Question

A monopolist faces inverse market demand of P = 140- TC(Q) = 20° + 10Q + 200. and has Total Cost given by (20 points) Find this monopolist's profit maximizing output level. Find this monopolist's profit maximizing price How much profit is this monopolist earning?

Answer 1

Inverse demand

P = 140-0.5Q

Total revenue = TR (Q) = P*Q = (140-0.5Q) = 140Q -0.5Q^​​2

TC (Q) = 2Q²+10Q+200

Marginal revenue = d(TR)/dQ

MR = d(140Q--0.5Q²)/dQ

MR = 140-Q

MC = Marginal cost = d(TC)/dQ

MC = d(2Q²+10Q+200)/dQ

MC = 4Q+10

1) For profit maximization output level

MC = MR

4Q+10 =140-Q

5Q = 130

Q = 26

2) Profit maximization price

P = 140-0.5Q

P = 140-(0.5*26) = 127$

3) Profit = TR - TC

Profit = (127*26) - (2*26*26+10*26+200)

Profit = 3302-1812 = 1490$