Suppose for a particular production function, the cost-minimizing level of labor is $L = 2 Q$ and the cost-minimizing level of capital is $K = 5 Q$. If $w = 5$ and $r = 2$, the long-run total cost curve is:
A) $T C = 7 Q$
B) $T C = 7$
C) $T C = 20 Q$
D) $T C = 20$

Question

Quizplus · Accepted Answer

The long-run total cost curve is given by the expression $T C = w L + r K$. Substituting the given values of $w$, $r$, $L$, and $K$ gives $T C = (5)(2 Q) + (2)(5 Q) = 20 Q$. Therefore, the correct answer is C. In the long run, the firm chooses the inputs to minimize the total cost of producing a given level of output. To find the long-run total cost curve, we need to write the cost function in terms of only one input.

Using the cost-minimizing levels of labor and capital, we can write the cost function as:

TC = wL + rK = 5(2Q) + 2(5Q) = 20Q

Therefore, the long-run total cost curve is given by TC = 20Q. Choice C is the correct answer.

Suppose for a Particular Production Function, the Cost-Minimizing Level of Labor