<p>1. (Aghion and Bolton, Contracts as a barrier to entry) A seller (incumbent)'s production<br/>cost is 1/2 ; and the valuation for a buyer who demands at most one unit is 1. At date 1, the<br/>buyer and seller signs a contract for the prices fp; p0g of the good, where p is the price that<br/>the buyer pays to the incumbent when there is trade between the buyer and the incumbent<br/>seller, and where p0 is the price that the buyer pays to the incumbent when there is no trade<br/>between the buyer and the incumbent seller. At date 2, an entrant (alternative seller) enters<br/>the market. The entrant's production cost is c 2 [0; 1]; which is uniformly distributed over the<br/>interval, i.e. its p.d.f. is 1. Further, c is known only to the entrant. However, the contracting<br/>parties know the distribution at date 1. At date 3, the entrant production cost is realized. If<br/>there is no entry at date 2, entrant make 0 profit and the incumbent charges the price 1. If<br/>entry, the incumbent and entrant compete in a Bertrand fashion.<br/>a) Suppose that there is no contract at date 1. Then, what is the consumer's expected net<br/>payoff?<br/>b) What is the interval of p for the buyer to accept the contract?<br/>c) When a contract is signed at date 1, what is the probability of entry?<br/>d) What is the optimal contract, p and p0? Note that the optimal contract can be found to<br/>maximize the incumbent's expected payoff.</p><p><br/>2. [Friedman (1971, RES)] Consider the Cournot game: There are two firms, A and B. The<br/>demand function p = a-q; where q = qA+qB: Each firm's marginal cost is c with no fixed cost.<br/>a) In the static game, find the Nash equilibrium, qC:<br/>b) If two firms collude, find the monopoly equilibrium, qM:<br/>Now consider the infinitely repeated game with the discount factor $,And each firm uses the<br/>following trigger strategy:<br/>Produce half the monopoly quantity, 1/2qM; in the first period. In the tth period, produce 1/2qM<br/>if both firms have produced 1/2qM in each of the t&nbsp;- 1 previous periods; otherwise, produce the<br/>Cournot quantity, qC:<br/>c) When firm A produces 1/2qM; what is the profit maximizing amount of production of firmB?<br/>d) Find the interval of discount factor which induces both firms to collude successfully.<br/></p><p>3. Suppose that a car dealer has a local monopoly in selling Volvos. It pays w to Volvo for<br/>each car that it sells, and charges each customer p. The demand curve that the dealer faces is<br/>q = 30&nbsp;- p:<br/>a) What is the profit maximizing price for the dealer to set?<br/>b) If Volvo charges w per car to its dealer, calculate how many cars the dealer will buy from<br/>Volvo.<br/>c) Suppose that Volvo's marginal cost is 5. What is the profit maximizing choice of w?<br/>d) If Volvo sells its cars directly to customers, what will be Volvo's profit maximizing price?<br/></p>