2. Two rms, X and Y, produce vertically differentiated goods. There are 300 consumers who might want to buy the rms' goods. Given their tastes, each consumer has a characteristic b, which tells us something abOut how much they like the goods. Specically, a consumer with characteristic bis willing to pay up to 130!) dollars for one of rmX's goods, and up to 1001:! dollars for one of rm Y's goods. Consumers' values of b are all between S and 15. More specically, for any two values of b between S and 15, bhigh and blow, with bhigh > blow, the number of consumers with values of b between bhigh and btow is 30 x (bhigh - brow) So, for example, the number of consumers with values of b between 7 and 11 is 30X(l 1-7)=120. The rms compete by simultaneously choosing prices for their goods, PX for firm X, Py for rm Y. Once the firms choose their prices, consumers decide which firm's good they want to buy (the goods are close substitutes, even if not identical, and no consumer gets any extra benet from owning a second good). A consumer will make her purchase based on consumer surplus; her conSumer surplus from buying a good from rm X would be 1301) PX; her conSumcr Surplus from buying a good from rm Y would be 100!) Py. (a) Suppose that the rms charge prices PX and Py, with P}: xmw, the number of consumers with values of x between army\" and 2:10\1. An industry has two firms, firm 1 and firm 2, which produce goods that consumers view as identical. Both firms have constant average and marginal cost equal to 60 dollars per unit of output (i.e, when firm 1 produces q1 units of output, its total cost is 60 x q1 dollars, and when firm 2 produces q2 units of output, its total cost is 60 x q2 dollars). Demand for the firms' output is described by the function P = 180 - Q, where O is the firms' combined output, q1 + 92. (a) Right now, the firms compete by choosing their outputs at the same time; i.e., they play a Cournot competition game. Find the predicted output for each firm. Then, find the economic (total) surplus from their predicted choices. (b) The two firms decide that they want to merge into a single firm. However, they know that the regulator will only allow a merger that increases economic surplus in their industry. To justify a merger, representatives from the firms meet, and determine that, if they merged, combining their technology would allow them to produce their good at a constant cost of only 40 dollars per unit (i.e., average and marginal cost would equal 40 at all quantities of output). Find the output and price the merged firm would choose (as a monopoly), and calculate the economic surplus from that choice, to determine whether the regulator will allow the merger