6. Production - Fakultät für Wirtschaftswissenschaften · ... Microeconomics| Chapter 6 Slide 3 | Introduction •In this chapter, we will focus on the supply side. ... • The

6. Production

Literature:

Pindyck und Rubinfeld, Chapter 6

Varian, Chapter 18

| 23.05.2017 | Prof. Dr. Kerstin Schneider| Chair of Public Economics and Business Taxation | Microeconomics| Chapter 6 Slide 2 |

Chapter Outline

• Production Technology

• Production with One Input Variable (Labor)

• Production with Two Input Variables

• Returns to Scale


Introduction

• In this chapter, we will focus on the supply side.

• Theory of the firm:

– How does a firm minimize costs or maximize profits with

regard to its production decisions?

– How do costs vary with production?

– Characteristics of market supply.


The Technology of Production

• The production process

– The combination of inputs or production factors required

to produce a certain level of output.

• Factors of Production

– Labor

– Material

– Capital



• The Production function

– Function showing the highest output that a firm can

produce for each specified combination of inputs.

– Describes what is technically feasible when the firm

operates efficiently, i.e., when the firm uses each

combination of inputs as efficiently as possible.



• A production function with a given technology of two inputs

is as follows:

Q = F(K,L)

Q = Output, K = Capital, L = Labor


Production with One Variable Input (Labor)

Amount Amount Total Average Marginal

of Labor (L) of Capital (K) Output (Q) Product Product

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

8 10 112 14 0

9 10 108 12 -4

10 10 100 10 -8



• Note that

1) with each additional unit of labor, the quantity (Q)

produced increases, reaches a maximum, and then

decreases.



• Note that

2) The average product of labor ( ), initially

increases with each additional unit of labor until

reaching a global maximum after which it decreases

with each additional unit of labor.

L

Output QAP

Labor input L

LAP



• Note that

3) The marginal product of labor ( ), the additional

output produced with each additional unit of labor,

increases rapidly and later decreases and becomes

negative.

( , )L

Output Q F L KMP orLLlaborinput

LMP



Total Product

A: tangent to the total product

curve with slope = MP (20)

B: slope of 0B = AP (20)

C: slope of 0C= MP & AP

Labor per month

Output

per

month

60

112

0 2 3 4 5 6 7 8 9 10 1

A

B

C

D



Average Product

8

10

20

Output

per

month

0 2 3 4 5 6 7 9 10 1

30

E

Marginal Product

Note

To the left of E, MP > AP, and AP is increasing.

To the right of E, MP < AP, and AP is decreasing.

At point E, MP = AP, and AP is at its maximum.

Labor per month



• The principle that as the quantity of

an input increases while other inputs remain fixed,

the resulting additions to output (marginal output) will

eventually began to decrease with each additional

unit of the respective input.

The Law of Diminishing Marginal Returns

2

2

( , )0

F K LL



• If labor input is low, MP increases due to

specialization.

• If labor input is high, MP decreases due to inefficiency.

The Law of Diminishing Marginal Returns


The Effect of Technological Improvement

Labor per time period

Output per time

period

50

100

0 2 3 4 5 6 7 8 9 10 1

A

O1

C

O3

O2

B

Even though any given

production process

exhibits diminishing

returns to labor,

labor productivity

(output per unit of labor)

can increase if there

are improvements in

technology.


Malthus and the food crisis

• Malthus predicted that as both the marginal and average

productivity of labor fell and there were more mouths to

feed, mass hunger and starvation would result.

• Why was Malthus’ prediction wrong?


Index of World Food Production per Capita

1948-1952 100

1960 115

1970 123

1980 128

1990 138

1995 140

2001 161

Year Index



• The data shows that increases in production exceeded population growth.

• Malthus did not take technological improvements into account.

• Over the past century, technological improvements have dramatically altered food production in most countries (including developing countries, e.g., India).

• As a result, the average product of labor and total food

production have increased.

• Therefore, technological improvements can create

surpluses and reduce prices.



• Question:

– Why does hunger remain a severe problem in some areas

of the world?



• Labor Productivity

total outputAverage Productivity

total labor input



• Productivity and the standard of living

– Consumers—in the aggregate—can only increase their

rate of consumption in the long run by increasing the total

amount they produce. Understanding the causes of

productivity growth is an important area of research in

economics.

– Determinants of productivity of labor

Stock of capital

Technological change


Labor Productivity in Developed Countries

1960-1973 4.70 3.98 7.86 2.84 2.29

1974-1982 1.73 2.28 2.29 1.53 0.22

1983-1991 1.50 2.07 2.64 1.57 1.54

1992-2001 0.86 2.10 1.19 1.98 2.00

Annual Growth Rate of Labor (%)

FR D J UK US

$62.461 $66.369 $52.848 $52.499 $75.575

GDP PER CAPITA (IN 2001 US DOLLARS)


Production with Two Variable Inputs

• There is a relationship between production and

productivity.

• Both labor and capital are variable in the long run.

• Analyze isoquants and compare the different combinations

of K & L and the respective quantities produced.

• Do you see similarities to indifference curves?


The Isoquants

• Isoquants show the flexibility that firms have when

making production decisions: they can usually obtain a

particular output by substituting one input for another.

• This information allows the producer to react

effectively to market changes for inputs, e.g., changes

in price, quality, and availability.

Input flexibility


The Isoquants

• Short run:

• Short-run production refers to production that can

be completed when at least one factor of

production is fixed.

• These inputs are called fixed production factors.

• Long run:

– A period of time in which all factors of production and

costs are variable.

The Short and the Long Run


Production with Two Input Variables (L, k)

Labor per year

1

2

3

4

1 2 3 4 5

5

Q1 = 55

The isoquants are derived from the

production function for a quantity

produced of 55, 75, and 90,

respectively.

A

D

B

Q2 = 75

Q3 = 90

C

E

Capital

per year Isoquants



• Substituting among production factors (inputs):

– Managers need to determine what combination of inputs

to use in order to maximize production.

– Their main concern is the trade-off between inputs.

– The slope of each isoquant gives the trade-off between

two inputs, holding the amount of goods constant.



Substituting among production factors (inputs):

– The marginal rate of technical substitution (MRTS):

Ä /Änderung des ArbeitskräfteeinesatzesGRTS - nderung des Kapitaleinsatzes

(for a fixed level )

or

KMRTS QL

dKMRTSdL


Marginal rate of technical substitution

Labor per month

1

2

3

4

1 2 3 4 5

5 Capital

per year Like indifference curves,

isoquants are negatively sloped

and convex.

1

1

1

1

2

1

2/3

1/3

Q1 =55

Q2 =75

Q3 =90


Production with Two Input Variables

1) Increasing labor from 1 to 5 leads to a decrease in MRTS from 2 to 1/3.

2) The diminishing MRTS occurs due to decreasing marginal returns, which implies that isoquants are convex.

3) The MRTS and the marginal product

The result of a change in labor resulting from a

change in the quantity of goods is equal to

L(MP )( L)



• Note:


• The result of a change in the quantity of

goods resulting from a change in the quantity

of capital is equal to

K(MP )( K)



• Note:


If quantity is fixed ( ) and labor input

increases, then

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

L K(MP ) / (MP ) - ( K / L) MRTS

0Q



• Or also

( , ) ( , )0

0L K

L

K

F K L F K LdL dK

L K

MP dL MP dK

MP dK MRTSMP dL


Marginal rate of technical substitution

• Cobb-Douglas-Technology:

ba LK)L,K(FQ

Thus, ba LaK

K

F 1

.LbK

L

F ba 1

and

The marginal rate of technical substitution is

.aL

bK

LaK

LbK

K/F

L/F

dL

dKba

ba

1

1


Isoquants when Inputs are perfect Substitutes

Labor

per month

Capital

per

month

Q1 Q2 Q3

A

B

C


Fixed-proportions production function (perfect complements)

Labor per month

Capital per

month

L1

C1 Q1

Q2

Q3

A

B

C


Example: A Production Function for Wheat

• Farmers must choose between a capital-intensive and

labor-intensive production function.


Isoquants describing the Production of Wheat

Labor

(hours per year)

Capital

(machine

hours per

year)

250 500 760 1000

40

80

120

100

90

Output = 13,800 Bushels

per year

A

B 10- K

260 L

Point A is more capital-intensive.

Point B is more labor-intensive.



• Note

1) For production in A

L = 500 hours and K = 100 machine hours).

2) For production in A

If we increase L to 760 and decrease K to 90, then

𝑀𝑅𝑇𝑆 = −

Δ𝐾

Δ𝐿= −

10

260= 0.04



• Note

3) MRTS < 1, this means that the cost for labor is less than that of capital, otherwise we would have replaced labor with capital.

4) If labor is costly, then the farmer will substitute labor for more capital (e.g., in the USA).

5) If labor is cheap, then the farmer will substitute his capital for more labor (e.g., in India).


Returns to Scale

• Returns to scale: rate at which output increases as inputs

increase proportionately.

1) Increasing returns to scale: situation in which output

more than doubles when all inputs are doubled.

A larger quantity of goods is associated with lower

costs (cars).

One company is more efficient than many companies

(public utilities).

The distance between the isoquants becomes

smaller.


Returns to Scale

Labor (hours)

Capital

(machine

hours)

10

20

30

Increasing returns to scale: the

isoquants move closer together as

inputs increase along line A.

5 10

2

4

0

A


Returns to Scale

2) Constant returns to scale: Situation in which output doubles when all inputs are doubled.

Size does not affect productivity.

There may be a large number of producers.

The distance between the isoquants is constant.


Returns to Scale

Labor (hours)

Capital

(machine

hours)

Constant returns to

scale: isoquants are

equally spaced,

since output

increases

proportionally.

10

20

30

15 5 10

2

4

0

A

6


Returns to Scale

3) Decreasing returns to scale: Situation in which output less than doubles when all inputs are doubled.

Efficiency decreases as size increases.

Reduces the firm’s production abilities.

The distance between the isoquants increases.


Returns to Scale

Labor (hours)

Capital

(machine

hours)

Decreasing returns to

scale: the distance

between the isoquants

increases.

10

20

30

5 20

2

8

0

A


Returns to Scale: Formula

For an input bundle, (K,L), we have the following:

( , ) ( , )F tK tL tF K L

Then we can say that this function has constant returns to

scale.

Example: t = 2; doubling the input leads to doubling the

output.




( , ) ( , )F tK tL tF K L

We can say that this function has increasing returns to

scale.

Example: t = 2; doubling the input leads to more than double

the output.




( , ) ( , )F tK tL tF K L

Then we can say that this function has decreasing returns

to scale.

Example: t = 2; doubling the input leads to less than

double the output.


Returns to Scale

y = f(x)

x

y

Decreasing returns

to scale

Increasing

returns to scale

A technology can have—locally—different returns to scale.


Returns to Scale, Cobb-Douglas

a bQ K L

Cobb-Douglas Production function:

Increase all input quantities proportionately by t:

( ) ( )

.

a b

a b a b

a b a b

a b

tK tL

t t K L

t K L

t Q


Returns to Scale

The Cobb-Douglas Production function is

.LKQ ba

.Qt)tL()tK( baba

The returns to scale of a Cobb-Douglas

technology are constant when a + b = 1,

increasing when a + b > 1, and decreasing when

a + b < 1.


Concluding Remarks

• A production function describes the maximum output that a

company can produce given any particular input

combination.

• An isoquant is a curve representing all input combinations

with which a given level of output can be achieved.


Concluding Remarks

• The average product of labor measures the productivity of

the average unit of labor, whereas the laborer's marginal

product measures the productivity of the last added unit of

labor.

• The law of decreasing marginal returns states that the

marginal product of an input ultimately decreases as its

quantity increases, ceteris paribus.

• Isoquants are always negatively sloped, because the

marginal product of all inputs is positive.

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6. Production - Fakultät für Wirtschaftswissenschaften · ... Microeconomics| Chapter 6 Slide 3 | Introduction •In this chapter, we will focus on the supply side. ... • The