Mr. O. Carr has the cost function c(y) = y2 + 100 if his output, y, is positive and c(0) = 0. If the price of output is 25, Mr. Carr's profit-maximizing output is zero.

Question

Quizplus · Accepted Answer

The profit function is given by 
p(y) = 25y - c(y)
= 25y - y^2 - 100

To maximize profit, we take the derivative of p(y) with respect to y and set it equal to zero:
p'(y) = 25 - 2y = 0
y = 12.5

Since y is positive, the profit-maximizing output is y = 12.5, not zero.

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