From Homework 3 A market or industry demand curve is describ

(From Homework #3) A market (or industry) demand curve is described by Q = 600 – 0.5P The monopolist firm’s cost function is TC = 8,550 + 20Q Find the profit-maximizing price. Enter as a value.

Solution

Demand curve is as follows -

Q = 600 - 0.5P

Deriving the inverse demand function -

Q = 600 - 0.5P

0.5P = 600 - Q

P = (600 - Q)/0.5

P = 1,200 - 2Q

Calculate the Total Revenue -

TR = P * Q

TR = (1,200 - 2Q) * Q = 1,200Q - 2Q²

Calculate the Marginal Revenue -

MR = dTR/dQ = d(1,200Q - 2Q²)/dQ = 1,200 - 4Q

Total cost function is as follows -

TC = 8,550 + 20Q

Calculate MC -

MC = dTC/dQ = d(8,550 + 20Q)/dQ = 20

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

Equating MR and MC

1,200 - 4Q = 20

4Q = 1,180

Q = 1,180/4 = 295

The profit-maximizing quantity is 295 units.

P = 1,200 - 2Q

P = 1,200 - (2*295) = 1,200 - 590 = 610

The profit maximizing price is 610.