Chapter 2: Monopoly pricing

We consider a monopoly firm with marginal costc. The demand varies withD1(p) =a1b1pin period 1 andD2(p) =a2b2pin period 2, witha1/b1> a2/b2.

1. Characterize the profit-maximizing price for each period. 2. Compare the two prices and discuss.

We assume now that, before choosing its production, the firm must choose the size of the infrastruc-

tureQwith a marginal cost of investmentC. That is, the fixed cost due to infrastructureQisQC. We

assume thatC <(b2b1)c. To produceqat a given period, the initial investmentQshould be at leastb1

q. To keep things simple, we assume thata1=a2= 1.

3. For a given productionq1in period 1 andq2in period 2, write down the total cost of production. 4. Assuming (and checking ex-post) thatq1> q2, characterize the profit-maximizing prices for the

two periods. Comment.

5. What sizeQshould the firm choose at the initial stage?