Consider a market with two types of consumers. Type 1 consumers have demand function D1(p1) = 100 - p1 and Type 2 consumers have demand function D2(p2) = 400 - 4p2. There is one of each type of consumer present in the market. The market is served by a monopolist with zero costs.

(a) Suppose that the monopolist can perfectly price discriminate via (separate) two-part tariffs. What per-unit prices and fixed fees does it charge to each type of consumer? How much profit does it receive?

(b) Suppose that the monopolist cannot distinguish consumers "exante" and uses the following pricing scheme:

• Per-unit price is p = 0.
• Lump-sum fee is $5000 if consumer buys Q =
• Lump-sum fee is X if consumer buys 100

What value of X maximizes the monopolist's profit?

3. [8 points total] Consider a market with two types of consumers. Type 1 con- sumers have demand function PI(pi) = 100 -p, and Type 2 consumers have demand function D2(p2) = 400 - 4p2. There is one of each type of consumer present in the market. The market is served by a monopolist with zero costs. (a) [4 points] Suppose that the monopolist can perfectly price discriminate via (separate) two-part tariffs. What per-unit prices and fixed fees does it charge to each type of consumer? How much profit does it receive? (b) [4 points] Suppose that the monopolist cannot distinguish consumers "ex- ante" and uses the following pricing scheme: . Per-unit price is p = 0. . Lump-sum fee is $5000 if consumer buys Q