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