Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K)is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run marginal cost is A)1000 + q³ B) $\frac { 3 q ^ { 2 } } { 100 }$ C)q³ D)2q³

Question

Quizplus · Accepted Answer

The short run marginal cost (MC) is derived from the total cost (TC) function, which in turn is based on the production function. In the short run, with capital fixed, the only variable input is labor. The cost of labor is the wage rate times the amount of labor used. The MC is the derivative of the TC with respect to quantity produced (q). Given the production function and the fixed capital, the correct formula for MC, without knowing the specific form of the production function, involves the relationship between q and the inputs. The choice $\frac { 3 q ^ { 2 } } { 100 }$ suggests a specific relationship between output and input costs that could be derived from a given production function, assuming labor is the variable input and its cost is incorporated. This choice implies a quadratic relationship between output and costs, which is plausible given the information provided.

Suppose a Production Function Is Q = K1/2L1/3 and in the Short

Suppose a Production Function Is Q = K^1/2L^1/3 and in the Short