A firm produces a product in a competitive industry and has a total cost function C=50+4q+2q2 and a marginal cost function MC=4+4q. At the given market price of $20, the firm is producing 5 units of output. Is the firm maximizing its profit? What quantity of output should the firm produce in the long run?
The price will be equal to marginal cost while maximizing the firm's profit. P=MC 20=4+4q, or q=4. The firm is not maximizing profit, since it is producing too much output. The current level of profit is profit = 20*5-(50+4*5+2*5*5) = –20, and the profit maximizing level is profit = 20*4-(50+4*4+2*4*4) = –18. Given no change in the price of the product or the cost structure of the firm, the firm should produce q=0 units of output in the long run since at the quantity where price is equal to marginal cost, economic profit is negative. The firm should exit the industry.