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Appendix
Using Graphs: A Review
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
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Two-Variable Diagrams
● Variable = something measured by a
number
♦ Examples: price and quantity
● View two variables together to see if they
exhibit a relationship.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
1: Quantities of Natural
Gas Demanded at Various Prices
TABLE
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
1: Hypothetical Demand
Curve for Gas
FIGURE
6
6
5
5
Price
Price
D
4
a
P
3
b
2
1
4
P
3
a
b
2
D
1
0
20
40
60
Q
80 100 120 140
Quantity
(a)
0
20
40
60
Q
80 100 120 140
Quantity
(b)
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
The Definition and
Measurement of Slope
● Slope = ratio of vertical change to
horizontal change
♦ Rise/run
♦ Measure of steepness of the line
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
The Definition and
Measurement of Slope
● 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.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE
2a: Negative Slope
Y
Negative
slope
0
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE
2b: Positive Slope
Y
Positive
slope
0
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
The Definition and
Measurement of Slope
♦ 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
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE
2c: Zero Slope
Y
Zero
slope
0
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE
2d: Infinite Slope
Y
Infinite
slope
0
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
The Definition and
Measurement of Slope
● 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.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
3:
How to Measure Slope
FIGURE
Y
Y
3
Slope = —
10
C
11
C
9
8
0
1
Slope = —
10
B
A
3
13
(a)
X
8
0
B
A
3
13
X
(b)
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
The Definition and
Measurement of Slope
● 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.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
4a:
Negative Slope in Curved Lines
FIGURE
Y
Negative
slope
0
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
4b:
Positive Slope in Curved Lines
FIGURE
Y
Positive
slope
0
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
The Definition and
Measurement of Slope
● 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.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
4c,d: Behavior of Slope
in Curved Lines
FIGURE
Y
Y
Negative
slope
Positive
slope
Negative
slope
Positive
slope
0
X
0
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
5: How to Measure Slope
at a Point on a Curve
FIGURE
Y
r
8
D
7
6
5
R
t
F
C
E
4
G
T
3
r
M
2
1
0
A
t
B
1
2
3
4
5
6
7
8
9
10
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
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
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6:
Rays through the Origin
FIGURE
Y
Slope = + 2
5
Slope = + 1
4
B
3 C
A
2
K
1
E
0
1
2
Slope = + 1
–
2
D
3
4
5
X
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
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
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8:
An Economic Contour Map
FIGURE
Y
Yards of Cloth per Day
80
70
60
50
A
40
Z = 40
B
30
Z = 30
20
Z = 20
10
Z = 10
0
10
20
30
40
50
60
70
80
X
Labor Hours per Day
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