Question

The inverse demand curve a monopoly faces is p= 120-20. The firm's cost curve is C(Q)= 30 +6Q. What is the profit-maximizing solution? The profit-maximizing quantity is . (Round your answer to two decimal places.) The profit-maximizing price is $ . (round your answer to two decimal places.)

Answer 1

Inverse demand function is as follows -

p = 120 - 2Q

calculate the total revenue function -

TR = p * Q

TR = [120 - 2Q] * Q

TR = 120Q - 2Q2

Calculate the marginal revenue function -

MR = dTR/dQ

MR = d(120Q - 2Q2)/dQ

MR = 120 - 4Q

Total cost function is as follows -

C = 30 + 6Q

Calculate the marginal cost function is as follows -

MC = dC/dQ

MC = d(30 + 6Q)/dQ

MC = 6

A monopolist maximizes profit when it produce that level of output corresponding to which MR equals MC.

MR = MC

120 - 4Q = 6

4Q = 114

Q = 114/4 = 28.50

p = 120 - 2Q

p = 120 - (2 * 28.50)

p = 120 - 57 = 63

Thus,

The profit-maximizing quantity is 28.50 units

The profit-maximizing price is $63 per unit.