Chapter 2a Consumers buy more frozen yogurt when the price

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Solution

1. Study the four accompanying diagrams. Consider the following statements and indi-

cate which diagram matches each statement. Which variable would appear on the

horizontal and which on the vertical axis? In each of these statements, is the slope

positive, negative, zero, or infinity?

Panel (a) Panel (b)

Panel (c) Panel (d)

d. Consumers buy more frozen yogurt when the price of ice cream goes up.

e. Research finds no relationship between the number of diet books purchased and

the number of pounds lost by the average dieter.

f. Regardless of its price, Americans buy the same quantity of salt.

1. a. Panel (a) illustrates this relationship. The higher price of movies causes consum-

ers to see fewer movies. The relationship is negative, and the slope is therefore

negative. The price of movies is the independent variable, and the number of mov-

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Appendix: Graphs in Economics

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c. Panel (d) illustrates this relationship. With the temperature on the horizontal

axis as the independent variable, and the consumption of hot dogs on the vertical

axis as the dependent variable, we see there is no change in hot dog consumption

2. During the Reagan administration, economist Arthur Laffer argued in favor of low-

ering income tax rates in order to increase tax revenues. Like most economists, he

believed that at tax rates above a certain level, tax revenue would fall because high

taxes would discourage some people from working and that people would refuse to

work at all if they received no income after paying taxes. This relationship between

tax rates and tax revenue is graphically summarized in what is widely known as the

Laffer curve. Plot the Laffer curve relationship assuming that it has the shape of a

nonlinear curve. The following questions will help you construct the graph.

a. Which is the independent variable? Which is the dependent variable? On which

axis do you therefore measure the income tax rate? On which axis do you measure

income tax revenue?

Solution

2. a. The income tax rate is the independent variable and so is measured on the hori-

zontal axis. Income tax revenue is the dependent variable and so is measured on

the vertical axis.

Income

3. In the accompanying figures, the numbers on the axes have been lost. All you know

is that the units shown on the vertical axis are the same as the units on the horizon-

tal axis.

Panel (a) Panel (b)

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Solution

3. a. In panel (a), the slope is −2. From any point on the line, moving one unit to the

right along the horizontal axis requires moving down two units along the vertical

axis in order to remain on the line. The slope is the “rise” (−2) over the “run”

4. Answer each of the following questions by drawing a schematic diagram.

a. Taking measurements of the slope of a curve at three points farther and farther

4. a. The accompanying diagram schematically shows this curve. The slope is negative

throughout. That means that the curve is downward sloping. Because the absolute value

of the slope is increasing, the curve becomes steeper. The slope is negative increasing.

Slope = –0.3

Slope = –0.8

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Solution

5. For each of the accompanying diagrams, calculate the area of the shaded right

triangle.

100

Panel (a) Panel (b)

5. a. In panel (a), the height of the shaded triangle is 5 − 0 = 5, and its base is

4 − 0 = 4. The area of the triangle is 5 × 4

2 = 10.

6. The base of a right triangle is 10, and its area is 20. What is the height of this right

triangle?

6. The area of a right triangle is calculated as

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Solution

7. The accompanying table shows the relationship between workers’ hours of work per

week and their hourly wage rate. Apart from the fact that they receive a different hour–

ly wage rate and work different hours, these five workers are otherwise identical.

7. a. If the wage rate is greater than your opportunity cost of time, you will choose

to work. So the wage rate is the independent variable and the number of hours

worked is the dependent variable.

b. The accompanying diagram illustrates the relationship between the hourly wage

rate and the number of hours worked. Since the hourly wage rate is the price paid

for labor, economists place wages on the vertical axis—just as in the case of other

types of prices.

$75

Wage rate

(per hour)

Quantity of labor Wage rate

Name (hours per week) (per hour)

Athena 30 $15

Boris 35 30

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Solution

8. An insurance company has found that the severity of property damage in a fire is

positively related to the number of firefighters arriving at the scene.

therefore ask the city to send fewer firefighters to any fire?

8. a. By drawing the diagram with number of firefighters on the horizontal axis and

amount of property damage on the vertical axis, you are assuming that the num-

ber of firefighters is the independent variable and amount of property damage is

the dependent variable. That graph is shown here. It makes the argument that as

Amount of

property

damage

9. The accompanying table illustrates annual salaries and income tax owed by five

individuals. Apart from the fact that they receive different salaries and owe different

amounts of income tax, these five individuals are otherwise identical.

Annual income

Name Annual salary tax owed

Susan $22,000 $3,304

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Solution

a. If you were to plot these points on a graph, what would be the average slope of the

curve between the points for Eduardo’s and Camila’s salaries and taxes using the

9. a. Annual salary is the independent variable and so is measured on the horizontal

axis. Annual income tax owed is the dependent variable and so is measured on the

vertical axis. As salary increases by $31,000 from Eduardo’s $63,000 to Camila’s

$94,000, income tax owed increases by $9,610. That is, the slope of the curve is

10. Studies have found a relationship between a country’s yearly rate of economic growth

and the yearly rate of increase in airborne pollutants. It is believed that a higher rate

of economic growth allows a country’s residents to have more cars and travel more,

thereby releasing more air borne pollutants.

a. Which variable is the independent variable? Which is the dependent variable?

b. Suppose that in the country of Sudland, when the yearly rate of economic growth

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Solution

10. a. According to the question, economic growth causes the increase in air borne

pollut ants. That is, the growth rate is the independent variable and the rate of

increase in air borne pollutants is the dependent variable. So the rate of increase in

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