Skateboards are produced according to the production function,q = 10K^0.25L^0.5 - L.At what quantity of labor does total product begin to decline given that capital is fixed at 16 units in the short-run?

Question

Quizplus · Accepted Answer

The correct answer is A because the total product begins to decline when the marginal product of labor is less than the average product of labor. The marginal product of labor is the change in total product divided by the change in labor, and the average product of labor is the total product divided by labor. When the marginal product of labor is less than the average product of labor, the average product of labor is decreasing. In this case, the marginal product of labor is 2.5K^0.25L^-0.5, and the average product of labor is 10K^0.25L^-0.5 - L. When K is fixed at 16, the marginal product of labor is 2.5(16)^0.25L^-0.5 = 10L^-0.5, and the average product of labor is 10(16)^0.25L^-0.5 - L = 40L^-0.5 - L. The marginal product of labor is less than the average product of labor when 10L^-0.5 < 40L^-0.5 - L, which simplifies to L > 100. Therefore, the total product begins to decline when L > 100.

Skateboards Are Produced According to the Production Function,q = 10K0

Skateboards Are Produced According to the Production Function,q = 10K⁰