1. A monopoly with constant marginal costs of $50 can sell to three groups of potential con- sumers, with demands Q1 = 800 − 0.2p, Q2 = 400 − p, and Q3 = 700 − 0.4p respectively. Find the optimal price-quantity combination in each market
(a) if the firm is able to price-discriminate;
(b) if it is not able to price-discriminate.
2. A firm with costs C(Q) = 1, 000 + 60Q + 0.1Q2 is able to price-discriminate between two groups of customers, with demands Q1 = 3, 000− 2p, and Q2 = 350− 0.5p respectively. How much does it sell to each group, and at what price? What would happen if it were forced to charge all its customers the same price?
3. A marketing order for oranges has a fixed total supply of Q = 1, 000 crates a month. Demand in the market for fresh oranges is Q1 = 220−0.2p and that in the market for processed orange products is Q2 = 1, 000 − 2p. Calculate the competitive market-clearing price. What is the deadweight loss in both markets if the price of a crate of fresh oranges is raised to $200?
4. A monopolist has two sets of customers. The inverse demand for Group 1 is described by P = 200 − X. For Group 2, the inverse demand is P = 100 − 2X. The monopolist faces constant marginal cost of 40
(a) Show that the monopolist’s total demand, if the two markets are treated as one is: X = 0;P ≥ 200 X = 200 − P ; 100 < P ≤ 200 X = 250 − (3/2)P ; 0 < P ≤ 100
(b) Show that the monopolist’s profit maximizing price is P = 120 if both groups are to be charged the same price. At this price, how much is sold to members of Group 1 and how much to members of Group 2? What is the consumer surplus of each group? What are total profits?
5. Now suppose that the monopolist in #4 can separate the two groups and charge separate, profit-maximizing prices to each group
(a) What will these prices be? What is consumer surplus? What are total profits?
(b) If total surplus is consumer surplus plus profit, how has price discrimination affected total surplus?