Question

6. When a firm uses K units of capital and L units of labor, it can produce 2 units of output with the production function 2=VLEVK Each unit of capital costs 2, and each unit of labor costs 1. a. The level of K is fixed at 16 units. Suppose 234. What will the firm's short-run total cost be? (Hint: How much labor will the firm need?) b. The level of K is fixed at 16 units. Suppose 2 4. Find the equation of the firm's short-run total cost curve.

Answer 1

Cost function:

C = w*L + r*K

Given w=1 and r=2; the total cost is given as

C = L + 2K

a) K is fixed at K=16. Put the value in the production function, we get

Q = L^0.5 + (16)^0.5

Q = L^0.5 + 4

For Q < = 4, the labor requirement is

L^0.5 < = 4 - 4 = 0

L^0.5 < = 0

It means, L < = 0

The short run cost will be, the cost of capital as labor can never be less than zero.

C = 0+12 * 16 = 32

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b) Q > 4,

L^0.5 > 4 - 4 = 0

L^0.5 > 0

L > 0

The short run cost will be, the cost of capital and labor depending on the amount of output.

$\therefore C=\left (Q-4 \right )^2&plus;2\times 16=Q^2-8Q&plus;48$..................[ for Q>4].