Unformatted text preview: Econ 121 – Fall 2010 UC Berkeley Professor Cristian Santesteban Problem Set 3 Due: Thursday, September 30th at the beginning of class Problem 2 Consider the market for a product with two types of potential users: those in proportion λ have inverse demand schedule P = 5 – 0.5 Q, while the remaining 1 − λ have inverse demand P = 10 − Q. Normalize the total number of consumers to 1, and let c = 2 be the constant marginal cost. a) What is the optimal (profit‐maximizing) two‐part tariff (as a function of λ) that induces both types of consumers to buy? (Hint: Use the fact that for an inverse demand curve of the form P = a − bQ, consumer surplus at price P is given by CS = (1/2b)(a − P)^2) b) Suppose the good is a competitively supplied secondary good, but the manufacturer has a monopoly over the associated primary good. Explain why there might be an incentive for tying. c) What is the optimal two‐part tariff when only high‐demand consumers purchase the good? d) If λ = 0.5, which of the pricing schemes [(a) or (c)] yields a higher total profit? What about when λ = 0.75? Problem 4 Suppose all firms in a monopolistically competitive industry were merged into one large firm. Would that new firm produce as many different brands? Would it produce only a single brand? Explain. Problem 5 Suppose that two competing firms, A and B, produce a homogeneous good. Both firms have a marginal cost of $50. Describe what would happen to output and price in each of the following situations if the firms are at (i) Cournot equilibrium, (ii) collusive equilibrium (where they are maximizing joint profits), and (iii) Bertrand equilibrium. a. Firm A must increase wages and its MC increases to $80. b. The marginal cost of both firms increases. c. The demand curve shifts to the right. Problem 6 Two firms compete by choosing price. Their demand functions are Q1 = 20 – P1 + P2 and Q2 = 20 + P1 – P2. Marginal costs are 0. a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What prices will each firm charge, how much will it sell, and what will its profits be? b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? c. Suppose you are one of these firms, and there are three ways you could play the game: (i) both firms set price at the same time; (ii) you set price first; (iii) your competitor sets price first. If you could choose among these options, which would you prefer and why? Problem 7 When firms choose outputs, as in the Cournot model, reaction functions slope downward. But when firms choose prices, as in the Bertrand model with differentiated products, reaction functions slope upward. Why do output reaction functions differ from price reaction functions in this way? Have fun and good luck! I encourage you to work in groups and to attend office hours. ...
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- Fall '07
- $50, $80, inverse demand, Professor Cristian Santesteban