Question

A poster company produces posters that are sold in tubes of 1,000 rolls. The market is perfectly competitive, with rolls currently selling at $90 per thousand. The company’s total and marginal cost curves are:

TC = 200,000+0.001Q²

MC = 0.002Q

where Q is measured in thousand roll bundles per year.

a. Calculate the company’s profit maximizing quantity. Is the firm earning a profit?

b. When should this company shut down?

Answer 1

Equilibrium quantity is determined at a point where price equals marginal cost (P=MC)

90 = 0.002Q

Q = 90/0.002 = 45000 (units in thousands) (this is profit max quantity, 45,000,000)

TC = 200,000+0.001Q² , ATC = TC/Q = 200,000/Q + 0.001Q

at Q = 45000, ATC = 200000/45000+0.001*45000 = 49.44

Profits = (P-ATC)*Q = (90-49.44)*45000 = 1825200 (in thousands, 1825200000)

VC = 0.001Q² , AVC = VC/Q = 0.001Q²/Q = 0.001Q

min AVC= 0.001 (the point of shut down is the minimum of AVC curve)