Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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Chapter 01 Limits, Alternatives, and Choices (+ Appendix)
Appendix Questions
1. Briefly explain the use of graphs as a way to represent economic relationships. What is an
inverse relationship? How does it graph? What is a direct relationship? How does it graph? LO7
Answer: Graphs help us visualize relationships between key economic variables in the
data. For example, the relationship between the price of oranges and the number of
As another example, the relationship between the quality of a textbook and the number of
textbooks sold is likely to be a direct relationship. A direct relationship is one where we
observe one variable increasing and the other variable increasing as a result (moving in
the same direction). Thus, as the quality of the textbook increases the number of books
sold also increases. Graphically, we represent this direct relationship as follows.
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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2. Describe the graphical relationship between ticket prices and the number of people choosing to
visit amusement parks. Is that relationship consistent with the fact that, historically, park
attendance and ticket prices have both risen? Explain. LO7
Answer: There is likely an inverse relationship between ticket prices and the number of
people visiting amusement parks. As ticket prices increase relative to other goods, people
3. Look back at Figure 2, which shows the inverse relationship between ticket prices and game
attendance at Gigantic State University. (a) Interpret the meaning of both the slope and the
intercept. (b) If the slope of the line were steeper, what would that say about the amount by which
ticket sales respond to increases in ticket prices? (c) If the slope of the line stayed the same but
the intercept increased, what can you say about the amount by which ticket sales respond to
increases in ticket prices? LO7
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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Answer:
Part a: The slope of this relationship tells us how much the price of a ticket must fall to
induce someone to buy an additional ticket. In this case, the slope of -2.5 tells us that the
Appendix Problems
1. Graph and label as either direct or indirect the relationships you would expect to find between
(a) the number of inches of rainfall per month and the sale of umbrellas, (b) the amount of tuition
and the level of enrollment at a university, and (c) the popularity of an entertainer and the price of
her concert tickets. LO7
Answer:
Part a:
Sale of Umbrellas
Direct Relationship
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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Feedback: Consider the following situations:
Part a: The number of inches of rainfall per month and the sale of umbrellas: There is
likely a direct relationship between the number of inches of rainfall per month and the
sale of umbrellas (more rain implies more umbrellas).
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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Student
Enrollment
Inverse Relationship
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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Part c: The popularity of an entertainer and the price of her concert tickets: There is likely
a direct relationship between the popularity of an entertainer and the price of her concert
2. Indicate how each of the following might affect the data shown in the table and graph in
Figure 2 of this appendix: LO7
a. GSU’s athletic director schedules higher-quality opponents.
b. An NBA team locates in the city where GSU plays.
c. GSU contracts to have all its home games televised.
Answer: (a) increase in demand; shift to the right; (b) decrease in demand; shift to the left;
(c) decrease in demand; shift to the left.
Feedback: Consider the three scenarios:
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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3. The following table contains data on the relationship between saving and income. Rearrange
these data into a meaningful order and graph them on the accompanying grid. What is the slope of
the line? The vertical intercept? Write the equation that represents this line. What would you
predict saving to be at the $12,500 level of income? LO7
Answer:
Income per Year
Saving per Year
0
-$500
$5,000
0
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Feedback: Consider the following data:
Income per Year
Saving per Year
$15,000
$1,000
0
-$500
$10,000
$500
$5,000
0
$20,000
$1,500
Income per Year
Saving per Year
$5,000
$500
$15,000
$1,000
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Graphically, we have the following.
To find the predicted amount of saving for a given level of income we substitute the
income level into the equation above. For example if income equals $12,500, then the
predicted level of saving equals -$500 + 0.1x$12,500. Thus the predicted level of saving
is $750 (= -$500 + $1250).
4. Construct a table from the data shown on the graph below. Which is the dependent variable
and which the independent variable? Summarize the data in equation form. LO4
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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Answer:
Study Time (hours)
Exam Score (points)
0
10
2
30
Feedback: Consider the following figure:
4
50
6
70
8
90
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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The table for this data is as follows:
Study
Time
(hours)
Exam Score
(points)
0
10
2
30
5. Suppose that when the interest rate on loans is 16 percent, businesses find it unprofitable to
invest in machinery and equipment. However, when the interest rate is 14 percent, $5 billion
worth of investment is profitable. At 12 percent interest, a total of $10 billion of investment is
profitable. Similarly, total investment increases by $5 billion for each successive 2-percentage-
point decline in the interest rate. Describe the relevant relationship between the interest rate and
investment in a table, on a graph, and as an equation. Put the interest rate on the vertical axis and
investment on the horizontal axis. In your equation use the form i = a + bI , where i is the interest
rate, a is the vertical intercept, b is the slope of the line (which is negative), and I is the level of
investment. LO7
4
50
6
70
8
90
Chapter 01 – Limits, Alternatives, and Choices (+ Appendix)
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Answer:
Interest
rate
(in percent)
Amount of
investment
(billions of dollars)
16
14
12
$ 0
5
10
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Interest
rate
(in percent)
Amount of
investment
(billions of dollars)
16
14
12
10
$ 0
5
10
15
Graphically we have the following relationship.
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6. Suppose that C = a + bY , where C = consumption, a = consumption at zero income, b = slope,
and Y = income. LO7
a. Are C and Y positively related or are they negatively related?
b. If graphed, would the curve for this equation slope upward or slope downward?
c. Are the variables C and Y inversely related or directly related?
d. What is the value of C if a = 10, b = .50, and Y = 200?
e. What is the value of Y if C = 100, a = 10, and b = .25?
Answers: (a) positively related; (b) upward; (c) directly related; (d) C = 110; (e) Y = 360.
Feedback:
(a) C and Y are positively related because the slope, b, is positive by assumption. As
individual income increases the individual will spend some of this additional income on
consumption.
7. The accompanying graph shows curve XX’ and tangents at points A , B , and C . Calculate the
slope of the curve at these three points. LO7
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Answer: Point A, slope = 4; Point B, slope = 0; Point C, slope = -4.
8. In the accompanying graph, is the slope of curve AA’ positive or negative? Does the slope
increase or decrease as we move along the curve from A to A’? Answer the same two questions
for curve BB’.
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Answer: Slope of AA’ is positive; increases; Slope of BB’ is negative; decreases.
Feedback: Consider the following figure: