1. Chapter 5: Production and Cost
Brickley, Smith, and Zimmerman, Managerial Economics and Organizational Architecture, 4th ed.
Chapter 5: Production and Cost

2. Production and cost objectives
Students should be able to
Write a production function and distinguish between returns to scale and returns to a factor
Use isocosts and isoquants to illustrate production trade-offs
Employ short- and long-run cost curves to describe firm characteristics

3. Production functions
A production function specifies maximum output from given inputs:

4. Empirical production functions
Cubic
Q=a0+a1XY+a2X2Y+a3XY2+a4X3Y+a5XY3
Cobb-Douglas
Q = aXbYc
log Q = log a + b log X + c log Y

5. Returns to scale
Defined: The relation between output and a proportional variation of all inputs together
Increasing returns to scale: Q=KL
Decreasing returns to scale: Q=K1/3L1/3
Constant returns to scale: Q=K1/2L1/2

6. Returns to a factor
Returns to a factor refer to the relation between output and variation in only one input
Total product
Average product Q/L
Marginal product Q/L

7. Production function: Q=S1/2A1/2
Returns to a factor
Production function: Q=S1/2A1/2 S A Q
MPS
APS 1 9
3.00 2
4.24
1.24
2.12 3
5.20
0.96
1.73 4
6.00
0.80
1.50 5
6.70
0.70
1.34

8. Returns to a factor a common case

9. Illustrating production choices with isoquants
Isoquants portray technical combination of inputs to produce a given level of output
Shape of isoquants indicates substitutability between inputs

10. Optimal input combination isoquants

11. Differing input substitutability isoquants

12. Isocost lines
Isocosts portray combinations of inputs that entail the same cost
Isocosts change as input prices change

13. Isocost lines

14. Isocost lines changes in input prices

15. Optimal input mix
Where MPi is the marginal product of input i and Pi is the price of input i.

16. Cost minimization

17. Optimal input mix input price changes

18. Cost concepts Total cost Marginal cost Average cost Opportunity cost
relation between total cost and output
Marginal cost
change in total cost when output rises one unit
Average cost
total cost divided by total output
Opportunity cost
value of best alternative resource use

19. Cost curves

20. Short run versus long run
at least one input is fixed
cost curves are operating curves
Long run
all inputs are variable
cost curves are planning curves
Fixed costs--incurred even if firm produces nothing
Variable costs--change with the level of output

21. Short-run cost curves

22. Long-run average cost envelope of short-run average cost curves

23. Long-run average and marginal cost curves

24. Additional cost concepts
Minimum efficient scale
plant size at which long-run average cost first reaches its minimum point (Q*)
Economies of scope
cost of producing a joint set of products is less than cost of producing separately in separate firms
Learning curves
costs decline with production experience

25. Learning curve

26. Economies of scale versus learning effects

27. Profit maximization
A firm should increase output as long as marginal revenue exceeds marginal cost
A firm should not increase output if marginal cost exceeds marginal revenue
At the profit-maximizing level of output,
MR=MC

28. Optimal output and changes in marginal cost

29. Factor demand Efficient production requires that MPi/Pi= MPj/Pj
The reciprocals represent marginal cost
Pi/MPi=Pj/MPj=MC
At the optimum output level
Pi/MPi=MR
From which we derive the demand curve for input i
Pi=MRMPi

30. Factor demand curve

31. Cost estimation
Effective management decisions should incorporate estimates of short- and long-run costs
Use regression analysis
Short-run costs may be approximately linear
VC = a + bQ