1. Graphs and Their Meaning
Chapter 1A
This appendix helps in understanding graphs, curves, and slopes as they relate to economics. It demonstrates how relationships between variables can be examined and how an equation that expresses that relationship can be derived.
Graphs and Their Meaning
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2. Construction of a Graph
A visual representation of the relationship between two variables
Horizontal axis
Vertical axis
Independent variable
Dependent variable
Ceteris paribus
The two dimensional graphs used in this textbook consist of a horizontal axis and a vertical axis. The point where the two meet is called the origin. As one moves away from the origin either up or to the right, the plotted values increase. Often the independent variable which is the variable that changes first, is placed on the horizontal axis and the dependent variable which is the variable that changes in response to the first variable changing, is placed on the vertical axis. However, in economics it is customary to always place price or cost data on the vertical axis even if it is the independent variable.
Economist invoke the ceteris paribus assumption in economics in order to be able to analyze just the two variables that are labeled on the axis. Ceteris paribus means to hold other things equal or constant and assumes that the only changes in the model are brought about by the dependent variable changing in response to the change in the independent variable.
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3. Direct and Inverse Relationships
Direct relationship
Both variables move in the same direction
Direct or positive relationships occur as the two variables change in the same direction. In other words, when the independent variable increases (decreases), the dependent variable also increases (decreases). This graphs as an upsloping line.
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4. Construction of a Graph
Table
Income
Consumption
Point
$ 0
100
200
300
400
$ 50
100
150
200
250 a b c d e
$400
300
200
100 e
Consumption (C)
Each pair of values in the table represents one point on the graph. This data represents variables that are positively or directly related, such as income and consumption, which will graph as an upsloping line. d c b a $
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Income (Y)

5. Direct and Inverse Relationships
Variables move in opposite directions
Inverse or negative relationships are those where the two variables move in opposite directions. So when the independent variable increases (decreases), the dependent variable decreases (increases). An inverse relationship graphs as a downsloping line.
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6. Construction of a Graph
Table
Graph a
Ticket
Price
Attendance,
Thousands
$ 50 40 30 20 10
Point
$ 50 40 30 20 10 4 8 12 16 20 a b c d e f b c
Ticket price (P) d
Each pair of values in the table represents one point on the graph. This data represents variables that are negatively or inversely related, such as ticket price and attendance at basketball games, which will graph as a downsloping line. e f
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Attendance in thousands (Q)

7. Slope of a Line Slope Slopes and measurement units
Slopes and marginal analysis
Infinite and zero slopes
Vertical intercept
The slope of a line can vary based on the units that are used to measure the slope. If in the ticket price and attendance example, if the number 4000 had been used instead of 4 for the horizontal change, the slope would have been instead of Slope is also important in economics when analyzing marginal changes. In the income example, a slope of 0.5 means that an increase of $1 in income will result in a $.50 increase in consumption spending. If there is no relationship between the two variables, the line will graph as a vertical line parallel to the vertical axis which reflects an infinite slope or it will graph as a horizontal line that is parallel to the horizontal axis which would exhibit a slope of zero.
The vertical intercept is the point where the line meets the vertical axis.
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8. Positive Slope of a Line
vertical change
+50 1 2
Slope = = =
= 0.5
horizontal change
+100
$400
300
200
100
As the independent variable, income, increases, the dependent variable, consumption, increases; this results in a positively sloped line.
Consumption (C) 50
Vertical
change
100
Horizontal change
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Income (Y)

9. Negative Slope of a Line
vertical change
-10 1 2
Slope = = -2
-2.5 = = 50
4030 20 10
horizontal change +4
Ticket Price $
Vertical
change
-10
As the independent variable, ticket price increases, attendance decreases. Here the variables are moving in opposite directions illustrating a negative slope. Note: though generally the independent variable is placed on the horizontal axis, when price is one of the variables, in economics it is customary to always place it on the vertical axis. 4
Horizontal change
Attendance
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10. Slope of a Line Slope = zero Slope = infinite Price of Bananas
Consumption
The graphs above show that the variables are unrelated. No matter what the price of bananas might be, the number of watches purchased remains the same. This is because the price of bananas does not affect the number of watches purchased. There is no relationship between consumption and the divorce rate. Consumption remains the same no matter how high or low the divorce rate is.
Purchases of watches
Divorce rate
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11. Equation of a Linear Relationship
y = a + bx, where
y is the dependent variable
a is the vertical intercept
b is the slope of the line
x is the independent variable
This is the general equation of a line and expresses the relationship between the two variables y and x. If you know the slope and the vertical intercept, you can solve for y or x.
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12. Equation of a Line Y = 50 + .5C $400 300 Consumption (C) 200 100
Consumption (C)
We calculated the slope of this line earlier, and we found that the slope is +.5. We can see from the graph that the vertical intercept is 50. Therefore the equation of this line is:
Y (income) = 50 (vertical intercept) + .5C (where .5 is the slope and C is the consumption). $
Income (Y)
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13. Equation of a Line
P = 50 – 2.5Q 50
4030 20 10
Ticket price
We calculated the slope of this line earlier, and we found that the slope is We can see from the graph that the vertical intercept is 50. Therefore the equation of this line is:
P (price) = 50 (vertical intercept) - 2.5Q (where -2.5 is the slope and Q is the quantity). In this case, the slope is being subtracted because the slope is negative.
Attendance
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14. Slope of a Nonlinear Curve
Slope always changes
Use a line tangent to the curve to find slope at that point
When calculating the slope of a nonlinear curve, the slope is always changing. This means the slope will be different at every point on the curve. In this case to find the slope, you must draw a line tangent to the curve and calculate the slope of the line by finding the change between two points along the tangent line.
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15. Slope of a Nonlinear Curve20 15 10 5
The slopes of a nonlinear curve will change along the curve. Here, the slope at these two points on the curve will be different from each other. To find the slope of a nonlinear curve, draw a straight line tangent to the curve and find the slope of that line by dividing the vertical change by the horizontal change of that line.
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