Question

2.a. How will a rise in the wage of labor affect a firm's short run marginal cost curve (assume labor is the input that can be varied in the short run).

b. Would you expect the rise in the wage to have a smaller effect on short run or long run marginal costs? Why?

c. Suppose a firm's production function is Q = (KL)^0.5. In the short run, this firm's capital stock is fixed at 100.

            i. Calculate the firm's short run total cost curve if w = 5 and v = 5.

            ii. It can be shown (using calculus) that this firm's short run marginal costs are .1Q. In

            order to maximize its profits, how much would the firm choose to produce if the market

            price of its output was $5, $10, or $20. For each price, calculate the firm's profits and

            indicate whether Q = 0 might be preferred.

Answer 1

(a)

An increase in wage rate will increase the marginal cost in short run, shifting the MC curve upward at every output.

(b)

Increase in wage rate will have smaller effect in long run because in long run all inputs are variable, so the firm can substitute cheaper capital with more expensive labor, lowering average cost.

(c)

Q = (KL)^0.5 = K^0.5L^0.5

When K = 100,

Q = (100)^0.5L^0.5 = 10L^0.5  

(i)

Total revenue (R) = P x Q

Total cost (C) = wL + vK = 5 x (Q²/10) + 5 x 100 = (Q²/2) + 500

MC = 0.1Q (Given)

A firm will equate Price with MC.

(A) P = 5

0.1Q = 5

Q = 50

R = 5 x 50 = 250

C = (50 x 50 / 2) + 500 = 1250 + 500 = 1750

Profit = 250 - 1750 = -1500 (Loss)

(B) P = 10

0.1Q = 10

Q = 100

R = 5 x 100 = 500

C = (100 x 100 / 2) + 500 = 5000 + 500 = 5500

Profit = 500 - 5500 = -5000 (Loss)

(C) P = 20

0.1Q = 20

Q = 200

R = 5 x 200 = 1000

C = (200 x 200 / 2) + 500 = 20000 + 500 = 20500

Profit = 1000 - 20500 = -19500 (Loss)

Since the firm is making a loss at every output level, it is better to produce nothing (Q = 0).