Problem 2 Two farmers live in a village. One of them raises pigs, while the other one runs a B&B on the farm. The pig farm generates externalities in the form of unpleasant odor and noise. The total cost function for the pig farmer is TC = 0.03P + 30P, where P stands for the number of pigs raised per year, while the total cost function for the B&B farm is TC2 = 0.0272 + 0.02TA + 57, where T denotes the number of nights spent on the farm by tourists per year. Both the market for pigs and the market for B&B are perfectly competitive. The price of an adult pig is $120, while the price of a single night at the B&B is $40. a) Find the output and annual profits of the pig farmer and the B&B, assuming that there is no government intervention and that farmers cannot communicate with each other. b) Find the socially efficient output of each farmer, assuming internalization of the externality. Compare profits of farmers in this case with those in point a). c) Find the Pigouvian tax rate correcting of the erroneous market allocation described in point a).