2 Suppose there are two inputs in the production function la

2. Suppose there are two inputs in the production function, labor and cap- ital, and these two inputs are perfect substitutes. The production func tion for how much output is produced in a week can be described by q(L, K) L +3K and the firm wants to produce q 100 units this week. The current price of the firm\'s output is P $500

Solution

q = 100 = L + 3K

(c) Total cost (TC) ($) = wL + rK = 300L + 750K

When L and K are perfect substitutes, firm will employ only one input.

From Production function,

When L = 0, K = 100/3 = 33.33 and TC ($) = 300 x 0 + 750 x (100/3) = 25,000

When K = 0, L = 100 and TC ($) = 300 x 100 + 750 x 0 = 30,000

Since TC is lower when L = 0 and K = 33.33, firm will employ only capital (33.33 units).

(d) TC ($) = 225L + 750K

From Production function,

When L = 0, K = 100/3 = 33.33 and TC ($) = 225 x 0 + 750 x (100/3) = 25,000

When K = 0, L = 100 and TC ($) = 225 x 100 + 750 x 0 = 22,500

Since TC is lower when L = 100 and K = 0, firm will employ only labor (100 units).