Appendix 1 Applying Graphs to

Economics

©1999 South-Western College Publishing

• Key Concepts• Summary• Practice Quiz•Internet Exercises

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What is aDirect Relationship

between two variables?When one increases,

the other increases and vice versa

* Return to previous slide while in slide show

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What is the Slope of a line?

The ratio of change in the variable on the vertical axis (the rise or fall) to change in the variable on the horizontal axis (the run).

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Slope = rise/run = vertical axis/horizontal axis

= Y/X

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Expenditure for Personal Computerat Different Annual Incomes

Personal Expenditure

Annual Income

$1,000$2,000$3,000$4,000

$10,000$20,000$30,000$40,000

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4

3

2

1

10 20 30 40

A

B

C

D

Y=1

X=10

Y

X

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What is an Inverse Relationship between

two variables?When one increases,

the other decreases and vice versa

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Quantity of Compact Discs Consumers Purchased at Different Prices

Price per compact disc

Quantity of compact discs

$20

$15

$10

25,000,000

50,000,000

75,000,000

$5 100,000,000

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20

15

10

5

25 50 75 100

A

B

C

D

Y=5

X=25

Negative Sloping Curve

X

Y

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What is an Independent Relationship between

two variables?When one variable changes,

the other variable remains unchanged

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Expenditure for Toothpasteat Different Annual Incomes

Personal Expenditure

Annual Income

$10$20

$30$40

$10,000$20,000$30,000$40,000

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40

30

20

10

10 20 30 40

A B C D

Y=0X=10

X

Y

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Can Slope vary along a curve?

Yes, the slope of a curve can vary along the curve

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4

3

2

1

10 20 30 40

AY=2

X=30 X

Y

15

20

15

10

5

25 50 75 100

AY=

X=50

-10

X

Y

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How can I tell the difference between a

movement along a curve and a shift in the curve?When price changes, there

is movement along a curve. When something other than price changes, the whole curve shifts.

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What can change other than price?

When income increases, for example, the whole demand curve shifts upward

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20

15

10

5

25 50 75 100

Annual Income $60,000

Annual Income $30,000 X

Y

19

20

15

10

5

5 10 15 20

C

D

Positive Sloping Curve

X

Y

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Key Concepts

©1999 South-Western College Publishing

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• What is a Direct Relationship between two variables?

• What is the Slope of a line?

• What is an Inverse Relationship between two variables?

• What is an Independent Relationship between two variables?

• Can Slope vary along a curve?

• What can change other than price?

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Summary

©1999 South-Western College Publishing

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Graphs provide a means to clearly show economic relationships in two-dimensional space. Economic analysis is often concerned with two variables confined to the upper right-hand (northeast) quadrant of the coordinate number system.

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4

3

2

1

10 20 30 40

A

B

C

D

Y=1

X=10

Y

X

A direct relationship

25

20

15

10

5

25 50 75 100

A

B

C

D

Y=5

X=25

An inverse relationship

X

Y

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40

30

20

10

10 20 30 40

A B C D

Y=0X=10

X

Y An independent relationship

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4

3

2

1

10 20 30 40

AY=2

X=30 X

Y Positive slope of an upward-sloping curve

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20

15

10

5

25 50 75 100

AY=

X=50

-10

X

Y Negative slope of an downward-sloping curve

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A shift in a curve occurs only when the ceteris paribus assumption is relaxed and a third variable not on either axis of the graph is allowed to change

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Appendix Quiz

©1999 South-Western College Publishing

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1. Straight line CD in Exhibit A-7 on the next page shows thata. increasing the value of X will increase the

value of Y.b. decreasing the value of X will decrease

the value of Y.c. there is a direct relationship between X

and Y.d. all of the above.

©1999 South-Western College Publishing

D. As the value of X increases, the value of Y increases, and vice versa; this is called a direct relationship.

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20

15

10

5

5 10 15 20

D

EXHIBIT A-7

X

Y

C

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2. In Exhibit A-7, the slope of straight line CD isa. 3.b. 1.c. -1.d. 1/2.

D. The slope of a line is measured by the rise over the run, or a change in vertical divided by a change in the horizontal. For example, as Y increases from 5 units to 15, X increases from 0 to 20. The slope is 10 divided by 20.

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3. In Exhibit A-7, the slope of straight line CD isa. positive.b. zero.c. negative.d. variable.

A. When both X and Y move in the same direction, it is said that they are directly related to one another.

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4. Straight line AB in Exhibit A-8 shows thata. increasing the value of X reduces the

value of Y.b. decreasing the value of X increases the

value of Y.c. there is an inverse relationship between

X and Y.d. all of the above.

D. When the value of X decreases, the value of Y increases and vice versa; this shows a direct relationship between X and Y.

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20

15

10

5

5 10 15 20

A

B

EXHIBIT A-8

X

Y

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5. As shown in Exhibit A-8, the slope of straight line ABa. decreases with increases in X.b. increases with increases in X.c. increases with decreases in X.d. remains constant with changes in X.

D. The slope of a straight line stays the same between the two points on the line.

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6. In Exhibit A-8, the slope of straight line AB isa. 3.b. 1.c. -1.d. -5.

C. There is a one to one inverse ratio between a change in X and a change in Y. For example, as Y decreases from 20 units to 0, X increases from 0 to 20. The slope is -20 divided by 20.

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7. A shift is a curve represents a change ina. the variable on the horizontal axis.b. the variable on the vertical axis.c. a third variable that is not on either

axis.d. any variable that is relevant to the

relationship being graphed.

C. A shift occurs when something changes other than the price.

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8. A change in a third variable not on either axis of a graph is illustrated with aa. horizontal or vertical line.b. movement along a curve.c. shift of a curve.d. point of intersection.

C. When price changes the movement is always along a stationary curve. When something changes other than price, the whole curve shifts.

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