microéconomie, chapter 6 - cescermsem.univ-paris1.fr/davila/teaching/sbs/ch06_pindyck-09.pdf · 4...

1 Solvay Business School – Université Libre de Bruxelles

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Production

Microéconomie, chapter 6


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List of subjets

 Production technology

 Production with a single input (labor)

 Isoquants

 Production with two inputs (labor and capital)

 Returns to scale


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The production decision of the firm

1.  It depends on the available technology   How can inputs be transformed into outputs

  inputs: labor, capital, raw materials…   outputs: cars, furniture, books…

  Different bundles or inputs deliver different amounts of outputs


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2.  It depends also on the production costs   The firm takes into account the prices of

capital, labor, and other inputs   The firm will produce, whatever she

chooses, at a minimum cost given technology and the inputs prices   If capital is much more expensive than labor,

the firm can choose to produce the chosen level of output with more labor and less capital.


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3.  The firm maximizes profits   Given the minimum cost of producing any

given level of output, the firm chooses the level of output that maximizes profits


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The technology of production

 The production function:  Gives the maximum output (q) the can be

produced with each bundle of inputs  Describes what is technologically feasible

using inputs efficiently  We will consider two inputs only: labor (L)

and capital (K)


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 The production function with two inputs: q = F(K,L)

 The level of output (q) depends on the amount of capital (K) and labor (L) used


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 Short run and long run  Adjusting the level of some inputs takes

longer the for other inputs  The firm must consider both which inputs to

adjust and over what time horizon  It needs to distinguish between short run and

long run


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 Short run  At least one input is a fixed input

 Long run  Horizon beyond which no input is fixed, all

inputs are variable inputs


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Production with one input

 In the short run only one input can be adjusted

 say capital is fixed and labor is variable  Output can be increased increasing labor

only


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Production with one input L K q 0 10 0 1 10 10 2 10 30 3 10 60 4 10 80 5 10 95 6 10 108 7 10 112

  Without labor output is zero

  The first units of labor are increasingly productive

  Additional units of labor are less and less productive


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 The average productivity of labor measures the contribution, on average, of each unit of labor to producing output

€

PML = outputlabor

=qL


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 The marginal productivity of labor measures the contribution of an additional unit of labor to the production of output

€

PMgL = ΔoutputΔlabor

=ΔqΔL


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L K q q/L dq/dL 0 10 0 - - 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4


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labor

output

0 2 3 4 5 6 7 8 9 10 1

Total output

60

112

A

B

C

D


80

30


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labor

output

0 2 3 4 5 6 7 8 9 10 1

60

112

A

B

C

D


Marginal productivity at B

Average productivity at B

Total output 80

30


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Production with one input In the previous example,  As labor increases beyond 3 units, output

increases less and less  At low levels of L additional units allow for a

better use of installed capital and thus the marginal productivity of labor is increasing

 At high levels of L additional units prevent from an efficient use of instaled capital and thus the marginal productivity of labor is decreasing


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Law of decreasing marginal returns

 As a factor increases, while others remain fixed, the corresponding increases in output become beyond some point smaller and smaller


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Law of decreasing marginal returns

  It is a consequence of some inputs being fixed in the short run

  assumes a constant capital stock  The productivity of labor increases with the stock of

capital   assumes constant technology

 Technical progress increases the output that can be obtained from each combination of inputs

 The productivity of labor increases with technical progress


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Capital accumulation

A higher capital stock increases the level of output at each level of

labor

labor

output

0 2 3 4 5 6 7 8 9 10 1

112

A

B

C

D

A’

B’

C’

D’

Increase in the stock of capital


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Technical progress

Technical progress increases the marginal

and average productivity of labor at

every level

labor

output

0 2 3 4 5 6 7 8 9 10 1

60

112

A

B

C

D

A’

B’

C’

D’

Technical progress


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Productivity of labor

  Wages (i.e. living standards) and productivity are directly linked   When firms maximize profits, inputs are

remunerated by their marginal productivity   Wages can increase only if labor productivity

increases   Labor productivity increases if

1.  the stock of capital increases 2.  there is technological progress


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1.  The increase in the stock of capital was the main source of the increase in labor productivity

2.  The postwar rate of growth of labor productivity in Europe was higher than in the US since the rate of capital accumulation was also higher, due to the reconstruction effort


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Production with two inputs

 In the long run firms can produce a given level of output with different combinations of labor and capital


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1 2 3 4 5 1 20 40 55 65 75 2 40 60 75 85 90 3 55 75 90 100 105 4 65 85 100 110 115 5 75 90 105 115 120

labor

capital


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 Isoquants link all the inputs combinations that allow to produce a given level of output


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Isoquants

labor 1 2 3 4 5

Example: 55 units of output can be

produced both with 3K and 1L (pt. A)

or 1K and 3L (pt. D)

q1 = 55 q2 = 75

q3 = 90

1

2

3

4

5 capital

D

A


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Decreasing returns

labor 1 2 3 4 5

For a given level of capital, labor has decreasing

returns (A, B, C)

q1 = 55 q2 = 75

q3 = 90

1

2

3

4

5 capital

A B C


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Decreasing returns of labor with a constant capital:

 If capital stays constant at 3 and labor increases 0 to 1, 2, and 3, then output increases at a decreasing rate (55, 20, 15)


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Decreasing returns

labor 1 2 3 4 5

Capital has decreasing returns, for a given level of

labor (C, D, E)

q1 = 55 q2 = 75

q3 = 90

1

2

3

4

5 capital

D

E

C


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Decreasing returns of capital with a constant labor:

 If labor stays constant at 3 and labor increases 0 to 1, 2, and 3, then output increases at a decreasing rate (55, 20, 15)


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 Inputs substitution  Firms can choose the combination of inputs

to produce any given level of output  A decrease in one input requires and

increase in the other input to keep output constant


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 Inputs substitution  The slope of each isoquant is the rate at

which inputs can be substituted at a given level of output

 The (absolute value of the) slope is the marginal rate of technical substitution (MRTS)   It is the increase in one input needed to

compensate a decrease in one unit of the other input in order to keep output constant


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 Marginal rate of technical substitution:

€

TMST = −variation of capitalvariation of labor

= −ΔK ΔL (q constant)


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Marginal rate of technical substitution

labor

1

2

3

4

1 2 3 4 5

5 capital The MRTS decreases along the

isoquant 2

1

1

1

2/3 1

Q1 =55

Q2 =75

Q3 =90


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 As labor substitutes capital  Labor becomes relatively less productive  Capital becomes relativively more productive  Less capital is needed to substitute one unit

of labor at constant output  The slope of the isoquant becomes smaller

(in absolute value)


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MRTS and decreasing marginal returns

 In the example, increasing labor from 1 to 4 decreases the MRTS from 2 to 1/3

 The decrease in the MRTS is a consequence of the decreasing marginal returns of inputs

 Why?


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 Assume labor increases and capital decreases so that output remains constant

 The change in output due to the change in labor is:

€

MgPL ⋅ ΔL


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 Assume labor increases and capital decreases so that output remains constant

 The change in output due to the change in capital is:

€

MgPK ⋅ ΔK


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 Since output does not change, both changes must compensate, i.e.

€

MgPL ⋅ ΔL + MgPK ⋅ ΔK = 0

€

MgPL

MgPK= −

ΔLΔK MRTS =


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Isoquants: special cases

  Tow special cases of inputs substitution 1.  Perfect substitutes

  The MRTS is constant


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labor

capital

Q1 Q2 Q3

A

B

C

Perfect substitutes Capital and labor substitute each other always at the same rate


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2.  Perfect complements   Inputs must be used in fixed proportions   There is no possible substitution between

inputs


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labor

capital

L1

K1 Q1 A

Q2

Q3

B

C

Perfect complements capital and labor must be used always in the same proportions


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Returns to scale

 Its the rate at which output increases as inputs increase by a common factor

 Returns to scale can be  Increasing  constant  decreasing


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Increasing returns to scale

 Output increases more than proportionally than inputs  when mass production is more efficient (e.g.

cars)  when a single supplier is more efficient

(utilities, natural monopolies)


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10

20 30

Output levels of the isoquants

increase quickly

labor 5 10

capital

2

4

A

Increasing returns to scale


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 Output increases in the same proportion than inputs

Constant returns to scale


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Output levels of the isoquants increase at a regular pace

20

30

labor 15 5 10

10

capital

2

4

6 A

Constant returns to scale


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 Output increases less than proportionally than inputs  Efficiency decreases with the output level

Decreasing returns to scale


52 labor

capital

Output levels of the isoquants

increase slowly

10

20

10

4

A

5

2

Decreasing returns to scale

microéconomie, chapter 6 - cescermsem.univ-paris1.fr/davila/teaching/sbs/ch06_pindyck-09.pdf · 4...

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