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profit maximization

Suppose a firm in an oligopolistic industry faces the following demand curve:

P = 4,900 - 2 Q for Q < 10,000
P = 20,000 - 0.6 Q for Q > 10,000

Suppose further its Cost function is as follows:

TC = 1,000 + 100Q +.5 Q2

a. What price do you suppose they will charge in the short run?
b. What do you suppose will happen in the long-run?

Solution Preview

For profit maximization, we set MC=MR
MC=dTC/dQ=100+.5*2Q=100+Q

MR = dTR/dQ
TR=P*Q
So we have TR=4900Q-2Q^2 for Q<10000
and TR = 20000Q-0.6Q^2 for Q>10000

MR= 4900-4Q for Q<10000 and MR=20000-1.2Q for Q>10000

Now let us assume that Q<10,000 then equating MC=MR, we ...

Solution Summary

This posting determines profit maximization.

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