1. Chapter 7 Production Theory

2. 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

3. Production Function Thomas Machine Company

4. Production Function Thomas Machine Company

5. Production Function Thomas Machine Company

6. 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.

7. 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.

8. 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.

9. Law of Diminishing Returns
As units of variable input (labor) are added to a fixed input, total product will increase . . .
Law of Diminishing Returns
Total Product
Total Product
First at an increasing rate . . . 80
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). 70 60
Units of Variable Resource
Total Product (Output)
Marginal Product
Average Product 50 40 1 8 2 20 30 3 34 4 46 5 56 20 6 64 7 70 10 8 74 9 75 1 2 3 4 5 6 7 8 9 10 10 73
Quantity of Labor

10. Law of Diminishing Returns
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).
Law of Diminishing Returns
Average and/or Marginal Product 16
Marginal Product
The Average Product curve will have the same general form except that its maximum point will be at a higher output level. 12
Average Product
Units of Variable Resource
Total Product (Output)
Important Note : MP always crosses AP at its maximum point.
Marginal Product
Average Product
-----
----- 8 1 8 8 8 2 20 12 10 3 34 14
11.3 4 46 12
11.5 4 5 56 10
11.2 6 64 8
10.7 7 70 6 10 8 74 4
9.3 9 75 1
8.3 1 2 3 4 5 6 7 8 9 10 10 73
- 2
7.3
Quantity of Labor

11. Law of Diminishing Returns
Graphed together, one can see the relationship between the TP, MP, and AP curves more clearly.
Law of Diminishing Returns
Average Product
Marginal Product
AP & MP
Quantity of Labor 5 4 3 2 1 8 12 16 6 7 9 10
Total Product TP 20 30 40 50 60 70 80

12. Marginal Revenue Product
The amount that an additional unit of the variable input adds to the firm’s total revenue
MRPY = DTR/DY

13. Marginal Expenditure MEY = DTC/DY
The amount that an additional unit of the variable input adds to the firm’s total costs.
MEY = DTC/DY

14. Optimal Level of Input Use
MRPY = MEY

15. Production Functions with Two Variable Inputs

16. Q = f (Labor, Machine Tools)

17. Isoquant
A curve showing all possible (efficient) combinations of inputs that are capable of producing a certain quantity of output
Iso quant
same quantity

18. Capital K2
300 K1
200
100
Labor L2 L1

19. 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 = -dX2 / dX1
= -MP1 / MP2

20. 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.

21. Capital
M/PK
Slope = -PK /PL
Labor
M/PL

22. Maximization of Output for Given Cost
Capital R
300
200
100
Labor

23. MPL/PL = MPK/PK
Labor
Capital
100
200
300 R

24. 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

25. Output Elasticity
The percentage change in output resulting from 1 percent increase in all inputs.
e > 1 ==> increasing returns
e < 1 ==> decreasing returns
e = 1 ==> constant returns

26. Three Types of Statistical Analysis
Time series data
Cross section data
Technical information