# 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?

https://brainmass.com/economics/oligopoly/solving-a-profit-maximization-265743

#### 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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