3. (40 pts) Conigan Box Company operates in a perfectly competitive market. It\'

Question

3. (40 pts) Conigan Box Company operates in a perfectly competitive market. It's total cost function is C(a) 23 12q2 +24q + 15. The prevailing price in the market is $24. 9 a. According to the output decision rule, how much should the company produce? b. Should the company stay in business or shut down at the current market price? Explain. c. What will profit be? d. What is the short-run supply function? e. At what market price would the firm break-even? f. Sketch the firm's MR, MC, ATC, and AVC curves on the same graph. Label the profit- 2 7 maximizing quantity, the price, ATC(q), shade in profit/loss, and highlight the firm's short-run supply curve.

Explanation / Answer

C(q) = 2q3 - 12q2 + 24q + 15

(a) Profit is maximized b equating Marginal cost (MC) with Price.

MC = dC(q) / dq = 6q2 - 24q + 24

Equating with price,

6q2 - 24q + 24 = 24

6q2 - 24q = 0

6q2 = 24q

q = 4 (Dividing both sides by 6q, assuming q is non-zero)

(b)

Total variable cost (TVC) = 2q3 - 12q2 + 24q

Average variable cost (AVC) = TVC / q = 2q2 - 12q + 24

When q = 4, AVC = (2 x 4 x 4) - (12 x 4) + 24 = 32 - 48 + 24 = 8

Since Price is higher than AVC, firm will stay in business.

(c) When q = 4,

Total revenue (R) = p x q = 24 x 4 = 96

C(q) = (2 x 4 x 4 x 4) - (12 x 4 x 4) + (24 x 4) + 15 = 128 - 192 + 96 + 15 = 47

Profit = R - C(q) = 96 - 47 = 49

(d) Short run supply function is the MC function:

MC = 6q2 - 24q + 24

p = 6q2 - 24q + 24 [Short run supply function]

NOTE: First 4 parts are answered.

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