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50 Chapter Highlights
Chapter 21
Cost Minimization
The treatment in this chapter is pretty standard, except for the material on
revealed cost minimization. However, by now the students have seen this kind
of material three times, so they shouldn’t have much difficulty with it.
It is worthwhile emphasizing the difference between the unconditional factor
demand functions of Chapter 18 and the conditional factor demand functions of
Chapter 19. Here we are looking at the best input choice holding the physical
level of output fixed. In Chapter 18 we looked for the best input choice holding
the price of output fixed, where the level of output is adjusted to its most
profitable level.
The material on returns to scale and the cost function is important to get
across, as we will refer in future chapters to cases of increasing average cost,
decreasing average cost, etc. It is important to be able to link these ideas to the
returns-to-scale ideas discussed in earlier chapters.
The material in Sections 21.4 and 21.5 lays the groundwork for ideas that
will be further explored in the next chapter. Both sections are just exploring
various definitions. Section 21.4 will be used in discussing the shapes of short-
run and long-run cost curves. Section 21.5 will be used to distinguish between
two different concepts of fixed costs in the short and long runs.
Cost Minimization
A. Cost minimization problem
1. minimize cost to produce some given level of output:
2. geometric solution: slope of isoquant equals slope of isocost curve. Figure
19.1.
3. equation is: w1/w2=MP1/M P2
6. examples
Chapter 21 51
B. Revealed cost minimization
1. suppose we hold output fixed and observe choices at different factor prices.
s
s
t
3. if choices minimize cost, then we must have
4. this is the Weak Axiom of Cost Minimization (WACM)
5. what does it imply about firm behavior?
6. multiply the second equation by −1andget
7. add these two inequalites:
8. roughly speaking, “factor demands move opposite to changes in factor
prices”
9. in particular, factor demand curves must slope downward.
C. Returns to scale and the cost function
D. Long-run and short-run costs
E. Fixed and quasi-fixed costs
