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10.1

Chapter 10 Theory of Production

and Cost in the Long Run(LR)j The theory of production in the LR provides the

theoretical basis for firm decision-making and LRcosts and supply.

j In essence, we will assume that the firms goal isto maximize output subject to a cost constraint.We will see that this is the same as minimizing thecost of producing a given level of output.

j Keep in mind that all inputs are variable in the LRplant size can be changed,

new locations can be chosen

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10.2

Production Isoquants

jAn isoquant is a locus of points indicating

different combinations of 2 inputs each of

which yields the same level of output.jNote 2 inputs are assumed since we desire

to present model graphically.

),( KLfQ !

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10.3

Characteristics of Isoquants

jNegative slope tradeoffs, if more of L

then less of K if output is held constant

jConvex to the origin diminishing MRTS,the more of L you have relative to K the

more able you are to trade L for K and hold

output constant.

j Isoquants cannot intersect

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10.4

Marginal Rate of Technical

SubstitutionjTheMRTS is the (negative of the) slope of

the isoquant. Therefore it reflects

L

KMRTS

(

(!

It is a measure of the number of units of K that must be

given up if L is increased by a single unit, holding output

constant. Note it will diminish as we move down an

isoquant.

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10.5

Concept of an Isoquant Map

jGraph of several isoquants each

representing different levels of output.

jThe higher (further from the origin) anisoquant, the greater the level of output.

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10.6

Marginal Product and MRTS

jMarginal product of an input is the change

in total product in response to increasing the

variable input by a single unit.jThe change in total product is given by the

following equation

)()( KMPLMPQ KL (y(y!(

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10.7

Marginal Product and MRTS

Along an isoquant the change in output is equal to zeroand

MRTSMP

MP

LK

LMPKMP

KMPLMP

K

L

LK

KL

!!(

(

(y!(y

(y(y!

)()(

)()(0

)()( KMPLMPQ KL (y(y!(

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10.8

The Cost Constraint Isocost

Linesj Suppose you have $100, C, to spend on two inputs, L & K, and the prices of each are $10, PL, and

$20, PK, respectively. Determine the equation

relating K to L reflecting your budget constraint.j 100 = 10L+20K or

j K=5-0.5L

j In general, the cost constraint is

j K = C/PK-(PL/PK)L

jNote linear and slope is ratio of prices

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10.9

Changes in Isocost

jWhat happens to the isocost if cost, C,

changes?

jWhat happens to budget line if one of theprices change?

jK = C/PK-(PL/PK)L, w=PL, r=PK,C-bar =

cost level then isocost is

Lr

w

r

CK !

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10.10

Change in Cost

Y

X10

5

Budget line I C=100, PX=10, PY=20

Budget Line II C=140, Prices same

I

14

7

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10.11

Change in Price

K

L10

5

Isocost I C=100, PL=10, PK=20

Isocost II C=100, PL=20, PK=20

I

14

7

5

II

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10.12

Determining the Optimal

Combination of InputsjProducers goal is to maximize profits:

Minimize cost of producing a constant level ofoutput

Maximize output subject to a cost constraint

jThe isocost line shows what combinationsof L and K that the producer is able to

purchase with a fixed cost level.jThe isoquant map shows the producers

preferences for X and Y.

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10.13

Minimizing Cost of Producing a

Given Level of OutputjThe Optimal Solution, where the producer

minimizes cost subject to an output

constraint, is found where the isocost line is

tangent to an isoquant. Since isoquants

cannot intersect this will be the highest

possible level of utility given the constraint.

jSee Figure 10.4 page 366.

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10.14

Cost Minimization

j At any tangency point the slopes of the two

relationships must be equal.

j Slope of isoquant is the MRTS the rate the

producer is willing to substitute K for L, holdingoutput constant.

j Slope of isocost line is the ratio of prices, PL/PK,

which reflects the rate the producer is able tosubstitute K for L and maintain constant cost.

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10.15

Cost Minimization

K

L

P

P

MRTS!

Rate willing to sub = Rate able to sub

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10.16

Cost Minimization

jRecall the Marginal Product interpretation

of the MRTS or slope of the isoquant. Note

PL

= w and PK

= r in text.

K

K

L

L

K

L

K

L

P

MP

P

MP

P

P

MP

MPMRTS

!

!!

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10.17

Equilibrium for the Firm

jA producer is hiring 20 units of labor and 6units of capital (bundle A). The price of laboris $10, the price of capital is $2, and at A, the

marginal products of labor and capital areboth equal to 20.

j Is the firm in equilibrium?

j No, MP to price ratios are not equal, should

use more capital and less labor.j Beginning at A, what happens to output and

cost if the producer increases labor by oneunit and decreases capital by 1 unit?

j Output remains constant and cost increases

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10.19

Expansion Path

jAn expansion path is a curve that shows the

least costly combination of two inputs

required to produce each level of output,

holding the input price ratio constant.

jSee Figure 10.6, page 373.

jAlong an expansion path,

K

K

L

L

K

L

K

L

P

MP

P

MP

P

P

MP

MPMRTS

!

!!

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10.20

Expansion Path

K

K

L

L

K

L

K

L

P

MP

P

MP

PP

MPMPMRTS

!

!!

The following is always true along an expansion

path.

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10.21

Cost Curve Derived from

Expansion Pathj Since the Expansion Path plots points the optimalcombination of inputs required to produce eachlevel of output, total cost for each level of output

can be determined since it is assumed that theprices of inputs are fixed.

j Thus, if the optimal quantity of labor and capitalto produce 100 units of output are 10 and 5respectively, and the wage rate is $20 and price ofcapital, $50 then the total cost is

$20(10) + $50(5) = $450

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10.22

Returns to Scale

j Returns to Scale deals with the impact on output

of a change in the scale(proportional changes in all

inputs) of a firms operations.

j Returns to scale can be classified as Constant: output changes proportionately to the change

in the inputs

Increasing: output changes more than proportionate to

the change in the inputs

Decreasing: output changes less than proportionate to

the change in the inputs

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10.24

Long Run Costs

jThe long run average, LAC, and marginal,LMC, cost curves have the same basicshape that the equivalent short run cost

curves.jHowever, the reason why each is U-shaped

is for different reasons, which are

Short run the Law of Diminishing Marginalreturns

Long run economies/diseconomies of scale

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10.25

Economies of Scale

jEconomies of Scale exist when LAC

decreases as output increases.

jDiseconomies of Scale exist when LACincreases as output increases.

Q

LAC

economies diseconomies

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10.27

Economies of Scope

jScope economies exist if the joint costs of

producing two or more products is less than

the separate costs of producing each

individually.

jAn example might be an auto air

conditioning repair shop that adds

radiator/cooling system repairs

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10.28

Relationship between SR and LR

Cost CurvesjThe LAC curve is a locus of points on SAC

curves, which represent the most efficient

(cost effective) way of producing each level

of output given that the firm has the

opportunity and ability to change the

quantity of any and all inputs.

jSee Figure 10.14 page 391.