Figure 2-10 Profits as a Function of Output
the curve is zero (because a tangent to the curve at point A is horizontal),
and so the marginal response of profits to output is zero.
Profits rise and then eventually fall as output rises. When the firm is
producing fewer than 2500 units annually, the marginal response of profit
to output is positive—that is, an increase in output leads to an increase in
profit. Beyond 2500 units annually, the marginal response is negative—an
increase in output leads to a reduction in profit. At point A, profits are
maximized and the marginal response of profit to output is zero. Because
the tangent at point A is horizontal, the slope of the curve is zero at that
point.
Now consider an example of a function with a minimum. You probably
know that when you drive a car, the fuel consumption per kilometre
depends on your speed. Driving very slowly uses a lot of fuel per
kilometre travelled. Driving very fast also uses a lot of fuel per kilometre
travelled. The best fuel efficiency—the lowest fuel consumption per