AP_Krugman_Textbook

The Slope of a Nonlinear Curve

A nonlinear curveis one in which the slope changes as you move along it. Panels (a),
(b), (c), and (d) of Figure A.4 show various nonlinear curves. Panels (a) and (b) show
nonlinear curves whose slopes change as you follow the line’s progression, but the
slopes always remain positive. Although both curves tilt upward, the curve in panel (a)
gets steeper as the line moves from left to right in contrast to the curve in panel (b),

appendix Graphs in Economics 39

Section I Basic Economic Concepts

figure A.4 Nonlinear Curves

In panel (a) the slope of the curve from Ato Bis = = 2.5,Δy

Δx

10

4

and from Cto Dit is = = 15. The slope is positive and in-

creasing; it gets steeper as it moves to the right. In panel (b) the

slope of the curve from Ato Bis Δy= = 10, and from Cto Dit

Δx

10

1

Δy

Δx

15

1

is = = 1. The slope is positive and decreasing; it gets flatter

as it moves to the right. In panel (c) the slope from Ato Bis

Δy

Δx

5

3

2

3

= = −3 , and from Cto Dit is = = −15. The slope

is negative and increasing; it gets steeper as it moves to the right.

Δy

Δx

− 10

3

1

3

Δy

Δx

− 15

1

And in panel (d) the slope from Ato Bis = = Δy −20, and

Δx

− 20

1

from Cto Dit is = = −1. The slope is negative and de-

creasing; it gets flatter as it moves to the right. The slope in each

case has been calculated by using the arc method—that is, by

drawing a straight line connecting two points along a curve. The

average slope between those two points is equal to the slope of

the straight line between those two points.

Δy

Δx

− 5

3

2

3

A

A A

B

B

B

C

C

D

C

1 2 345 6789 11 12

45

40

35

30

25

20

15

10

5

0 10 x

45

40

35

30

25

20

15

10

5

0

y

(a) Positive Increasing Slope

1 2 345 678910 11 12 x

y

45

40

35

30

25

20

15

10

5

0

45

40

35

30

25

20

15

10

5

0

yy

(b) Positive Decreasing Slope

A

B

C

D

1 2 345 678910 11 12 x

(c) Negative Increasing Slope

1 2 345 678910 11 12 x

(d) Negative Decreasing Slope

D D

Δx = 4

Δy = 10

Δx = 1

Slope = 15

Slope =

10

Slope =

–20

Slope =

–3

Slope = 1

Slope = –15

Slope = 2.5

Positive slope

gets steeper.

Δy = 15

Δx = 3

Δx = 1

Δy = –10

Δy = –15

Negative slope

gets steeper. Δy = –20

Δy = –5

Δx = 3

Δx = 1

Negative slope

gets flatter.

Δx = 1

Δx = 3

Δy = 10

Δy = 5

Positive slope

gets flatter.

2

3

1

3

Slope = –1^23