A competitive firm has a long-run total cost function c(y) = 2y2 + 288 for y 0 and c(0) = 0. Its long-run supply function is described as

Question

A competitive firm has a long-run total cost function c(y) = 2y2 + 288 for y > 0 and c(0) = 0. Its long-run supply function is described as

Quizplus · Accepted Answer

In the long-run, a competitive firm will produce where price equals marginal cost, which is equal to the minimum point on the long-run average cost curve. The long-run average cost function for the firm is given by AC(y) = c(y)/y = 2y + 288/y. To find the minimum point of this function, take its derivative with respect to y and set it equal to zero:

d/dy[AC(y)] = 2 - 288/y^2 = 0

Solving for y, we get y = sqrt(144) = 12. Plugging this back into the AC function, we get AC(12) = 48. Therefore, the firm will produce positive output levels for prices greater than or equal to 48, and will shut down for prices less than 48. Thus, the long-run supply function is given by y = if p ≥ 48, y = 0 if p < 48. The answer is therefore C.

A Competitive Firm Has a Long-Run Total Cost Function C(y)