A monopolist faces a demand curve given by P40Q while its ma

A monopolist faces a demand curve given by P=40-Q, while its marginal cost is given by MC=4+Q. Its profit maximizing output is

a. 8 b. 9 c. 10 d. 11 e. 12

why is the answer (e)?

Demand curve of monopolist is as follows -

P = 40 - Q

Calculate the Total revenue function -

TR = P * Q = (40 - Q) * Q = 40Q - Q²

Calculate the marginal revenue -

Marginal revenue function can be calculated by deriving the first derivative of total revenue function.

MR = dTR/dQ = d(40Q - Q²)/dQ = 40 - 2Q

Marginal cost function is as follows -

MC = 4+Q

A monopolist maximizes profit when it produce that level of output corresponding to which marginal revenue equals marginal cost.

Equating marginal cost and marginal revenue to ascertain profit maximizing output,

40 - 2Q = 4 + Q

2Q + Q = 36

3Q = 36

Q = 36/3 = 12

The profit maximizing level of output is 12 units.

Hence, the correct answer is the option (e).

MR = MC