Chapter 7Production Theory

Production Function

A table, graph, or equation showing the maximum output rate of the product that can be achieved from any specified set of usage rates of inputs

Production FunctionThomas Machine Company

Amount of Labor Output of Parts AP Labor MP Labor(annual # units) (hundreds/year)

1 12 12.0 12 27 13.5 153 42 14.0 154 56 14.0 145 68 13.6 126 76 12.7 87 76 10.9 08 74 9.3 -2

Production FunctionThomas Machine Company

0

20

40

60

80

0 2 4 6 8 10

Labor

Par

ts

Production FunctionThomas Machine Company

-5

0

5

10

15

20

0 5 10

Labor

Par

ts AP Labor

MP Labor

Law of Diminishing Marginal Returns

If equal increments of an input are added to a production process, and the quantities of other inputs are held constant, eventually the marginal product of the input will diminish

Note: 1) This is an empirical generalization.

2) Technology remains fixed.

3) The quantity of at least one input is

held fixed.

Law of Diminishing Returns

Law of Diminishing Returns: as more units of a variable resource are applied to a fixed resource, output will eventually increase by a smaller and smaller amount.

Product Curves

Total Product: total output of a good associated with different levels of a variable input.

Marginal Product: the change in total product due to a one unit increase in variable input.

Average Product: Total product divided by the number units of the variable input.

Total Product

0

TotalProduct

54321

• As units of variable input (labor) are added to a fixed input, total product will increase . . .

20

30

40

50

60

70

80

10

6 7 8

0

9 10

AverageProduct

MarginalProduct

TotalProduct(Output)

Units of Variable

Resource

1 8 2 20 3 34 4 46 5 56 6 64 7 70 8 74 9 75

10 73

• First at an increasing rate . . . • Then at a declining rate . . . • Note that the Total Product curve is smooth, indicating that labor can be increased by amounts of less than a single unit (it is a continuous function).

Quantity of Labor

Law of Diminishing Returns

Average Product

Marginal Product

0

Average and/or Marginal Product

54321

• The Marginal Product curve will initially increase (when TPC is increasing at an increasing rate), reach a maximum, and then decrease (as TPC increases at a decreasing rate).

4

8

12

16

6 7 8

0

9 10

AverageProduct

MarginalProduct

TotalProduct(Output)

Units of Variable

Resource

1 8 2 20 3 34 4 46 5 56 6 64 7 70 8 74 9 75

10 73

-----8

12141210 8 6 4 1- 2

-----8

1011.311.511.210.7109.38.37.3

• The Average Product curve will have the

same general form except that its maximum point will be at a higher output level.

Important Note : MP always crosses AP at its maximum point.

Quantity of Labor

Law of Diminishing Returns

Average Product

Marginal Product

AP & MP

Quantity of Labor

54321

4

8

12

16

6 7 8 9 10

Total Product

TP

54321

20

30

40

50

60

70

80

10

6 7 8 9 10Quantity of Labor

• Graphed together, one can see the relationship between the TP, MP, and AP curves more clearly.

Law of Diminishing Returns

Marginal Revenue Product

The amount that an additional unit of the variable input adds to the firm’s total revenue

MRPY = TR/Y

Marginal Expenditure

The amount that an additional unit of the variable input adds to the firm’s total costs.

MEY = TC/Y

Optimal Level of Input Use

MRPY = MEY

Production Functions with Two Variable Inputs

Number of Machine ToolsAmount of Labor 3 4 5 6

1 5 11 18 242 14 30 50 723 22 60 80 994 30 81 115 1255 35 84 140 144

1 2 3 4 5

Number ofMachine Tools

0

50

100

150

Labor

Q = f (Labor, Machine Tools)

Isoquant

A curve showing all possible (efficient) combinations of inputs that are capable of producing a certain quantity of output

Iso quant

same quantity

Labor

Capital

0

K2

100

200

300K1

L2 L1

Marginal Rate of Technical Substitution

Shows the rate at which one input can be substituted for another input, if output remains constant. (Slope of the isoquant.)

Given Q = f(X1, X2)

MRTS = -X2 / X1

= -MP1 / MP2

Isocost Curves

Various combinations of inputs that a firm can buy with the same level of expenditure

PLL + PKK = M

where M is a given money outlay.

Labor

Capital

0

M/PK

M/PL

Slope = -PK /PL

Maximization of Output for Given Cost

Labor

Capital

0100

200300

R

MPL/PL = MPK/PK

Labor

Capital

0100

200300

R

Returns to Scale

If the firm increases the amount of all inputs by the same proportion:

Increasing returns means that output increases by a larger proportion

Decreasing returns means that output increases by a smaller proportion

Constant returns means that output increases by the same proportion

Output Elasticity

The percentage change in output resulting from 1 percent increase in all inputs.

> 1 ==> increasing returns< 1 ==> decreasing returns= 1 ==> constant returns

Three Types of Statistical Analysis

Time series dataCross section dataTechnical information