(pp. 199 - 207) Diminishing Returnsyamamoto/files/May_30-1.pdf · Diminishing Returns (pp. 199 -...

Chapter 6 1©2005 Pearson Education, Inc.

Diminishing Returns (pp. 199 - 207)

Labor per year1 2 3 4 5

Increasing laborholding capital

constant (A, B, C)OR

Increasing capitalholding labor constant

(E, D, C

q1 = 55

q2 = 75

q3 = 90

1

2

3

4

5Capitalper year

D

E

A B C


Production: Two Variable Inputs (pp. 199 -207)

�Substituting Among Inputs�Companies must decide what combination of

inputs to use to produce a certain quantity ofoutput

�There is a trade-off between inputs, allowingthem to use more of one input and less ofanother for the same level of output (Do youknow the Luddites in England in the early19th century?)



�Substituting Among Inputs�Slope of the isoquant shows how one input

can be substituted for the other and keep thelevel of output the same

�The negative of the slope is the marginalrate of technical substitution (MRTS)� Amount by which the quantity of one input can

be reduced when one extra unit of another inputis used, so that output remains constant



� The marginal rate of technicalsubstitution equals:

)( qLKMRTS

InputLaborinChange

InputCapitalinChangeMRTS

of level fixed a forΔΔ−=

−=


Production: Two Variable Inputs(pp. 199 - 207)

�As labor increases to replace capital�Labor becomes relatively less productive

�Capital becomes relatively more productive

�Need less capital to keep output constant

�Isoquant becomes flatter (convex to theorigin)

q = L K


Marginal Rate ofTechnical Substitution (pp. 199 - 207)

Labor per month

1

2

3

4

1 2 3 4 5

5Capital per year

Negative Slope measuresMRTS;

MRTS decreases as move downthe indifference curve

1

1

1

1

2

1

2/3

1/3

Q1 =55

Q2 =75

Q3 =90


MRTS and Marginal Products (pp. 199 - 207)

� If we increase labor and decrease capitalto keep output constant, we can see howmuch the increase in output is due to theincreased labor�Amount of labor increased (i.e., ΔL positive)

times the marginal productivity of labor

))(( LMPL Δ=



�Similarly, the decrease in output from thedecrease in capital can be calculated�Decrease in output from reduction of

capital(ΔK is negative) times the marginalproduce of capital

))(( KMPK Δ=



� If we are holding output constant, the neteffect of increasing labor and decreasingcapital must be zero

�Using changes in output from capital andlabor we can see

0 K))((MP L))((MP KL =Δ+Δ



�Rearranging equation, we can see therelationship between MRTS and MPs

MRTSK

L

MP

L

K

=Δ

Δ−=

Δ=Δ

=Δ+Δ

)(

)

))(

L

KL

KL

(MP

K))((MP- (MP

0 K))((MP L))((MP


Isoquants: Special Cases (pp. 199 - 207)

� Two extreme cases show the possiblerange of input substitution in production

1. Perfect substitutes� MRTS is constant at all points on isoquant

� Same output can be produced with a lot ofcapital or a lot of labor or a balanced mix


Perfect Substitutes (pp. 199 - 207)

Laborper month

Capitalper

month

Q1 Q2 Q3

A

B

C

Same output can bereached with mostlycapital or mostly labor(A or C) or with equalamount of both (B)


Isoquants: Special Cases (pp. 199 - 207)

2. Perfect Complements� Fixed proportions production function

� There is no substitution available betweeninputs

� The output can be made with only a specificproportion of capital and labor

� Cannot increase output unless increaseboth capital and labor in that specificproportion


Fixed-ProportionsProduction Function (pp. 199 - 207)

Labor per month

Capitalper

month

L1

K1Q1

A

Q2

Q3

B

C

Same output canonly be producedwith one set ofinputs.


A Production Function forWheat (pp. 199 - 207)

� Farmers can produce crops with differentcombinations of capital and labor�Crops in US are typically grown with capital-

intensive technology

�Crops in developing countries grown withlabor-intensive productions

�Can show the different options of cropproduction with isoquants


A Production Function forWheat: Ex. 6-3 (pp. 199 - 207)

�Manager of a farm can use the isoquantto decide what combination of labor andcapital will maximize profits from cropproduction�A: 500 hours of labor, 100 units of capital for

13,800 bushels per year�B: decreases units of capital to 90, but must

increase hours of labor by 260 to 760 hours�This experiment shows the farmer the shape

of the isoquant


Isoquant Describing the Productionof Wheat : Ex. 6-3 (pp. 199 - 207)

Capital

Labor250 500 760 1000

40

80

120

10090

Output = 13,800 bushels per year

A

10- K =ΔB

260 L =Δ

Point A is more capital-intensive, and

B is more labor-intensive.


A Production Function for Wheat :Ex. 6-3 (pp. 199 - 207)

� Increase L to 760 and decrease K to 90the MRTS =0.04 < 1

04.0)260/10( =−−=ΔΔ= L

K- MRTS

�When wage (i.e.,cost of labor) is equal tocost of running a machine, more capitalshould be used

�Unless labor is much less expensive thancapital, production should be capital intensive


Returns to Scale (pp. 207 - 210)

� In addition to discussing the tradeoffbetween inputs to keep production thesame

�How does a firm decide, in the long run,the best way to increase output?�Can change the scale of production by

increasing all inputs in proportion

�If double inputs, output will most likelyincrease but by how much?



�Rate at which output increases as inputsare increased proportionately�Increasing returns to scale

�Constant returns to scale

�Decreasing returns to scale



� Increasing returns to scale: outputmore than doubles when all inputs aredoubled�Larger output associated with lower cost

(cars)

�One firm is more efficient than many(utilities)

�The isoquants get closer together


Increasing Returns to Scale (pp. 207 - 210)

10

20

30

The isoquantsmove closertogether

Labor (hours)5 10

Capital(machine

hours)

2

4

A



�Constant returns to scale: outputdoubles when all inputs are doubled

� Size does not affect productivity

� May have a large number of producers

� Isoquants are equidistant apart



ConstantReturns:

Isoquants areequally spaced

20

30

Labor (hours)155 10

A

10

Capital(machine

hours)

2

4

6



�Decreasing returns to scale: outputless than doubles when all inputs aredoubled

� Decreasing efficiency with large size

� Reduction of entrepreneurial abilities

� Isoquants become farther apart

Exercise: Problem 8 on page 212. (To beincluded in your HW)



Labor (hours)

Capital(machine

hours)

Decreasing Returns:Isoquants get further apart

10

10

4

A

18

5

2


Returns to Scale: Carpet IndustryEx. 6-4 (pp. 207 - 210)

� The carpet industry has grown from a small industry to alarge industry with some very large firms

� There are four relatively large manufacturers along with anumber of smaller ones

� Growth has come from� Increased consumer demand

� More efficient production reducing costs

� Innovation and competition have reduced real prices


The U.S. Carpet Industry (pp. 207 - 210)


Returns to Scale: Carpet Industry(pp. 207 - 210)

�Some growth can be explained byreturns to scale

�Carpet production is highly capitalintensive�Heavy upfront investment in machines for

carpet production

� Increases in scale of operating haveoccurred by putting in larger and moreefficient machines into larger plants


Returns to Scale: Carpet IndustryResults (pp. 207 - 210)

1. Large Manufacturers� Increases in machinery and labor

� Doubling inputs has more than doubledoutput

� Economies of scale exist for largeproducers


Returns to Scale: Carpet IndustryResults (pp. 207 - 210)

2. Small Manufacturers� Small increases in scale have little or no

impact on output

� Proportional increases in inputs increaseoutput proportionally

� Constant returns to scale for smallproducers


Returns to Scale: Carpet Industry (pp.207 - 210)

From this we can see that the carpetindustry is one where:

1. There are constant returns to scale forrelatively small plants

2. There are increasing returns to scale forrelatively larger plants� These are limited, however

� Eventually reach decreasing returns

(pp. 199 - 207) Diminishing Returnsyamamoto/files/May_30-1.pdf · Diminishing Returns (pp. 199 -...

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