Suppose the short-run production function is q = L⁰.⁵.If the marginal cost of producing the tenth unit is $5,what is the wage per unit of labor?
A) $1
B) 5¢
C) 25¢
D) It cannot be determined without more information.

Question

Quizplus · Accepted Answer

The marginal cost (MC) is the change in total cost when producing an additional unit. We are given that when producing the 10th unit, the MC is $5. 
Using the rule of marginal product, we know that MPL = dQ/dL = 0.5L^(-0.5). To find the wage rate, we need to find the value of MPL when L = 10. 
MPL = 0.5(10)^(-0.5) = 0.5/√10 = 0.158. 
Since MC = wage rate x MPL, we can solve for the wage rate: 
$5 = wage rate x 0.158 
wage rate = $5/0.158 = $31.65 
Therefore, the wage per unit of labor is $31.65/10 = 25¢. 
Thus, the answer is C.

Suppose the Short-Run Production Function Is Q = L⁰