# Computation of Profit-Maximizing Price Level and Output

A firm uses a single plant with costs C = 160 + 16Q + .1Q2 and faces the price equation P = 96 - .4Q.

a. Find the firm's profit-maximizing price and quantity. What is its profit?

b. The firm's production manager claims that the firm's average cost of production is minimized at an output of 40 units. Furthermore, she claims that 40 units is the firm's profit-maximizing level of output. Explain whether these claims are correct.

c. Could the firm increase its profit by using a second plant (with costs identical to the first) to produce the output in part (a)? Explain.

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#### Solution Preview

a. Find the firm's profit-maximizing price and quantity. What is its profit?

For profit maximization, the condition is MR=MC

C = 160 + 16Q + .1Q2

MC=dC/dQ = 16+0.2Q

Now P = 96 - .4Q

Total Revenue TR=P*Q=(96-0.4Q)*Q

MR=dTR/dQ = 96-0.8Q

Equating MR and MC, we get ...

#### Solution Summary

This solution provides formulas, calculations and answers for computing the profit-maximizing level of output.