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

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

Step-by-step explanation:

Given:

`Q = (0.5K^{(1)/(3)} + 0.5L^{(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^{(1)/(3)})^3 \\\\\to 8= 0.5K^{((1)/(3))}^3\\\\\to 2= 0.125 \ K \\\\\to K=16`

`K=16 \ units \\\\ L=0 \ units`