Question

1. Consider the production function Q = (0.5K1/3 + 0.5L1/3)3 . Suppose the firms want to minimize the cost of producing 8 units of output. It pays a wage rate W of $40 and capital cost R of $10. How many units of labor and capital should the firm use?

Answer 1

Answer:

The answer is "k= 16 units and L=0 units"

Explanation:

Given:

$Q = (0.5K^{\frac{1}{3}} + 0.5L^{\frac{1}{3}})^3$

Since K and L are ideal replacements, their company should select its cheapest of two for production. Its business chooses only money.

$\to Q(K,L)=(0.5 K^{\frac{1}{3}})^3 \\\\\to 8= 0.5K^{(\frac{1}{3})}^3\\\\\to 2= 0.125 \ K \\\\\to K=16$

$K=16 \ units \\\\ L=0 \ units$