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Consider a monopolistic firm. The firm faces a market described by the de- mand function p = A - By, A, B > 0, where p is the price the firm receives if it sells quantity y of output. The firm's cost function is given by C(y) = =y'. (a) Find the profit-maximizing quantity of output and the corresponding profit for this firm. (b) Show that if the firm could sell more output at the equilibrium price, it would do so. (To do this, take the derivative of the firm's payoff under the assumption that price is constant rather than a function of output, and then evaluate the derivative at the equilibrium price and quantity from part (a).) Explain briefly why the firm does not sell more. (c) Let p* be the equilibrium price and y" the equilibrium quantity, so that p" = A- By" . Now suppose the demand in the market shifts, so that the new demand curve is p = A' - B'y, with A' > A and B' > B, but with it still being the case that p* = A'-B'y". Hence, if the firm does not change its quantity, its price will also not change. Is the quantity of output y" still optimal, given this new demand curve? If not, will the firm decide to produce more or less? Formulate your first-order condition from part (a) in terms of the elasticity of demand, and use this to explain your result. Suppose you must design a tax on the monopoly. (d) First consider a sales tax of 10% on this market. Suppose that the firm has to pay the tax, as is typically the case with sales taxes. Hence, if the firm produces quantity y of output, the price paid by consumers is p = A - By, but the price received by the firm is .9p = .9(A - By)