First, we examine a monopolistic firm. The firm faces a market described by the demand function p= A - By, 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) = y2. (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 constant) equilibrium price, it would do so. (To do this, take a derivative of the firm payoff under the assumption that price is constant rather than a function of output, and then evaluate this derivative at the equilibrium price and quantity from part la.) (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, which 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 (la) in terms of the elasticity of demand, and use this to explain your result in this part