1 1 appendix using graphs: a review appendix using graphs: a review

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AppendixUsing Graphs: A Review

Copyright© 2006 South-Western/Thomson Learning. All rights reserved.

Graphs Used in Economic Analysis

● Display large quantity of data quickly● Facilitate data interpretation and analysis● Important statistical relationships more

apparent than from written descriptions or long lists of numbers


Two-Variable Diagrams

● Variable = something measured by a number

♦ Examples: price and quantity

● View two variables together to see if they exhibit a relationship.

TABLE 1: Quantities of Natural Gas Demanded at Various Prices


Q

b

a P Pric

e

Quantity (a)

140 120 100 80 60 40 20 0

1

2

3

4

5

6

D

D

b

a

Q

P Pric

e

Quantity (b)

140 120 100 80 60 40 20 0

1

2

3

4

5

6

FIGURE 1: Hypothetical Demand Curve for Gas



The Definition and Measurement of Slope

● Slope = ratio of vertical change to horizontal change♦ Rise/run♦ Measure of steepness of the line



● The slope of a straight line♦ Negative slope = one variable rises while the

other variable falls■ The two variables move in opposite directions.

♦ Positive slope = two variables rise and fall together■ The two variables move in the same direction.

FIGURE 2a: Negative Slope

Negative slope

0 X

Y


FIGURE 2b: Positive Slope

Positive slope

0 X

Y




♦ Zero slope = the variable on the horizontal axis can be any value while the variable on the vertical axis is fixed■ Horizontal line

♦ Infinite slope = the variable on the vertical axis can be any value while the variable on the horizontal axis is fixed■ Vertical line

FIGURE 2c: Zero Slope

Zero slope

0 X

Y


FIGURE 2d: Infinite Slope

Infinite slope

0 X

Y




● The slope of a straight line♦ Slope is constant along a straight line.♦ Slope can be measured between any two

points on one axis and the corresponding two points on the other axis.

FIGURE 3: How to Measure Slope

3 — 10 Slope =

1 — 10 Slope =

(b) (a)

A

X

B

C

13 3 0

Y

8

11

X

A B

C

13 3 0

Y

8 9




● The slope of a curved line♦ Slope changes from point to point on a

curved line.■Curved line bowed toward the origin has a

negative slope.● Variables change in opposite directions.

■Curved line bowed away from the origin has a positive slope.

● Variables change in the same direction.

FIGURE 4a: Negative Slope in Curved Lines

Negative slope

0 X

Y


FIGURE 4b: Positive Slope in Curved Lines

Positive slope

0 X

Y




● The slope of a curved line♦ A curved can have both a positive and

negative slope depending on where on the curve is measured.

♦ The slope at a point on a curved-line is measured by a line tangent to that point.

FIGURE 4c,d: Behavior of Slope in Curved Lines

Negative slope

Positive slope

0 X

Y

Negative slope

Positive slope

0 X

Y


FIGURE 5: How to Measure Slope at a Point on a Curve

r

r

t

t A B

R

M

G T

E F

D

C

Y

X 10 9 8 7 6 5 4 3 2 1 0

8

7

6

5

4

3

2

1



Rays Through the Origin and 45-degree Lines

● Y-intercept = point at which a line touches the y axis

● Ray through the origin = straight line graph with a y-intercept of zero

FIGURE 6: Rays through the Origin

1 – 2 Slope = +

Slope = + 1

Slope = + 2

B

E

K

A C

D 0

5

4

3

2

5 4 3 2 1

1

Y

X



Squeezing 3 Dimensions into 2: Contour Maps

● Some problems involve more than two variables

● Economic “contour map” called a production indifference map♦ Shows how variable Z changes as we change

either X or Y

FIGURE 8: An Economic Contour Map

Z = 40

Z = 30

Z = 20

Z = 10

Yard

s of

Clo

th p

er D

ay

Labor Hours per Day

Y

X 80 70 60 50 40 30 20 10 0

10

20

30

40

50

60

70

80

B

A


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