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Question 3 [40 points]. Consider two firms located next to each other. The first firm is a coal mine, which has a cost function of C(y) = y where y is the output of coal. The second firm is a bakery, which has a cost function of C(B) = B2 + 2y, where B is the output of baked goods. Note that due to air pollution from the coal mine, the cost of the bakery is higher when the coal output is higher. (For example, the bakery has to install and run extra air filters to block out air pollution from the coal mine.) The output prices are given as Py = 8 and PB = 10. (3a) [10 points] Suppose one company owns both firms, so that it maximizes the joint profits of the two firms. Find the optimal outputs of the coal mine and the bakery. What are the individual profits of the two firms and what's the company's total profit? (3b) [10 points] Suppose the two firms and separately owned, and the coal mine has the right to pollute. Find the outputs of both firms, and their profit levels. (3c) [10 points] Suppose the two firms and separately owned, but the bakery has the right to clean air. Find the outputs of both firms, and their profit levels. (3d) [10 points] Continue with the setup in (3c). Suppose the coal mine approaches the bakery to negotiate a deal. Suppose further that the bakery, with the full property rights over clean air, has all bargain power. Without any transaction costs of bargaining, what are the output levels of the two firms after bargaining? How much would the coal mine pay to the bakery? What are their ending profit levels