1 1 appendix using graphs: a review appendix using graphs: a review
DESCRIPTION
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. ●Variable = something measured by a number ♦ Examples: price and quantity ●View two variables together to see if they exhibit a relationship.TRANSCRIPT
1
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
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.
TABLE 1: Quantities of Natural Gas Demanded at Various Prices
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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
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
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.
FIGURE 2a: Negative Slope
Negative slope
0 X
Y
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FIGURE 2b: Positive Slope
Positive slope
0 X
Y
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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
FIGURE 2c: Zero Slope
Zero slope
0 X
Y
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FIGURE 2d: Infinite Slope
Infinite slope
0 X
Y
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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.
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
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
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.
FIGURE 4a: Negative Slope in Curved Lines
Negative slope
0 X
Y
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FIGURE 4b: Positive Slope in Curved Lines
Positive slope
0 X
Y
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
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.
FIGURE 4c,d: Behavior of Slope in Curved Lines
Negative slope
Positive slope
0 X
Y
Negative slope
Positive slope
0 X
Y
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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
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
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
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
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
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
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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