A firm has the long-run cost function C(q)= 7q2 + 175.In the long run, it will supply a positive amount of output, so long as the price is greater than
A)$70.
B)$148.
C)$35.
D)$140.
E)$75.

Question

Quizplus · Accepted Answer

In the long run, a firm will supply a positive amount of output if the price is greater than the minimum average cost. The given cost function is $C(q) = 7q^2 + 175$. To find the minimum average cost, we first find the average cost (AC) function by dividing the total cost by q: $AC = \frac{7q^2 + 175}{q} = 7q + \frac{175}{q}$. To find the minimum of this function, we take its derivative with respect to q and set it equal to zero: $AC' = 7 - \frac{175}{q^2} = 0$. Solving for q gives $q^2 = \frac{175}{7} = 25$, so $q = 5$. Substituting q = 5 back into the AC function gives the minimum average cost: $AC_{min} = 7(5) + \frac{175}{5} = 35 + 35 = 70$. Therefore, the firm will supply a positive amount of output as long as the price is greater than $70.

A Firm Has the Long-Run Cost Function C(q)= 7q2