Question

3. a) Suppose that a firm has a capital cost (r) of $8 and a labor cost (w) of $4. Graph an isocost line associated with spending $1,000. On the same graph, draw another isocost line associated with spending $2,000. What are the slopes of these lines?

b) Using our cost-minimizing (economic efficiency) condition, what is the optimal ratio of the marginal product of labor to the marginal product of capital for this firm? Why? Use a production isoquant on your graph to demonstrate your answer.

c) Suppose the cost of labor is actually $8, rather than $4. How do your isocost lines change? How does your answer to b) change? How would you expect the firm’s behavior to change?

Answer 1

Iso cost line equation: M= wL+ rK

w is price of labor i.e wage , r is price of capital i.e rental price, L is quantity of labor, K is quantity of capital.

•Iso cost line: 1000= 4L+ 8K

Slope = w/r = 4/8 = 1/2

•X intercept ( keeping K=0)= 250

• Y intercept ( keeping L=0) = 125

• New iso cost line:  2000= 4L+8K

Slope= w/r= 4/8= 1/2

• X intercept (keeping K=0) = 500

• Y intercept ( keeping L=0) = 250

The new iso cost line is CD with X intercept 500 anf Y intercept 250.

Answer b) At optimization MPL/PL= MPK/PK

where, PL= w, PK= r

so ,MPL/MPK= w/r

MPL/MPK= 4/8 = 1/2

Answer c) if w= 8

New budget line: 1000= 8L+8K

New slope= w/r= 8/8= 1

So, at optimal new MPL/MPK= 1

• X intercept ( putting K=0)= 125

• Y intercept ( putting L=0) = 125

• If labor is a normal factor of production then with a rise in price of labor now , firm will hire less labor.

• Since the slope has increased from 1/2 to 1 the new isocost line will be steeper .

• The new isocost line will rotate inward from X axis from AB to AB'.