Question

Short questions:

a. A firm has production function f(K, L) = 2L + 3K. The price of L is w and the price of K is r. Derive the cost function of the firm.

b. A firm in a competitive industry takes account of the fact that the demand curve it faces has a negative slope. True or false?

c. A profit-maximizing firm continues to operate even though makes negative profits. It sells its product at a price of $100. Which of the following statements are certainly true?

○ Marginal cost is everywhere increasing.

○ Average fixed cost is less than $100.

○ Average total cost is more than $100.

○ Average variable cost is less than $100.

○ Marginal cost is decreasing.

d. The area under the marginal cost curve measures total variable costs. True or false?

e. If the average cost curve is U-shaped, then the marginal cost curve must cross the average cost curve at the bottom of the U. True or false?

f. As long as the marginal cost of production is greater than the average variable cost, the average variable cost is increasing. True or false?

Answer 1

a. f(K, L) = 2L + 3K = Q
Optimal input combination will depend on the relationship between MRTS and w/r.
MRTS = MPL/MPK =

If, 2/3 > w/r then only labor will be used. So, K = 0
So, 2L = Q
Thus, L = Q/2 = 0.5Q
Cost, C = wL + rK = w(0.5Q) + r(0) = 0.5wq

If, 2/3 < w/r then only capital will be used. So, L = 0
So, 3K = Q
Thus, K = Q/3
Cost, C = wL + rK = w(0) + r(Q/3) = rQ/3

b. False. The demand curve a firm in a competitive industry faces is perfectly elastic.

c. Marginal cost is everywhere increasing.
Average total cost is more than $100.
Average variable cost is less than $100.
A firm only operates on rising part of demand curve as long as AVC is less than price and as firm is making negative profits so ATC > 100.

d. True
Area under marginal costs curve gives total variable costs.

e. True
MC cuts AC from below at the minimum of U shaped AC.

f. True
MC cuts AVC from below and beyond that MC is greater than AVC and AVC is rising.