Question

Study a monopolist where the market demand curve for the produce is given by P = 420 – 2Q. This monopolist has marginal costs that can be expressed as MC = 50 + 2Q and total costs that can be expressed as TC = 50Q + Q2 + 50.

a) Given the above information, what is this monopolist’s profit maximizing price and output?

b) Given the above information, calculate this single price monopolist’s profit

Answer 1

The Profit maximizing price and output is at the point where MR = MC

TR = P*Q

TR = (420 – 2Q)*Q

TR = 420Q – 2Q²

MR = 420 – 4Q

TC = 50Q + Q² + 50

MC = 50 + 2Q

Equating MR = MC

420 – 4Q = 50 + 2Q

6Q = 370

Q = 370/6 = 61.67

P = 420 – 2Q

P = 420 – 2(61.67)

P = 420 – 123.34

P = 296.66

Profit

Profit = TR – TC

Profit =  420Q – 2Q² - (50Q + Q² + 50)

Profit =  420(61.67) – 2(61.67²) - (50*61.67 + 61.67² + 50)

Profit =  25,901-7606.38-6936.69

Profit = 11,357.93