Chapter 09 Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter...

8/19/2019 Chapter 09 Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09

1/26

Copyright © 2008 by the McGraw-Hill Companies, Inc. All

McGraw-Hill"IrwinManagerial #conomics,

Managerial Economics ThomaMaurininth edition

Copyright © 2008 by the McGraw-Hill Companies, Inc. All

McGraw-Hill"IrwinManagerial #conomics,

Managerial Economics ThomaMaurininth edition

Chapter 9

Production & Cost in

the Long Run


2/26

Managerial Economics


9-2

Production Isoquants

• In the long run, all inputs are variable& isoquants are used to studyproduction decisions

• An isoquant is a curve showing all possibleinput combinations capable of producing agiven level of output

• Isoquants are downward sloping; ifgreater amounts of labor are used, lesscapital is required to produce a givenoutput


3/26



9-3

Typical Isoquants (Figure 9.1)


4/26



9-4

arginal Rate o! Technical

"u#stitution• The MRTS is the slope of an isoquant& measures the rate at which the twoinputs can be substituted for one

another while maintaining a constantlevel of output

∆

= − ∆

K

MRTS L

∆ ∆

MRTS

K L

The minus sign is added to make a positivenumber since , the slope of the isoquant, is

negative


5/26



9-5

arginal Rate o! Technical

"u#stitution• The MRTS can also be expressed asthe ratio of two marginal products:

= L

K

MP MRTS

MP

L

K

MP

MP MRTS

As labor is substituted for capital, declines &rises causing to diminish

∆= − =

∆

L

K

MP K MRTS

L MP


6/26



9-6

Isocost Cur$es

• Represents amount of capital that ma be purchasedif !ero labor is purchased

( C ) ( w, r )

Show various combinations of inputs thatmay be purchased for given level of

expenditure at given input prices

•

• K C r -intercept is

= −C w

K Lr r

•

−( w r )

Slope of an isocost curve is the negative

of the input price ratio


7/26

Managerial EconomicsManagerial Economics

9-7

Isocost Cur$es (Figures 9.% & 9.)

l

l


8/26


9-8

'ptial Co#ination o! Inputs

• Two slopes are equal in equilibrium

• Implies marginal product per dollar spent on last

unit of each input is the same

Q

Q

inimi!e total cost of producing by

choosing the input combination on the

isoquant for which is "ust tangent to an

isocost curve

•

= = L L K

K

MP MP MP w

MP r w r or

M i l E i

M i l E i


9/26


9-9

'ptial Input Co#ination to iniie

Cost !or *i$en 'utput (Figure 9.+)

M i l E i

M i l E i


10/26


9-

'ptiiation & Cost

• ,-pansion path gives the efficient#least-cost$ input combinations forevery level of output

• "erived for a specific set of input prices• Along e#pansion path, input$price ratio is

constant & equal to the marginal rate of

technical substitution

M i l E i

M i l E i


11/26


9-

,-pansion Path (Figure 9.)

M i l E i

M i l E i


12/26


9-

Returns to "cale

• If all inputs are increased by a factor of c &

output goes up by a factor of then, ingeneral, a producer experiences:• Increasing returns to scale if ! % c ; output goes up

proportionatel more than the increase in inputusage

• "ecreasing returns to scale if ! c ; output goes upproportionatel less than the increase in input usage

• 'onstant returns to scale if ! ( c ; output goes up bthe same proportion as the increase in input usage

f(cL, cK) = zQ

M i l E i

M i l E i


13/26


9-

Long/Run Costs

• %ong-run total cost (LTC) for agiven level of output is given by:

LTC = wL0 + rK 0 )here w & r are prices of labor & capital,

respectivel, & (L0 , K 0 ) is the input combinationon the e#pansion path that minimi!es the totalcost of producing that output

M i l E i

M i l E i


14/26


9-

Long/Run Costs

• %ong-run average cost (LAC) measures thecost per unit of output when productioncan be ad"usted so that the optimal

amount of each input is employed• LAC is *$shaped

• +alling LAC indicates economies of scale

• Rising LAC indicates diseconomies of scale

=

LTC LAC

Q

M i l E i

M i l E i


15/26


9-

Long/Run Costs

• %ong-run marginal cost (LMC) measuresthe rate of change in long-run total cost asoutput changes along expansion path

• LMC is *$shaped• LMC lies below LAC when LAC is falling

• LMC lies above LAC when LAC is rising

• LMC = LAC at the minimum value of LAC

∆=

∆

LTC LMC

Q




16/26


9-

eri$ation o! a Long/Run Cost

"chedule (Ta#le 9.1) %east-cost combination of utput %abor

#units$'apital#units$

Total cost

#2 ( )*, r ( )+$

L3C LC

--

.--

/--

0--

1--

2--

3--

LC

-

2-

.0

0

0-

1-

/-

3

00

1-

4

-

.

20

50-

20-

./-

2-

0--

1--

30-

560-

-642

-671

-63-

-6/3

-63.

6-1

560-

60-

62-

-60-

-6/-

6--

6/-




17/26


9-

Long/Run Total4 3$erage4 &

arginal Cost

(Figure 9.9)




18/26


9-

Long/Run 3$erage & arginal

Cost Cur$es

(Figure 9.15)




19/26


9-

6arious "hapes o! L3C (Figure 9.11)




20/26


9-

Constant Long/Run Costs

• hen constant returns to scaleoccur over entire range of output

• +irm e#periences constant costs in thelong run

• LAC curve is flat & equal to LMC at alloutput levels




21/26


9-

Constant Long/Run Costs(Figure 9.1%)




22/26


9-

,conoies o! "cope

• .xist for a multi-product firm when the "oint cost of producing two or more goodsis less than the sum of the separate costs

of producing the two goods• /or two goods, X & Y , economies of scope

exist when:

C(X, Y) < C(X) + C(Y)

• 0iseconomies of scope exist when:

C(X, Y) > C(X) + C(Y)




23/26


9-

Relations 7et2een "hort/Run &

Long/Run Costs• LMC intersects LAC when the latter is at its

minimum point

• 1t each output where a particular ATC is

tangent to LAC , the relevant SMC = LMC

• /or all ATC curves, point of tangency with LAC is at an output less #greater$ than the

output of minimum ATC if the tangency isat an output less #greater$ than thatassociated with minimum LAC




24/26


9-

Long/Run 3$erage Cost as the

Planning 8orion (Figure 9.1)




25/26


9-

Restructuring "hort/Run Costs

• 2ecause managers have greatestflexibility to choose inputs in the longrun, costs are lower in the long run than

in the short run for all output levelsexcept that for which the fixed input isat its optimal level

• 8hort$run costs can be reduced b ad9ustingfi#ed inputs to their optimal long$run levelswhen the opportunit arises




26/26


9

Restructuring "hort/Run Costs (Figure 9.1+)

Chapter 09 Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter...

Documents

Transcript of Chapter 09 Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter 09Chapter...