Answer to Question #261996 in Macroeconomics for Frank

Question

A firm operating in a competitive industry has it cost function as TC =100+4Q-10Q²+⅓Q² if the market price P=30

Require

Find the profit maximizing unit of outline and the total profit at the level of output ratio

Answer 1

The firm will maximize profit by producing at a point where the marginal cost is equal to marginal revenue.

$TC =100+4Q-10Q^²+\frac{1}{3}Q^3$

$MC=4-20Q+Q^2$

$TR=P\times Q\\=30Q$

$MR=30$

$MR=MC\\30=4-20Q+Q^2\\Q^2-20Q-26=0\\Q=21.225\\\approx21$

$profit=TR-TC\\=[30\times 21]-[100+4(21)-10(21)^2+\frac{1}{3}(21)^3]=1,769$

so the maximizing units of output is 21 and the profit is 1,769