Question #314701

The market demand and supply functions for an electronic typewriter are

QD = 20,000 – 10P

QS = 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?


1
Expert's answer
2022-03-21T12:49:29-0400

A) Given that the demand function is

QD=2000010PQ_D=20000-10P

And MC=10+2QMC=10+2Q

TR=P×QTR=P×Q

P=20000.1QP=2000-0.1Q

TR=(20000.1Q)QTR=(2000-0.1Q)Q

TR=2000Q0.1Q2TR=2000Q-0.1Q^2

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

Where MR is:

MR=TR=20000.2QMR=TR'=2000-0.2Q

20000.2Q=10+2Q2000-0.2Q=10+2Q

Q=905Q^*=905


B) π=TRTC\pi=TR-TC at Q=905

Where TC is

TC=AC×QTC=AC×Q

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

TC=1000+10Q+Q2TC=1000+10Q+Q^2

π=2000Q0.1Q2(1000+10Q+Q2)\therefore \pi=2000Q-0.1Q^2-(1000+10Q+Q^2)

2000(905)0.1(905)2(1000+10(905)+90522000(905)-0.1(905)^2-(1000+10(905)+905^2

π=899022.5\pi=899022.5



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