Question

You are the manager of a monopolistically competitive firm. The inverse demand for your product is given by P = 200 - 10Q and your marginal cost is MC = 5 + Q.

a. What is the profit-maximizing level of output?
b. What is the profit-maximizing price?
c. What are the maximum profits?

Answer 1

P = 200-10Q and MC = 5+Q

a) Profit maximing level of output is where MR=MC

P = 200-10Q

TR = 200Q - 10Q² ( as TR = P * Q)

MR = 200-20Q

MC = 5+Q

200 -20Q = 5 + Q

195 = 21Q or Q = 9

b) P = 200 -10*9

P = 200 - 90 = 110

so, profit maximizing price is $110.

c) Profits = TR -TC

we have TC = 5Q + 0.5Q²

profits = (110 * 9 ) - ( 5*9 + 0.5*81)

profits= 990 - ( 45 + 40.5)

profits = $904.5