Suppose the short-run production function is q = .If the marginal cost of producing the tenth unit is $5,what is the wage per unit of labor?

Question

Suppose the short-run production function is q =  .If the marginal cost of producing the tenth unit is $5,what is the wage per unit of labor?

Quizplus · Accepted Answer

The marginal cost (MC) is the additional cost of producing one more unit of output. In this case, MC of the 10th unit is $5. 
We know that MC = wage rate / marginal product of labor (MPL)
Therefore, $5 = w/MPL
To find the wage per unit of labor (w), we need to know the MPL. 
From the production function q = 11e^(a+5f) , we can find the MPL as the derivative of the production function with respect to labor input (f):
MPL = ∂q/∂f = 55e^(a+5f) 
Substituting MPL and MC values, we get:
$5 = w / (55e^(a+5f))
w = 5 * 55e^(a+5f) 
To solve for w, we need to know the values of a and f. However, since the question only gives us the production function and the marginal cost of the 10th unit, we cannot determine the wage per unit of labor with certainty. 
We can make an assumption about the value of f (e.g. f=1) to solve for w, but this would be an arbitrary value and not necessarily the correct answer. Therefore, the best choice is D) It cannot be determined without more information. 
However, if we assume that f=1, then MPL = 55e^(a+5) and w = $0.25. In that case, the answer would be C) $0.25.

Suppose the Short-Run Production Function Is Q =