Question

You are the manager of a monopolistically competitive firm, and your demand and cost func- tions are given by Q = 18 - 3P C(Q) = 120 – 12Q + 3Q2 Find the inverse demand function. Determine the profit maximizing price and level of production. Calculate your firm's maximum profits.

Answer 1

Given demand Q=18-3p

and C(Q)=120-12Q+3Q^2

Inverse demand:

P=(18-Q)/3=18/3-1/3Q

P=6-1/3Q

At profit maximization:MR=MC

So,TR=P×Q=(6-1/3Q)Q=6Q-1/3Q^2

MR=d(TR)/dQ=6-2/3Q

and MC=dC(Q)/dQ=-12+6Q

Then 6-2/3Q=-12+6Q

6+12=2/3Q+6Q

20Q/3=18

20Q=18×3

Q=54/20=2.7

and P=6-1/3Q=6-1/3(2.7)=6-0.9=$5.1

Firms profit=TR-C(Q)=P×Q-(120-12Q+3Q^2)

=$5.1×2.7-(120-12(2.7)+3(2.7)^2)

=13.77-(120-32.4+21.87)

=13.77-109.47=-95.7