Answer to Question #266208 in Microeconomics for farouk

Question

You are the manager of a monopoly that faces an inverse demand curve described by P = 200 − 15Q. Your costs are C = 15 + 20Q. The profit-maximizing price is

a. $135

b. $110

c. $20

d. $290

Answer 1

Solution:

The correct answer is b.). $110

Profit maximizing is where: MR = MC

TR = P x Q

TR = (200 – 15Q)Q = 200Q – 15Q²

MR = $\frac{\partial TR} {\partial Q}$ = 200 – 30Q

 

MC = $\frac{\partial TC} {\partial Q}$ = 20

Set MR = MC:

200 – 30Q = 20

200 – 20 = 30Q

180 = 30Q

Q = 6

Profit maximizing quantity = 6

Substitute in the demand function to determine price:

P = 200 – 15Q = 200 – 15(6) = 200 – 90 = 110

Profit maximizing price = $110