Question: In the model of perfect competition, all firms are price-takers since they treat price as a market-determined constant. Firm Perfcomp's total revenue function is
TR(Q) = P.Q,
in which P equals the output price. Assume that P = 12 and the total cost function is
TC(Q) = Q3 - 4.5Q2 + 18Q - 7.
a) Determine the firm's profit function and the level of output at which Firm Perfcomp should produce in order to maximize profits. Confirm that this quantity represents maximum profits for the firm by using the second-order condition.
b) According to microeconomic theory, perfectly competitive firms will maximize profits by producing at the quantity where price equals marginal cost and where the slope of the marginal revenue curve is less than that of the marginal cost curve. Show that the theory holds in this example.