A firm has a long-run cost function, C(q)  8q²  288.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

A) $200.
B) $192.
C) $96.
D) $48.
E) $101.

To determine the price above which the firm will supply a positive amount of output, we need to find the minimum point of the average cost (AC) curve, which is where the marginal cost (MC) equals the average cost. The given cost function is $C(q)=8q^2+288$ . The average cost (AC) is $AC=\frac{C(q)}{q}=8q+\frac{288}{q}$ . The marginal cost (MC) is the derivative of the total cost with respect to quantity, $MC=\frac{dC}{dq}=16q$ . Setting MC equal to AC to find the minimum point, we get $16q=8q+\frac{288}{q}$ . Simplifying, we find $8q^2=288$ , which gives $q^2=36$ , so $q=6$ . Substituting $q=6$ back into the MC or AC formula, $MC=16q=16(6)=96$ , we find that the firm will supply a positive amount of output as long as the price is greater than $96.