Question

A monopolist faces a demand function defined as Q = 40 – 2P. The monopolist's marginal cost is equal to $15 at all levels of output. What price should the firm charge in order to maximize profits?

Answer 1

The demand function is given as:

Q = 40 - 2P or P = 20 - 0.5Q

The total revenue can be calculated by multiplying the price and quantity. So,

TR = PQ = (20 - 0.5Q) (Q) = 20Q - 0.5Q²

The marginal revenue is:

MR = d(TR)/dQ = 20 - Q

The marginal cost is $15.

The monopolist maximizes the profit when the marginal cost equals marginal revenue. So,

20 - Q = 15

Q = 5

The profit-maximizing level of production is 5 units.

Putting Q = 5 in the demand function:

P = 20 - 0.5Q²

P = 20 - 0.5(25) = 20 - 12.50 = 7.50

So, the profit-maximizing price is $7.50.