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1Appendix
Using Graphs: A Review
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Graphs Used in EconomicAnalysis
Graphs Used in EconomicAnalysis
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
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
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Two-Variable Diagrams
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.
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TABLE 1: Quantities of NaturalGas Demanded at Various Prices
TABLE 1:Quantities of NaturalGas Demanded at Various Prices
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Q
b
aPPrice
Quantity(a)
140120100806040200
1
2
3
4
5
6
D
D
b
a
Q
PPrice
Quantity(b)
140120100806040200
1
2
3
4
5
6
FIGURE 1: Hypothetical DemandCurve for Gas
FIGURE 1: Hypothetical DemandCurve for Gas
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The Definition andMeasurement of Slope
The Definition andMeasurement of Slope
Slope = ratio of vertical change to
horizontal change
Rise/run
Measure of steepness of the line
Slope = ratio of vertical change to
horizontal change
Rise/run Measure of steepness of the line
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The Definition andMeasurement of Slope
The Definition andMeasurement 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 thesame direction.
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 thesame direction.
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FIGURE 2a: Negative SlopeFIGURE 2a: Negative Slope
Negative
slope
0X
Y
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FIGURE 2b: Positive SlopeFIGURE 2b: Positive Slope
Positiveslope
0X
Y
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FIGURE 2c: Zero SlopeFIGURE 2c: Zero Slope
Zero
slope
0
X
Y
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FIGURE 2d: Infinite SlopeFIGURE 2d: Infinite Slope
Infinite
slope
0X
Y
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FIGURE 3:How to Measure Slope
FIGURE 3:How to Measure Slope
310Slope =
110
Slope =
(b)(a)
A
X
B
C
1330
Y
8
11
X
AB
C
1330
Y
8
9
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The Definition andMeasurement of Slope
The Definition andMeasurement 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 apositive slope.
Variables change in thesame direction.
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 apositive slope.
Variables change in thesame direction.
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FIGURE 4a:Negative Slope in Curved Lines
FIGURE 4a:Negative Slope in Curved Lines
Negativeslope
0
X
Y
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FIGURE 4b:Positive Slope in Curved Lines
FIGURE 4b:Positive Slope in Curved Lines
Positiveslope
0X
Y
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The Definition andMeasurement of Slope
The Definition andMeasurement of Slope
The slope of a curved line
A curved can have both a positive and
negative slope depending on where on thecurve is measured.
The slope at a point on a curved-line is
measured by a line tangent to that point.
The slope of a curved line
A curved can have both a positive and
negative slope depending on where on thecurve is measured.
The slope at a point on a curved-line is
measured by a line tangent to that point.
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FIGURE 4c,d: Behavior of Slopein Curved Lines
FIGURE 4c,d: Behavior of Slopein Curved Lines
Negativeslope
Positiveslope
0X
Y
Negativeslope
Positiveslope
0X
Y
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FIGURE 5: How to Measure Slopeat a Point on a Curve
FIGURE 5: How to Measure Slopeat a Point on a Curve
r
r
t
t
AB
R
M
GT
E
F
D
C
Y
X109876543210
8
7
6
5
4
3
2
1
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Rays Through the Origin and45-degree Lines
Rays Through the Origin and45-degree Lines
Y-intercept = point at which a line
touches they axis
Ray through the origin = straight linegraph with ay-intercept of zero
Y-intercept = point at which a line
touches they axis
Ray through the origin = straight linegraph with ay-intercept of zero
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FIGURE 6:Rays through the Origin
FIGURE 6:Rays through the Origin
12Slope = +
Slope = + 1
Slope = + 2
B
E
K
A
C
D
0
5
4
3
2
54321
1
Y
X
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Squeezing 3 Dimensionsinto 2: Contour Maps
Squeezing 3 Dimensionsinto 2: Contour Maps
Some problems involve more than two
variables
Economic contour map called aproduction indifference map
Shows how variableZchanges as we change
eitherXorY
Some problems involve more than two
variables
Economic contour map called aproduction indifference map
Shows how variableZchanges as we change
eitherXorY
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FIGURE 8:An Economic Contour Map
FIGURE 8:An Economic Contour Map
Z= 40
Z= 30
Z= 20
Z= 10
Y
ardsofCloth
per
Day
Labor Hours per Day
Y
X80706050403020100
10
20
30
40
50
60
70
80
B
A