Question 2 You have probably encountered "Bertrand competition" as a form of duopolistic or oligopolistic com- petition. In Bertrand competition, each producer chooses a price at which to sell, and consumers buy from the lowest price producer (or demand is split equally between all the producers that charge the lowest price). Once firm sets a price, it sells any amount of the good that consumers demand from it at that price. This is different from the more familiar Cournot competition, where producers choose quantities of the good they want to sell, and the market determined the price by putting this total supply equal to market demand. Suppose that, for a good, the market demand curve is given by Qd = 1000 - p There are two producers, 1 and 2, and producer i can produce any amount of the good at a constant marginal cost ci. The firms compete in Bertrand fashion. a. Suppose c1 = c2 = 100. What price will each firm charge in equilibrium, and how much will each firm sell? b. Explain (i) why this is the equilibrium, and (ii) why any different configuration of prices is not equilibrium. c. Now suppose c1 = 100, and c2 = 150. Find the equilibrium outcome; i.e., what price does each firm set, and how much does each firm sell?! You may suppose for convenience that firms can only set prices at whole dollars. d. The Bertrand game (the problem that you just analysed) can be viewed as one of the auctions we studied in week 4. Explain which auction it is equivalent to, and why. e. Suppose the government wants this good to be available to consumers at a lower price, and does not care about the profit of the firms. This would be true, for example, if the government's utility was determined by the amount of consumer surplus generated in this market. To pursue its goal the government can provide a small subsidy per unit of output to one or both firms. Suppose the subsidy cannot be larger than $ 5 per unit. Explain: (i) How much subsidy should be offered to firm 1, and how much subsidy should be offered to firm 2? Explain why. (ii) How much will the price paid by consumers change? (iii) How much will the subsidy program cost the government in the new equilibrium