Assignment
1. Suppose there are two potential customers in the market. One has demand function D1(p) =10-p. The other has demand function D2(p) = 20-2p. The only firm in this market has constant marginal cost of 2.
(1) Draw the two demand curves in a graph, with price on the vertical axis and demand on the horizontal axis.
(2) (3rd-degree price discrimination) If the monopoly can identify the two consumers and charge different prices to them, what is the optimal price charged to each consumer? At the optimal prices, is there a relationship between price and elasticity of demand?
2. Suppose there are two firms competing in a market. Both firms produce identical products. Firm One is an efficient firm and has total cost function C1 = 5q1; Firm Two is a less efficient firm and has total cost function C2 =10q2. Market demand for this product is given by Q =150 *2p .
If two firms compete in quantities of production, find out the best response function of each firm and the equilibrium output level of each firm.
3. Two firms compete in prices in a market for a homogeneous product. In this market there are N consumers; each buys one unit from the firm selling at a lower price, as long as the price does not exceed $10. In case both firms charge the same price, assume that N/2 consumers buy from each firm.
(1) Assume zero production cost for both firms. Find the Bertrand equilibrium prices for a simultaneous-move game.
(2) Suppose that the unit production cost of firm 2 is $4, but the unit cost of firm 1 remains zero. Find the Bertrand equilibrium prices for the simultaneous-move game.