Please answer the above

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 rm sets a price, it sells any amount of the good that consumers demand from it at that price. This is dierent 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 : 100039 There are two producers, 1 and 2, and producer a" can produce any amount of the good at a constant marginal cost 03-. The rms compete in Bertrand fashion. a. Suppose c1 : c2 : 100. What price will each rm charge in equilibrium, and how much will each rm sell? b. Explain (i) why this is the equilibrium, and (ii) why any different conguration of prices is not equilibrium. c. Now suppose cl = 100, and 02 = 150. Find the equilibrium outcome; i.e., what price does each rm set, and how much does each rm sell?l 1You may suppose for convenience that rms 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 prot of the rms. 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 rms. Suppose the subsidy cannot be larger than 35 5 per unit. Explain: (i) How much subsidy should be offered to rm 1, and how much subsidy should be offered to rm 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