Mr. O. Carr has the cost function c(y) = y2 + 64 if his output, y, is positive and c(0) = 0. If the price of output is 12, Mr. Carr's profit-maximizing output is zero.

Question

Quizplus · Accepted Answer

The profit function is p(y) = 12y - c(y). To find the profit-maximizing output, we need to find the value of y that maximizes p(y). Taking the derivative of p(y) with respect to y gives us:
p'(y) = 12 - 2y
Setting p'(y) = 0 and solving for y, we get y = 6. 
We also need to check the endpoints of the feasible region, which in this case is y ≥ 0. Evaluating p(y) at y = 0, we get p(0) = 0 - c(0) = 0, so y = 0 could be a profit-maximizing output. 
However, evaluating p(y) at y = 6, we get p(6) = 12(6) - (6^2 + 64) = -2, which is negative. Therefore, the profit-maximizing output is y = 0, but the resulting profit is zero.

Mr O Carr Has the Cost Function C(y) = Y2