Profits are at their ma xima and
non-n egative throughout. Here there is no such correspondence;
there may weU be divergence, either at the margin: bliss-profitB may
be at a minimum , or in
toteUs.
Th e private totals in terms of wh ich
producers in an (idealized) ma rket calculate total revenue minus
tota l c ost will no t reliably signal th e social co sts and benefits
implied by the relevant social indifference curves.* Hence at th e
set of prices which would correctly ration the bliss point bUl of goods,
that biU of goods may not be prodilced by profit seekers, or even by
Lange-Lemer civil servants.*
bility where tliere are interplant fiows and transport takes resources, aee T. C.
Koopmans and M. Beckmann, Asdgnment Froblems and the Location of
Economic A ctivities, Econometrica, Vol. 25 (Jan. 1057).
3.
More correctly, there would be such correspondence, if only the
p s
could
be po liced.
4. This is particularly awkward since the very nonconvexities which cause
a diveigence between privato and aodal total conditions render outputrmix cal-
culations based on margins alone wholly inadequato. Eiven if bliss gives all local
profit maxima, there may be several such open to any one
producer,
hence he muat
make total calculations in order to choose.
5. There is one qualification to be mAde to tbe above. It may be tba t the
bliss configuration gives unique and podtive profit maxima throughout, though
some production functions exhibit nonconvexities at a distance. It was to ex dud e
this case that we assumed that increadng retunis or individbility obtun in the
relevant ranges. Should this happen, no externality dive igsnc e of sod al
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THE ANATOMY OF MARKET FAILURE
A poin t to not e, in all this, is th at in relation to technical
naUties th e nonappropriabiUty notion, as generaUy co nc dv ed , tends
to miss the point. Strictiy speaking, it is, of course, true th at price
me diation, if effident, cann ot be counted on to appropriate th e
fuU social benefits of activities showing increasing retums to scale
or othc typ es of indivisibUity to those engaged in them . B ut the
existence of such uncom pensated services has in this case noth ing
wh atever to do with divorce of scarcity from own ership, w ith
feasibility limitations on exclusion. It is en tir dy feasible to own
a bridge and profitably ration crossings; indeed, a private owner
would do so. Th e point is, rather, th at such profitable rationing,
such com pensation for services rendered, would ineffidently mis-
aUocate th e ou tpu t of bridge crossings. If in term s of scarce
resouree inputs the marginal cost of an additional crossing is zero,
any podtive toU wiU, in general, have the usual monopoUstic effect:
the resulting output configuration wUl not be effident.*
This, incidentally, is where most pecuniary extemal economies
lead: a supplier is required to produce in a range of declining AC due
to intemal technological economies of scale and hence cannot make
ends m eet at the socially correct price. Th e cm cial associated
difficulty at the levd of social organization is monopoly.
Can we leave matters at that? N o t quite. There is a third kind
of extemality, recently emphadzed by I^essor Samuelson, caused
by so-caUed pubUc go od s.
Type S): Pub lic Good E xtemalities
In som e recent writings on public expenditure theory, S am uelson
ha s rdntro duced th e notion of the coUective or pubUc good . Th e
defining quality of a pure public good is tha t each individual's con-
sumption of such a good leads to no subtractions from any other
indiv idual's consump tion of th at good . . . ,' hen ce, it differs from
a private consumption good in that each man's consumption of it,
Xl
and Xf respectivdy , is related to the total
Xt
by a condition of
is convex throughout, the existence of such a locally stable tangenqy cannot be
taken as evidence that the point is in fact the bliss-pcnnt a difficulty of con-
siderable significance for dynamical effidenqy.
6. Of course, if at bliss the bridge were to be used to capad ty, it is pos-
dble that the iAgrangean ration price (now podtive) would make commercial
operation profitable. If so, an administered price setup would effidentiy mediato
the demand and supply of crossings. Bu t while a Lange-Lemer qrstom would
work fine, laisses-faire marketa would fail by stmc ture.
7. F. A. Samudson,
Review cf conomics and Statistics,
XXXVI (Nov.
1054), 887.
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3 7 0 QUARTERLY JOURNAL OF ECONOMICS
equalityrather than of summ ation. Th us, b y definition, Xi = Xt and
XI =
Xt.'
As Samuelson has shown, the form of the marginal rate of sub-
stitu tion c ond itions wh ich define the Pareto-efficient utU ity possibUity
frontier in a world where such public goods exist, or at least where
there are outp uts with imp ortant pubUc qualities, renders any
kind of price-market routine virtuaUy useless for the computation of
output-mix and of distributirai, hence, also, for organizational decen-
tralization. W here some restraints in the maximum problem take
the form: total production of
X equals
consumption by Crusoe of
X equals
consum ption of X by Friday , Pare to efficiency requires tha t
the marginal rate of transformation in production between X and Y
equal not the (equalized) MRS d each separate consumer, but rather
the algebraic
sum d
such
MRS'a.
Th is holds, of course, in wh at in
other respects is a conventionaUy neoclassical world: preference and
production functions are of wdl-behaved curvature, all is convex.
If, then , at th e bliss point, w ith Yas numeraire,Px is equated to
the marginalY eaBt
ai X in
production (as is required to g et optimal
produ ction), and
X
is offered for sale at th at
p ^
preference-maximizing
consumers adjusting their purchases so as to equate their individual
MRS'B to
pt
wiU necessarily under-use
X.
M oreover, a pricing gam e
wUI no t induce consumers tmth fuU y to reveal their preferences. It
pays each consumer to understate his desire for X relative to Y,
since his enjoyment of X is a function only of total X, rather than,
as is tm e of a pure private good, just of th at fraction of ic he pays for.
The two Samuelson artides* explore both the analytics and the
general implications of public goo ds. Here the notion is of rd e-
vanc e because much extem ality is due precisely to the pubUc
quaUties of a great ma ny activities. For example, the extem ality
associated with the generation of ideas, knowledge, etc., is due in
good part to the pubUc character of these comm odities. M any
interconsumer extem alities are of this sort: m y par ty is m y neighbor's
disturbance, your nice garden is any passerby's nice view, my chU-
dren's education is your chUdien's good company, my Strategic Air
Comm and is your Strategic Air Com mand, etc. Tlie same con sump -
tion item enters, positivdy or n^ativdy, both our preference func-
8. F. A. Samudson, Review of
conomics
and Statistics, XXXVII (Nov.
1055), 850.
0. And a third unpublished paper, which was read at tbe 1055 American
Economic Assodation meetings and to a copy of which I came to bave access
while this piqier wa s being written. For earlier writings on public goods, by
W icksdl, Iind ahl, Musgrave, B owen and others see references in the above dte d
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THE ANATOMY O F MARKET FAILURE 371
tions. Th e consum ptions involv ed are intrinsicaUy and essentially
joint.
This kind of extemaUty is distinct from dther of the other two
pure typ es. Here technological non convex ities need in no w ay be
involved. In fact the MRT = XMRS condition is certain to hold
true precisely where production takes place at constant or non-
increasing retums, and hence where the production possibility set
is necessarily con vex. Further, there are no decentra lized organiza-
tional rearrangements, no private bookkeeping devices, which would,
if only feadbiUty w ere no t at issue, eliminate the difficulty. It is the
central implication of the Samuelson model that where public good
phenom ena are present, there does n ot exist a set of prices associated
w ith the (perfectiy definable) bliss poin t, which would sustain th e bliss
configuration. T he set of prices wh ich wou ld induce profit-seeking
com petitors to produce th e optimal biU of goods, would be necessarily
ineffident in aUocating that bUl of good s. M oreover, even abstracting
from production, no single set of relative prices wiU efficientiy ration
an y fixed biU of goods so as to place the system o n its contract
locus, except in the singular case where at that output and income-
distribution MRS B d every individual are identically the same
(or zero for all bu t on e). There is failure by existence.
IV. COHHENTB
Type (1). In a sense. Ty pe (1) is not symm etrical with the other
tw o categories. One can think of some nontrivial instances where the
institutional dem en t does appear to be binding : skill-training of
people, for exam ple. Bu t even there, it could be argued th at the
cmcial elements are durability, uncertainty, and the fact that slavery
as a mod e of organization is itself in th e nature of a pubUc good w hich
enters people's preference functions, or the implicit social welfare
function, inseparably from the narrowly economic variables. In
those instances, in turn, where bookkeeping feasibUity appears to be
the cause of the trouble, the question arises why bookkeeping is less
feasible than where it is in fact being done. In the end, it m ay b e
that much of what appears to partake of Type (1) is really a com-
pound of Types (2) and (3), with dynamical durability and uncer-
tain ty elements tiirown in. A t an y rate, a deeper analysis of this
category may cause it substantially to shrink.
Nonproduced scarcities.
One particular instance where wh at
appears Uke Type (1) is really Type (2) warrants special mention.
Public own ership of nonproduced resources, e.g., t he lakes and m oun -
tains of national parks, may make it appear that extemality is due
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3 7 2 QUARTERLY JOURNAL OF ECONOMICS
to statutory barriers to private ownership and commereial rental.
B ut this is missing the point. Tak e, for instance, a com mu nity wh ich
ha s availab le a single source of fresh water of fixed capacity . Assum e
that the bliss solution gives out a positive ration-price per gaUon
such as would make sale of the water comm ercially profitable. Y et
a laissez-faire syst em wou ld faU, by stm ctu re, to sustain bliss. A
private owner of the single indivisible well, if given his head, would
take advantage of the tilt in the demand curve. The real cause of
externality is not the arbitrary rapaciousness of public authority but
the indivisibility of the source of supply. Th is case, by the way , is
akin to where indivisibility or increasing returns to scale within a
range allow profitable scope for one or a few effident producers, but
for no more. At the bliss price all wUl do the right thing, but if
prices are no t adm inistered, oligopoly or mo nopo ly wUl result. A
capitalist Lange-Lemer system with private ownership but adminis-
tered prices would work fine, but laissez-faire markets would fail.
Meade's atmosphere. The relation of my tri-comered ordering
to M eade 's polar categories is of interest.' H is first category , unpaid
factors, is identical to m y Ty pe (1). B ut his second, labd ed atmo s-
phere, is a rather curious comp osite. M eade's qua litative charac-
terization of atm osphere : e.g., of afforestation-induced rainfaU,
comes very close to the pubUc good notio n.' H e Unks this, however,
as necessarily bound up with increasing retums to scale in production
to society at large, hence a J. B. Clark-like overexhaustion, adding-up
problem.*
If, following Meade, one abstracts from shared water-table phe-
nomena (let rain-caused water input be rigidly proportional to area)
then Farmer Jones' rain is Farmer Smith's rain and we have my
Ty pe (3 ). B ut nothing in this situation requires th at dth er farmer's
fuU production function (with an axis for rain) need show increasing
returns to scale. It m ay be tha t retums to additional bund les of
non-rain inputs, with given constant rainfall, diminish sharply, and
that it takes proportional increases of land, labor
and rain
to get a
proportional effect on outpu t. If so, M eade's overexh austion problem
1.
Op.dt. (Thia and tbe next aection can be omitted w ithout loss of con-
tinuity.)
2.
See esp. bottom of p. 61 and top of p. 62,
op. dt.
8. Since bis argument ia restricted to compietitive dtuations, hence neces-
sarily exdudes increadng-retum-to-paid-factors such as would reqiure produc-
tion at a loss, Meade spedfies constant retums to proportional variation of labor
and land in wheat farming, though the full production function for wheat, indud-
ing the atmosphere input (rain), exhibits increasing retums to scale. But the
individual fanner does not pay for rain, bence bis factor paym ents just matob bia
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THE ANATOMY OF MARKET FAILURE
373
wiU no t arise. B ut aU would no t be weU: the p ublic good quaUty of
rainfall would cause an independent difficulty, one that Meade, if I
understand him correctiy, does not take into account, i.e., that rain
oug ht to be produced by timber growers until its
M C
is equal to
the sum of all the affected farmers MRS'B for rain as an inpu t, wh at-
ever may be the curvature of the latter's production functions.*
On the other hand, Meade's formal mathematical treatment of
atmo sphere, as distinc t from his verbal characterization and his
example, suggests that it is a nonappropriable, and therefore unpaid,
factor which gives rise to increasing retums t o scale to soc iety thou gh
no t to the individual producer. A t least this is aU he needs for the
effect he is looking for: a self-policing thou gh n onoptimal com petitive
situation, where, because the full production functions (i.e., with an
axis for rain) are of greater than first degree, the correction of exte>
naUty via subsidies to promote the creation of favorable atmosphere
requires ne t add itions to society's fiscal burden. If this is the c m cial
consequence of atmosphere, then it need ha ve no pubUc quaUty.
AU this would happen even though Smith and Jones were compet-
ing for the water from the shared wateivtable under their subsoU,
just like bees competing for nectar.
Sdtovskj^s two concepts. ^
Professor Scitovsky, in tum, in his
sugg estive 1954 article, distinguishes betw een th e statical direct inter-
actions of equilibrium theory and the kinds of pecuniary extemal
econom ies emph asized in the economic develop men t literature. H e
classifies the former as consumer-consumer, producer-consumer, and
producer-producer interactions, labels the last as extemal economies
and asserts that they are rare and, on the whole, unimportant.
WhUe Sd to vsk y does not raise the q uestion of what give s rise to
such producer-producer interactions, both his examples, and his con-
clusion that they are of Iittie significance, suggest that he is thinking
4. Formally, Meade denotes atmospbere as a dtua tion where the pro-
duction function, e.g., of farmen takes the form
Xi = Hi(Li,Ci)Ai(X,),
with
L
as labw, as capital and A the atmosphere effect on X , of
X t.
The full function
exhibits increasing retum s to scale but theHfunction sJone, with A constant, is
homogeneous oi first degree. Bu t why can't this be put in terms of Meade's un-
paid factor type function where
Xi
-
Hi(Li,Ci,X,)1
Example:
X,
- L^
C\-' Xt.
All this has nothing to do with whether
A - Ai + A,m
rather A - A . - At.
Unfortunately, the example itsd f tends to midead . Th e fact that exdusion of
ram-users (farmers) by producers (timbergrowers) is hardly feadble, i.e., tbat
rain is like Type (1), distracts attention from the important pdnt that
if
rain is,
as Meacle tdls us, a public good, then rationing it by price would be inefficient
even if it were feadble. (It should be said tbat Meade concludes his artid e:
But, in fact, of coura^ extemal economies or diseconomies may not fall into
dth er of these precise divido ns and may contain features of both of them . )
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3 7 4
QUARTERLY JOURNAL OF ECONOMICS
primarily of Ty pe (1 ): nonappropriability. Bu t this is to ignore
public goods sur dy a more importan t cause of interaction. M ore-
over, by taking full account of these, Sd to vs ky 's fifth and important
case, which, however, does not quite fit into . . . (his) . . . classifica-
tion . . . , where society provides social services through communal
action and makes these available free of charge to aU persons and
firms, can be m ade nicely to faU in to place.*
Samuelson on Types i) and S). WhUe the pubUc good model
h d p s to sort out the plienoiiiena M eade lumped under atmosphere,
Samuelson himself emphasizes the analytical bond between Indivisi-
biUty and public good situations. In both an expUcit summing in
is required of aU direct and ind irect utiUties and co sts in all social
de cision s. ' In Tjrpe (2) situa tion s it is the intramarginal consumer's
and producer's siupluses associated with various all or nothing deci-
sions in-the-lump tha t hav e to be properly (interpersonally)
weighted and summed, while in Type (3) it is only utiUties and costs
at the margin th at require adding. Bu t, and this is the cmc ial shared
quaUty of the two categories, both make it necessary to sum utiUties
over many people.*
Exdusion.
One more comm ent m ay be warranted on th e signifi-
cance, in a pubUc good ty pe situa tion , of nonappropriabiUty. Exc lu-
sion is alm ost never impo ssible. A recluse can build a waU around
his garden, Jones can keep his educated children away from those of
6. Ibid. fn. 8 , p. 144. Sd tov sky , following Meade, restricts his first con-
cept of extemal economies to phenomena consistent with competitive equilib-
rium. He treats individbilities and increasing retum s to scale as bdon ging to
bis second concept which has to do with disequilibrium, investm ent ded dona,
and growth. It is, of course, entird y legitimato to restrictaaalym to competitive
dtua tions. Bu t the Sd tov sky treatment must not be taken to imply that lumpi-
ness is irrelevant to statical analysis of stationary solution points. If m e is inter-
ested in the statical effidency of decentralised price calculations, thqr are crucial.
Bu t this is caiping. Sd tovs ky's important contribution lies in em pba ddn g and
clarifying the pcdnt first hinted a t b y F . N . Rosenstdn-R odan that in a worid of
disequilibrium djmamics pecuniary extemal economies may play an indqiendent
role one distinct, that is, from simply being an unreliable signal of monopoly
troubles EconomicJournal,LIII, 1048, 202 -11).
7.
Ibid.
p. 0.
8. There is one qualification to be made: if all public good and increasing
retums to scale industries produce only intennediato products, all estemalities
may cancel out in intrspbudness-sector transactions. If so, only total revenues
and total costs have to be summed. Incidentally, the expodtion m ay nusiead-
ingly suggest another symmetry between Typ es (2) and (8 ). In a pure IV pe (8)
dtuation, if tbere are no public producera' goods, tben wbile prices cannot^ be
used to ration the bliss point output-mix, t h ^ can be used efficiently to mediato
production. In Ty pe (2), on tbe other hand,i fall final consumables are dividble,
price calculations, while failing in production, will work in exchange. Th is
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THE ANATOMY OF MARKET FAILURE 375
Sm ith, etc. B u t if thereby some people (e.g., the reduse ) are ma de
happier and some (e.g., the passers-by) less hap py, an y decision ab ou t
whether to exclude or not implies an algebraic summ ing of the
somehow -weighted utilities of the people involved . An d if the waU
requires scarce resources, the final utility sum must be matched
against the cost of the waU. W hen Ty pe (3) blends with indiviabiUty
in production, as it does in the case of the waU, or in the case of a
li^thouse, the comparison has to be made between intramarginal
totals. W here no lumpiness is involv ed (e.g., the decibels at w hich
I play my radio) only M RS and perhaps M C calculations are called
for. B ut the really cm cial decision ma y weU be abo ut how m uch
perfectiy feasible appropriation and exclusion is desirable.
Arrangements tooffset It is of interest to speculate what, if any,
organizational rearrangements could offset the three categories of
extemaUty and avoid the need for centrally calculated tax-subsidy
schemes.* In concept. Ty pe (1) can be offset by rearrangements of
ownership and by proper bookkeeping, such as need not vi d a te
the stm ctura l requirements of decentralized com petition. Further,
no resort to nonmarket tests would be required.'
Types (2) and (3) are not so amenable to correction consistent
with decentralized institution s. Th e easiest pos db le case occurs
where increasing returns obtain on the level of single producers'-good
plants, much of whose production can be absorbed by a single user
firm. Here vertical integration tak es care of the problem. N o t every
process inside a weU-mn firm is expected to cover its cost in teims
of the correct set of inte m al accoun ting (shadow ) prices. To tal
profits are the on ly criterion, and it m ay pay a firm to b uild a pr ivate
bridge between its two installations on opposite sides of a river yet
charge a zero accoun ting price for its use by the va rious d ecentralized
manufacturing and administrative divisions; the bridge would make
accoun ting losses, ye t total company profits wiU hav e increased. A s
long, then, as sudi integration is consistent with the many-firms
requirement for com petition, no extrarmarket t est s are required.*
Th e private total conditions:
TR
less
TC,
correctiy account for social
gain.
0. For illustntive derivation of the formulas for corrective taxes and sub-
ddies in l^pe (1) dtuations, see Meade
op.
ed.).
1. Tb e E ma ndpation Frodam ation could co nstitute, of course, a substantial
barrier.
2. If, however, tbe break even scale of operation of the integrated firm
(i.e., where
MC
cuts
AC
from bdow) is much greater than if the river had not
been tbere to span, or could be spanned b y some means of a lower fixed-cost-to-
variable-cost latio , tbe monopoly problem may dmp ly be pusbed forward to
consumer markets.
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3 7 6 QUARTERLY JOURNAL OF ECONOMICS
Where a producers'-good firm, required to produce at a stage of
faUingAC, sd ls to m any customer firms and industries, an adding up
(tf aU the associated
TR a
and TC's at the precalculated as if com -
petitiv e prices associated with th e bliss point w ould again effectively
mopup all social costs and benefits.* B ut the institutio nal reorgan-
ization required to get correct decentraUzed calculation involves hori-
zontal and vertical integration, and the monopoly or oligopoly
problem looms large indeed . T he T yp e (.3) case of a pure producers
public good belongs here: only input MRS a along production func-
tions require summ ing.
In the general case of a mixed producer-consumer good (or of a
pure consumer good) which is pubUc or is produced under cond i-
tions of increasing retums to scale, it is impossible to avo id com parison
of multiperson utilit y tota ls. ExpUcit adm inistrative consideration
must be given, if you like, to consumer's and producer's surpluses for
which no market-institution tests exist short of that provided by a
perfectly discriminating m ono polist. Bu t to invoke perfect discrim-
ination is to beg the question. It imp lies know ledge of aU preference
functions, while as Samuelson has emphasized,* the cmcial game-
theoretical quality of the situation is that consumers will not cor-
rectly reveal their preferences: it wiU pa y them to chea t.
Blends. Exam ination is needed of various blends of Ty pe s (2)
and (3), such as Sidgwick's lighthouse;' or, for that matter, and as
suggested by Samudson, of blends of pubUc and private goods even
where all production functions are fully convex. There are ma ny
puzzling cases. D o bridge crossings differ in kind from radio programs?
Both involve indivisibility and, where variable cost is zero for the
bridge, zero
M C s.
The correct price for an extra stroUer, as for an
extra listener, is clearly zero. Ye t bridge crossings ha ve a distinctiy
private quality: bridges get congested, physical capacity is finite.
Th is is not true of a broadca st. There is no finite limit to th e number
8. Aaauming tbat all conaumer gooda are finely dividble and require no
lumpy dedsions by consumers.
4. Cf. any of the three Fublic Expenditure artidea (supra).
5. Sidgwick, by the way, aa also Figou, thought of a lighthouse aa of Type
(1).
It is, of courae, inconvenient to levy tolls on ships, but it is hanily impos-
sible to exdude, for instance by means of scrambling devices (thou t^ poor
Sidgwick could hardly have known about such things) . Th e point is, rather,
that it would be ineffident to doao:the marginal coat to sodety of an additional
ship taking directional guidance from the beacon atop tbe Statue of Liberty ia
sero,
ipso price diould be cero. In the case of a lighthouse tbis is twice true:
because tbe beacon is in the nature of a public good: more for the Queen Maiy
means no leaa for the Ubertd; and becauae a lij^thouse ia virtually an all-fixed-
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THE ANATOM Y OF MARKE T FAILURE 2 11
d sets th at can costiessly tun e in.* Ra dio programs, then , hav e a
pubUc dimension. Y et, in a sense, so do bridges. W hift your bridge
crossing is not my bridge crosdng, in fact could limit my crossings,
you r bridge is m y bridge. W hat is involved here is tha t m ost thing s
are multidimensional and more than one dimension may matter.
V. EFF ICIEN CT, M AB KE TS AND CHO ICE OF INSTTFITTIONB
AU the above has to do with the statical efficiency of price-
directed allocation in more or less idealized market situation s. Re le-
vance to choice of institutions depends, of course, on the prevalence
of the phenomena which cause externality and on the importance to
be attach ed to statical efficiency. Space precludes extensive discus-
sion of these important issues, but a few casual comments, in the
fonn of
dicta
are perhaps warranted.
How important are nonappropriability, nonconvexity and pubUc
goods? I would be inclined to argue tha t while nonappropriabiUty
is of smaU imp ort,' the same cannot be said of the other two . T m e
enough , it is difficult to think of man y exam ples of pure public goods.
Most things even battieships, and certainly open air concerts and
schools (thou gh n ot know ledge) ha ve an "if more for you then
less for m e" quaUty. B ut this is of little comfort. A s long as activ-
ities hav e even a trace of pubUcness, price calculations are ineffident.*
And it is surdy hard to gainsay that some degree of public quaUty
pervades much of even narrowly "economic" activity.
Lumpiness, in tum, and nonUnearity of the increasing retums
sort, while in m ost instan ces a ma tter of degree, and, within lim its, of
choice, are also in the nature of thin gs. Th e universe is fuU of singu -
larities, thresholds and nonproportionalities: speed of light, gravita-
tional constant, the relation of circumference to area, etc. A s econo-
mists we can cajole or bully engineers into designing processes and
installations that save on congealed inputs and give smaUer maximal
service yid d s, especiaUy when d esigning for low-income co mm unities.
But the economicaUy perhaps arbitrary, not completdy physics-
imposed quality of indivisibilities associated with standsurd designs
6. Richard Eckaus bas suggested to me that it is posdble to exbaust the
space to which the broadcast is limited and tbat this makes the dtuation a Iittie
more Hke tha t of a bridge. N dtb er of us is entird y satisfied, however.
7. Excep t for labor skills and these would tak e us beyond the bounds
of reverdble statics.
8. Th is is not to say that there exist otber feadble modes of soda calculation
and organisation which are more effident.
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3 7 8 QU RTERLY JOURN L OF ECONOMICS
and ways
d
doing things should not blind. NonU nearity and lumpi-
ness are evident facts of nature.*
M ore imp ortant, at th is le vd of discourse' though perhaps i t
hardly need be said is th at statical m arket efficiency is n dt he r
suffident nor necessary for market institutions to be the prefen ed
mod e of social organization. Qu ite apar t from institution al considera^
tions, Pare to efficiency a s such ma y not be ne cess aiy for bliss.* If,
e.g., people are sensitive not only to their own jobs but to other
people's as weU, or more generaUy, if such things as relative status,
power, and the like, matter, the injunction to maximize ouQiut, to
hug the production-possibUity frontier, can hardly be assum ed neu-
tral, and points on the utility frontier m ay associate with p oints
inside the production frontier.* Furthermore, there is no thin g pre-
ordained about welfare functions which are sensitive only to indi-
vidual consumer's preferences. As a m atter of fact, few people wo uld
take such preferences seriously enough to argue against any and all
protection of individuals against their own mistakes (though no
extemal effects be involved).
AU this is tm e even w hen maxim ization is subject only t o techno-
logical and resource limitatio ns. Once we adm it other side relations,
which link input-ou tput variables with noneconomic poUtical and
organizationiJ value s, m atter s becom e mu ch more compU cated. If
markets be ends as weU as means, thdr nonefficiency is hardly suffi-
cient ground for rejection.'* On the other hand, efficient markets may
9. Thdr quantitative aignificance is, of course, veiy sendtive to scale, to
dse
of markets. Th is explains tbe particular emphasis on the role of aodal
overheads in low income countriea.
1.
Where recourse to atrategic condderations of feadbility, cnidal though
t h ^ be, is quito out of order.
2. Th at it ia never auffident ia, of courae, w dl known. Of the infinito
Fareto-effident configurationa at best only one: th st which gives the ri|^ t
distribution of income in terma of the TT-function tiiat is to count, has normative,
prescriptive dgnificance. Moreover, most interesting IF-functions are likely to
be sen dtiv e to noneconomic factors, such as are, if not incon dsten t, at least
extraneous to Faretian condderations. Where such additional values of a political
or social nature are separable from input-output value