Question

Tri-pak Packaging produces cardboard boxes that are sold in bundles of 1000 boxes. The market is highly competitive, with boxes currently selling for R100 per thousand. Tri-pak’s total and marginal cost curves are:

TC = 3,000,000 + 0.001Q2

MC = 0.002Q

where Q is measured in thousand box bundles per year. a) Calculate Tri-pak's profit maximizing quantity. Is the firm earning a profit? [6] b) Analyse Tri-pak's position in terms of the shutdown condition. Should Tri-pak operate or shut down in the short-run? [4

Answer 1

a. Given the competitive nature of the industry, Tri-pak Packaging  should equate P to MC.

100 = 0.002Q

Q = 50,000

To determine profit: $\pi$$= TR - TC$

TR = PQ

TR = $100 50,000

TR = 5,000,000

$TC = 3,000,000 + (0.001\times(50,000))$

$TC = 3,000,000 + 2,500,000$

$TC = 5,500,000$

$\pi$ $= 5,000,000 - 5,500,000$

$\pi$$= -500,000$

Tri-pak Packaging  is losing 500,000 per year.

b). To determine if the firm should operate or shutdown, we must compare P to AVC.

$AVC=\frac{TVC}{Q}$

$TVC = TC - TFC$

$TVC = 5,500,000 - 3,000,000$

$TVC = 2,500,000$

$AVC = \$\frac{2,500,000}{50,000}=\$50$

$AVC = 50$ ; $P = \$100$ The firm should operate since $P>AVC$