Question

The market demand and supply functions for an electronic typewriter are

Q_D = 20,000 – 10P

Q_S = 10,000 + 20P

               Western Electronics Inc. is one of many firms in this perfectly competitive industry. Its marginal and average cost functions are

                                               MC = 10 + 2Q

                                               AC = (1,000/Q) + 10 + Q

               a/ What is the profit-maximizing output rate for Western?

               b/ How much economic profit will be earned at that rate of output?

Answer 1

A) Given that the demand function is

$Q_D=20000-10P$

And $MC=10+2Q$

$TR=P×Q$

$P=2000-0.1Q$

$TR=(2000-0.1Q)Q$

$TR=2000Q-0.1Q^2$

The profit maximizing output is given at the equilibrium, $MR=MC$

Where MR is:

$MR=TR'=2000-0.2Q$

$2000-0.2Q=10+2Q$

$Q^*=905$

B) $\pi=TR-TC$ at Q=905

Where TC is

$TC=AC×Q$

$TC=(\frac{1000}{Q}+10+Q)Q$

$TC=1000+10Q+Q^2$

$\therefore \pi=2000Q-0.1Q^2-(1000+10Q+Q^2)$

$(905)-0.1(905)^2-(1000+10(905)+905^2$

$\pi=899022.5$