College of Charleston
Econ 201- Introductory Macroeconomics
Fall 2011
Homework 2
Answer key
1. Problem 3, chapter 7, page 196 K&W
All figures are in billions of dollars.
a. Consumer spending is $1,082.8 + $2,833.0 + $5,794.4 = $9,710.2.
b. Private investment spending is $2,134.0 − $3.6 = $2,130.4.
c. Net exports are $1,662.4 − $2,370.2 = −$707.8.
d. Government purchases of goods and services and investment spending are $1,695.5 +
$979.3 = $2,674.8.
e. Gross domestic product is $9,710.2 + $2,130.4 + $2,674.8 − $707.8 = $13,807.6.
f. Consumer spending on services as a percentage of total consumer spending is
($5,794.4/$9,710.2) × 100 = 59.7%.
g. Exports as a percentage of imports is ($1,662.4/$2,370.2) × 100 = 70.1%.
h. Government purchases of goods and services on national defense as a percentage of
federal purchases of goods and services is ($662.2/$979.3) × 100 = 67.6%.
2. Problem 8, chapter 7, page 196 K&W
a. Real GDP is greater than nominal GDP for all years before 2000 because from
1960 to 2000 prices rose. So to calculate real GDP for the years 1960, 1970, 1980, and
1990, we would multiply output in those years by the higher prices that existed in 2000.
To calculate nominal GDP, we would multiply output by the lower prices that existed in
those particular years. Since prices rose from 2000 to 2007, valuing the output in 2007
using 2000 prices (real GDP) will result in a lower number than valuing the output in
2007 using 2007 prices. Real GDP equals nominal GDP in 2000 because the year 2000
is the base year and we use the same set of prices to value both real and nominal GDP in
that year.
b. The accompanying table shows the percent change in real GDP from 1960 to 1970,
1970 to 1980, 1980 to 1990, and 1990 to 2000. The percent change in real GDP was the
highest during the 1960s.
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c. We can calculate real GDP per capita by dividing real GDP by population. The
accompanying table shows real GDP per capita for each of the years in the table.
Remember that real GDP is measured in billions and population is measured in
thousands. Real GDP per capita in 1960 was $13,847.27 (equal to
$2,501,800,000,000/180,671,000).
d. The accompanying table shows the percent change in real GDP per capita from 1960
to 1970, 1970 to 1980, 1980 to 1990, and 1990 to 2000. The percent change in real GDP
per capita was the highest during the 1960s.
e. In this example, the percent change in real GDP is larger than the percent change in
real GDP per capita. As long as the population is growing, the two will always have this
relationship.
3. Problem 9, chapter 7, page 198 K&W
a. The percent change in the price of an English textbook from 2005 to 2007 is 14.0%
(equal to (($57 − $50)/$50) × 100).
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b. The percent change in the price of a math textbook from 2005 to 2007 is 5.7% (equal
to (($74 − $70)/$70) × 100).
c. The percent change in the price of an economics textbook from 2005 to 2007 is 25%
(equal to (($100 − $80)/$80) × 100).
d. To create an index of textbook prices, you must first calculate the cost of the market
basket (three English, two math, and four economics textbooks) in each of the three
years; then normalize it by dividing the cost of the market basket in a given year by the
cost of the market basket in the base period; and then multiply by 100 to get an index
value (base period of 2005 = 100).
Cost of textbooks in 2005 = (3 × $50) + (2 × $70) + (4 × $80) = $610
Cost of textbooks in 2006 = (3 × $55) + (2 × $72) + (4 × $90) = $669
Cost of textbooks in 2007 = (3 × $57) + (2 × $74) + (4 × $100) = $719
Index value for 2005 = ($610/$610) × 100 = 100
Index value for 2006 = ($669/$610) × 100 = 109.7
Index value for 2007 = ($719/$610) × 100 = 117.9
e. The percent change in the price index for textbooks from 2005 to 2007 is 17.9% (equal
to ((117.9 − 100)/100) × 100).
4. Problem 10, chapter 7, page 198 K&W
CPI for the retired person and for the college student, we need to weight the CPI for each
component with the importance of that component in his or her market basket. The CPI
for the retired person is 286.93 and for the college student is 150.54. Since the CPI for
the average consumer was 210.2, the CPI overstates the increase in the cost of living for
the college student and understates it for the retired person.
For the retired person:
For the college student:
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5. The accompanying table describes the labor market status of the citizens of Dodgertown. Use
this data to complete the following computations.
a.
b.
c.
d.
What is the size of the labor force?
What is the labor force participation rate?
What is the unemployment rate?
If we include the discouraged workers, what is the unemployment rate?
Table: Population in Dodgertown
a. The labor force is the sum of the employed and the unemployed that are looking for work. LF =
7000 + 900 = 7900.
b. The labor force participation rate is the labor force divided by the population aged sixteen and
older. LFPR = 7900/9600 = 82.3%.
a. The unemployment rate is the number of unemployed looking for work divided by the labor
force. UR = 900/7900 = 11.4%.
b. Inclusion of the discouraged workers increases the ranks of the unemployed by 500 and also
increases the labor force by 500. New UR = 1400/8400 = 16.7%.
6. Kelli is a server at a casual restaurant in a small town. In each of the following situations,
explain what type of unemployment Kelli is experiencing.
a. The local economy is experiencing a minor recession and the restaurant lays Kelli off. The
owner assures her that she will be rehired when business picks up again.
This is cyclical unemployment because it is due to the temporary dip in the business
cycle.
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b. A large factory, the major employer in the town, permanently closes and this hurts all
restaurants in town. The restaurant fires Kelli because the owner can only afford to stay open on
the weekends.
This is structural unemployment because it is due to a permanent decrease in the demand
for this labor. At the current wage, there is now a surplus of labor.
c. Kelli is dissatisfied with her schedule at the restaurant and quits her job. She is qualified to
work at other restaurants and immediately begins to send her resume to restaurants all over town.
This is frictional unemployment because she is voluntarily seeking a better match for her
skills and needs in the labor market.
7. Ted is looking to borrow money from a local bank. He is told that the nominal rate is 8% and
that includes an inflation expectation of 5% and a real interest rate of 3%. If there were
unexpectedly high inflation over the term of this loan, would Ted be hurt or would the bank be
hurt? Explain your answer.
Answer: Ted and the bank entered into this contract with an expectation that inflation
would be 5%. If inflation is higher, the bank receives payments that have lost purchasing
power. The bank, as lender, is losing due to this unexpectedly high inflation. Ted is
repaying the loan with dollars that have a lower real value than had been expected.
8. A nation's real GDP increased from $250 billion to $265 billion in one year. In that same year,
the nation's population increased from 125 million to 130 million. Calculate the nation's real GDP
per capita growth rate.
Real GDP per capita in year 1 = $250 000 mill/125 mill = $2,000
Real GDP per capita in year 2 = $265,000 mill/130 mill = $2048.5
Real GDP per capita growth rate =[$2048-2000/2000]X100=1.9%
9. The accompanying graph shows a nation's aggregate production function. Does this
production function exhibit diminishing returns to physical capital? Explain.
Answer: Yes. At first when the nation's stock of physical capital per worker is low, a one
unit increase will cause a large increase in real GDP per capita. However as the nation's
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physical capital per worker grows, a one unit increase will cause a smaller increase in
real GDP per capita. Graphically this is seen as a positive but declining slope of the
production function.
10. The accompanying graph shows the aggregate production function of two nations, A and B.
Suppose that in 1958 each nation had $100 of physical capital for each worker and in 2008 each
nation had $400 of physical capital per worker. Compute the growth of real GDP per capita for
both nations.
Nation A: ($5000–3000)/3000 = 67%
Nation B: ($2000–1000)/1000 = 100%
11. Problem 2, chapter 9, page 254 K&W
a. The accompanying table shows the number of years it would take for real GDP per
capita to double according to the Rule of 70 using the average annual growth rate in real
GDP per capita per decade in each country. Values corresponding to years with negative
growth rates are left uncalculated because we cannot apply the Rule of 70 to a negative
growth rate.
b. If each nation continues to grow as it did from 1990 to 2000, real GDP per capita will
have doubled in Argentina by 2018, in Ghana by 2033, and in South Korea by 2011.
12. Problem 4, chapter 9, page 255 K&W
a. The curve reflecting the relationship between physical capital per worker and output
per worker is drawn holding human capital per worker and technology fixed. Both
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Albernia and Brittania experience diminishing returns to physical capital since in both
countries equal successive increases in physical capital per worker— holding human
capital per worker and technology constant—will result in smaller and smaller increases
in real GDP per worker.
b. Albernia should increase its physical capital per worker to ($30,000)B.
c. If it were possible to increase the amount of human capital per worker, or improve the
technology, or both, then Productivity1 could shift to Productivity2 and Albernia could
double real GDP per worker without a change in the physical capital per worker. On the
accompanying diagram, Albernia would move from point A to point C.
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