AP_Krugman_Textbook

which gets flatter. A curve that is upward sloping and gets steeper, as in panel (a), is

said to have positive increasingslope. A curve that is upward sloping but gets flatter, as in

panel (b), is said to have positive decreasing slope.

When we calculate the slope along these nonlinear curves, we obtain different values

for the slope at different points. How the slope changes along the curve determines the

curve’s shape. For example, in panel (a) of Figure A.4, the slope of the curve is a positive

number that steadily increases as the line moves from left to right, whereas in panel (b),

the slope is a positive number that steadily decreases.

The slopes of the curves in panels (c) and (d) are negative numbers. Economists

often prefer to express a negative number as its absolute value,which is the value of

the negative number without the minus sign. In general, we denote the absolute value

of a number by two parallel bars around the number; for example, the absolute value of

−4 is written as |−4| =4. In panel (c), the absolute value of the slope steadily increases

as the line moves from left to right. The curve therefore has negative increasingslope.

And in panel (d), the absolute value of the slope of the curve steadily decreases along

the curve. This curve therefore has negative decreasingslope.

Maximum and Minimum Points

The slope of a nonlinear curve can change from positive to negative or vice versa. When

the slope of a curve changes from positive to negative, it creates what is called a maxi-

mum point of the curve. When the slope of a curve changes from negative to positive, it

creates a minimum point.

Panel (a) of Figure A.5 illustrates a curve in which the slope changes from positive to

negative as the line moves from left to right. When xis between 0 and 50, the slope of

the curve is positive. At xequal to 50, the curve attains its highest point—the largest

value of yalong the curve. This point is called the maximum of the curve. When xex-

ceeds 50, the slope becomes negative as the curve turns downward. Many important

curves in economics, such as the curve that represents how the profit of a firm changes

as it produces more output, are hill-shaped like this one.

40 section I Basic Economic Concepts

0

y

x

50

Maximum point

y increases as

x increases.

y decreases as

x increases.

0

y

x

50

Minimum point

y decreases as

x increases.

y increases as

x increases.

(a) Maximum (b) Minimum

Maximum and Minimum Points

Panel (a) shows a curve with a maximum point, the point at which

the slope changes from positive to negative. Panel (b) shows a

curve with a minimum point, the point at which the slope changes

from negative to positive.

figure A.5