A firm has the long-run cost function C(Q) = 4Q2 +196. In the long run, it will supply a positive amount of output, so long as the price is greater than
A) $120.
B) $112.
C) $56.
D) $28.
E) $61.

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 average cost function is AC(Q) = (4Q^2 + 196)/Q = 4Q + 196/Q. To find the minimum, take the derivative and set it to zero: d(AC)/dQ = 4 - 196/Q^2 = 0, solving gives Q = 7. Plug Q = 7 back into AC to get the minimum average cost: AC(7) = 4(7) + 196/7 = 28 + 28 = 56. Thus, the price must be greater than $56.

A Firm Has the Long-Run Cost Function C(Q) = 4Q2