Question

Denek Box company produces card boxes In bundles of 1,000 boxes. The market Is highly competitive, with boxes currently selling for $100 per thousand. Denek's total and marginal cost curves are:

TC = 3,000,000 + 0.001Q2

2

MC = 0.002Q

Q Is measured In thousand box bundles per year.

a. Calculate Denek's profit maximizing quantity.

b. Is the firm earning a profit/loss?

c. Analyze Denek's position in terms of the shutdown condition.

Answer 1

a. For a perfectly competitive firm, profit maximizing quantity is given at the point where:

Price = Marginal Cost

100 = 0.002Q

$Q*= \frac{100}{0.002}=50000$

b. Profit = Total Revenue (TR) – Total Cost (TC)

$= PQ* - (3000000+0.001Q^2) \\ = 100 \times 50000 – 3000000 – 0.001(50000)^2 \\ = 5000000 – 3000000 – 2500000 \\ = -500000$

The firm is making a loss of $500000

c. A firm should operate in perfect competition as long as price is greater than average variable cost (AVC)

P>AVC

$AVC = \frac{Total \; variablr \; cost \;(TVC)}{Q} \\ = \frac{0.001Q^2}{Q} \\ = 0.001Q$

When Q* = 50000

AVC = $0.001 \times 50000 = 50$

Thus, P>AVC, so the firm should continue the production.