1. 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. Returns to a factor a common case

8. 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

9. Optimal input combination isoquants

10. Differing input substitutability isoquants

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

12. Isocost lines

13. Isocost lines changes in input prices

14. Cost minimization

15. Optimal input mix input price changes

16. 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

17. Cost curves

18. 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

19. Short-run cost curves

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

21. Long-run average and marginal cost curves

22. 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

23. Learning curve

24. Economies of scale versus learning effects

25. 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

26. Optimal output and changes in marginal cost

27. 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

28. Factor demand curve