AP_Krugman_Textbook

In contrast, the curve shown in panel (b) of Figure A.5 is U-shaped: it has a slope
that changes from negative to positive. At xequal to 50, the curve reaches its lowest
point—the smallest value of yalong the curve. This point is called the minimumof the
curve. Various important curves in economics, such as the curve that represents how a
firm’s cost per unit changes as output increases, are U–shaped like this one.

Calculating the Area Below or Above a Curve

Sometimes it is useful to be able to measure the size of the area below or above a curve.
To keep things simple, we’ll only calculate the area below or above a linear curve.
How large is the shaded area below the linear curve in panel (a) of Figure A.6? First,
note that this area has the shape of a right triangle. A right triangle is a triangle in which
two adjacent sides form a 90°angle. We will refer to one of these sides as the height of the
triangle and the other side as the baseof the triangle. For our purposes, it doesn’t matter
which of these two sides we refer to as the base and which as the height. Calculating the
area of a right triangle is straightforward: multiply the height of the triangle by the base
of the triangle, and divide the result by 2. The height of the triangle in panel (a) of Figure
A.6 is 10 − 4 =6. And the base of the triangle is 3 − 0 =3. So the area of that triangle is

= 9

How about the shaded area above the linear curve in panel (b) of Figure A.6? We can
use the same formula to calculate the area of this right triangle. The height of the tri-
angle is 8 − 2 =6. And the base of the triangle is 4 − 0 =4. So the area of that triangle is

6 × (^4) = 12
2

6 × 3

2

appendix Graphs in Economics 41

Section I Basic Economic Concepts

0 12 345

(a) Area Below a Linear Curve

10

9 8 7 6 5 4 3 2 1

y

Base of

triangle =

3 – 0 = 3

Height of

triangle

= 10 – 4

= 6 Height of

triangle

= 8 – 2

= 6

x 0 12 345

(b) Area Above a Linear Curve

10

9 8 7 6 5 4 3 2 1

y

Base of triangle

= 4 – 0 = 4

x

Area =^6 ×^3 = 9

2

Area =^6 ×^4 = 12

2

Calculating the Area Below and Above a Linear Curve

The area below or above a linear curve forms a right triangle. The

area of a right triangle is calculated by multiplying the height of

the triangle by the base of the triangle, and dividing the result by

2. In panel (a) the area of the shaded triangle is 9. In panel (b) the
   area of the shaded triangle is 12.

figure A.6