3.5 A monopolist has the cost function
1
C(q) 1oo + 6q +
2
1. If the demand function is given by
1
[q]2
q 24 – 4 p
calculate the output-price combination which maximises profits.
2. Assume that it becomes possible to sell in a separate second market with demand determined by
3
q 84 – 4 p.
Calculate the prices which will be set in the two markets and the change in total output and profits from case 1.
3. Now suppose that the firm still has access to both markets, but is prevented from discriminating between them. What will be the result?
The pioneering work on revealed-preference analysis is due to Samuelson (1938, 1948) and Houthakker (1950); for a thorough overview see Suzumura (1983), chapter 2. The
representation theorem 4.1 is due to Debreu (1954); for a comprehensive treatment of axiomatic models of preference see Fishburn (1970). On indifference curve analysis
the classic reference is Hicks (1946). There are several neat treatments of the Slutsky equation – see for example Cook (1972). The indirect utility function was
developed in Roy (1947), the concept of consumer's surplus is attributable to Dupuit (1844) and the relationship of this concept to compensating and equivalent
variation is in Hicks (1956). For a discussion of the use of consumer's surplus as an appropriate welfare concept see Willig (1976).
