978-0077660772 Chapter 1 Appendix Part 2

Chapter 01 Appendix

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. LO8

Answer:

Study Time (hours) Exam Score (points)

0 10

2 30

The dependent variable is Exam Score (points); Study Time (hours) is the

Feedback: Consider the following figure:

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Chapter 01 Appendix

The table for this data is as follows:

Study

Time

(hours)

Exam Score

(points)

0 10

2 30

The dependent variable is Exam Score (points) because we assume Study Time (hours)

The vertical intercept for this relationship is your exam score if you choose not to study

(zero hours). From the table above this value is 10.

To find the slope we divide the change in your Exam Score by the change in Study Time

Thus, the equation representing this relationship is: Exam Score = 10 + 10 x

Study Time

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-

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Chapter 01 Appendix

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. LO8

Answer:

Interest

rate

(in percent)

Amount of

investment

(billions of dollars)

16

14

$ 0

5

Interest Rate

Feedback: Consider the following data as an example:

Suppose that when the interest rate on loans is 16 percent, businesses find it unprofitable

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Chapter 01 Appendix

Interest

rate

(in percent)

Amount of

investment

(billions of dollars)

16

14

$ 0

5

Chapter 01 Appendix

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?

Feedback:

(a) C and Y are positively related because the slope, b, is positive by assumption.

(b) The curve would slope upward because the slope is positive.

(c) C and Y are directly related because C and Y are positively related (move in

(d) Consider the following values: If a = 10, b = .50, and Y = 200, then C = 110. If

(e) Consider the following values: Y if C = 100, a = 10, and b = .25, then Y = 360.

If a = 10 and b = .25, then the consumption function takes the following form C =

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. LO8

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Feedback: Consider the following figure as an example:

To calculate the slope of the function use the “rise-over-run” approach. The “rise” is the

Point A has a slope that equals 4. To see this we use the two entries (2,10) and (12,50).

Point B has a slope equal to zero. There is no “rise” here, so we do not need coordinates

to calculate this value.

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Chapter 01 Appendix

Point C has a slope that equals -4. To see this we use the two entries (16,50) and (26,10).

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’.

Feedback: Consider the following figure:

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Chapter 01 Appendix

Slope of AA’ is positive (rising from left to right). The slope increases as we

Slope of BB’ is negative (dropping from left to right). The slope becomes more

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