Answer to Question #1160 in Microeconomics for mothusi ditlou

Question

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?

Answer 1

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.