Question

A firm uses labor (L) and capital (K) as inputs, and has a short run cost function C=15+ 10q+ q². Capital is fixed at K̅ 

a. Give the formula for the firm's marginal cost function. Any method of deriving the marginal cost function is acceptable. (Hint: When calculating MC, you can assume that increases by a very, very small amount, so that q2 = q1 + ε ≈ q and q1 + q2 ≈ 2q.) 

b. Give the formula for the firm's average cost function. 

c. Is AVC increasing, decreasing, or at its minimum if the firm is currently producing 8 units? 

d. What is the firm's average product of labor if it is currently producing 8 units and labor costs $9 per unit? 

e. How many units of labor must the firm be using in the short run if it is currently producing 8 units?

Answer 1

Answer: C = 15+10q+q2

a. Marginal cost or MC = d(C)/dq = 10+2q

b. Firms average cost function or ATC =C/q = (15/q) + 10 + q

c. AVC = Variable cost/q = (10q+q2)/q = 10+q

Now AVC is increasing as q increases. Hence, at q = 8, AVC is increasing.

d. Average product of labor = output/total quantity of labor

Since, the only variable factor is labor, the variable cost is the cost of labor.

Variable cost = 10q+q2 and at q=8, Variable cost = 10*8+82 = 144

Since price of labor = $9, total number of workers = 144/9 = 16

Hence, Average product of labor = 8/16 = 0.5 output per worker

Answering first 4 parts of a question is as per HOMEWORKLIB RULES.