Question

Suppose that mountain spring water can be produced at no cost and that the inverse demand is given by: P = 400 - Q. What is the profit-maximizing price of mountain water for a monopolist?

Group of answer choices

200

250

125

100

Answer 1

A profit maximizing monopolist produces at the point where MR = MC and sets it's profit maximizing price at the point where profit maximizing quantity lies on the demand curve.

Given that, demand: P = 400 - Q

Multiplying both sides by Q we get,

PQ = Total Revenue (TR) = 400Q - Q²

Or, MR = d(TR)/dQ = 400 - 2Q

Also given that, MC = 0

Therefore, setting MR = MC we get,

400 - 2Q = 0

Or, 2Q = 400

Or, Q = 200

Therefore, the profit maximizing output is 200 units. From the demand equation we get when Q = 200, P = 400 - 200 = 200.

Answer: 200