A competitive firm in a competitive labor market faces the following conditions: Q = 12K^½L^½,with the market output price of $100 per unit and the market wage rate of $60 per unit of labor and a market rental price of capital of $100 per unit.How many units of capital should the firm use? A)30 B)36 C)43 D)52

Question

Quizplus · Accepted Answer

To determine the optimal amount of capital the firm should use, we need to calculate the marginal product of capital (MPK) at different levels of capital and choose the level that maximizes it. Taking the partial derivative of the production function with respect to K, we get:

MPK = (6Q/K)^(1/2)

Substituting the given values, we get:

MPK = (6(12)(36)^(1/2)(1)(100)^(1/2)(1)^(1/2)(60)^(-1/2)(100)^(1/2))^1/2 = 120

So, the marginal product of capital is highest when the firm uses 36 units of capital. Therefore, the optimal choice is to use 36 units of capital.

A Competitive Firm in a Competitive Labor Market Faces the Following