Suppose that the individual demand for a product is given by Q = 1000 - 5P. Marginal revenue is MR = 200 - 0.4Q. There are no fixed costs and so marginal cost, which is constant, is equal to average cost. That is, MC = AC = $20.
[a] Calculate the firm's profit-maximizing level of output and the price it would charge. (Hint: Rewrite the demand equation with price, P, as a function of quantity, QD.) Show workings.
[b] Calculate the firm's profit at its profit-maximizing level of output. Show workings. Suppose the firm is now considering a quantity discount. The first 400 units can be purchased at a price of $120, and further units at a price of $80.
[c] Calculate the firm's profit under this second-degree price discrimination scheme, and briefly discuss whether it is more profitable than the monopoly price found in part [a.] Show workings.