Nathan Grawe
Principles of Macroeconomics
PROBLEM SET 1
In this problem set you will be asked to do a variety of tasks using Excel. While there are times
when you will find it most desirable to add text, there is no time that you should need to actually
type in data. The data already is there and Excel has the ability to move it around in appropriate
ways. Since this problem set is designed to get you familiar with Excel, to circumvent this by
retyping data that is already there works against the whole point of the exercise.
There is no one way to do any of these exercises, but I wouldn’t be surprised if you had to make
good use of some fairly well hidden tools in Excel. For example, you might check out the “Paste
Special” command. In particular, the “Paste Values” and “Transpose” commands can be pretty
helpful at times. Also, in making Charts, the “Chart – Source Data” can be a very helpful tool
when putting multiple series into one Chart. Lastly, if you want to do something but do not know
how, use the “help” feature in Excel. It can be quite good.
Part A
Go to the web site for the appendix tables in the Economic Report of the President
(http://w3.access.gpo.gov/usbudget/fy2001/erp.html) and download the excel version of the Table
B-58. This should be the file “b-58.xls.” This is a table of price indices for major expenditure
groups. Download this file and save it. Included here is the Urban CPI since 1958.
1. Use the Urban CPI index and the Energy Price Index to derive a “real price index” for Energy
for the years going from 1958 to 1999.
2. Use the Urban CPI index and the Medical Care Price Index to derive a “real price index” for
Medical care for the years going from 1958 to 1999.
3. Use the Urban CPI index and the Apparel Price Index to derive a “real price index” for Apparel
for the years going from 1958 to 1999.
4. Use the Urban CPI index and the Food Price Index to derive a “real price index” for Food for
the years going from 1958 to 1999.
5. Use the Urban CPI index and the Housing Price Index to derive a “real price index” for
Housing for the years going from 1967 to 1999.
6. Plot all these indices (i.e. Real Energy Price Index, Real Medical Care Price Index, …) on one
diagram with the year on the horizontal axis and the real price index on the vertical axis.
7. Explain in one short paragraph what you think this diagram is telling us.
Part B
Go to the web site for the appendix tables in the Economic Report of the President
(http://w3.access.gpo.gov/usbudget/fy2001/erp.html) and download the excel version of Table B1a and B-1b. When put together these two files present the data in Table B-1 of the ERP
concerning Gross Domestic Product. Download this file and save it. Then download the excel
version of Table B-67. This is the Table with Money Stock Measures. Download and save this
file.
1. Import or Paste the Urban CPI index from the previous section of this assignment.
2. Calculate Real GDP using the GDP series in Table B-1 and the Urban CPI.
3. On one graph, plot real GDP and M1 money stock against time.
4. Plot real GDP against M1 money stock.
5. Calculate the annual percent growth in real GDP and the M1 money stock for each year.
(Note: You will have one less observation for growth rates than you did for levels of this
variables.)
6. Using a scatter plot, plot the growth rate of real GDP (y axis) against the growth rate in the M!
money stock (x axis).
7. In one short paragraph describe what you think these graphs tell us about the correlation
between M1 and real GDP.
Part C
Go to the Internal Revenue Service Web site and find income tax return data for Minnesota and
Mississippi (http://www.irs.gov/tax_stats/soi/ind_st.html). Look for the files “98in24mn.xls” and
“98in25ms.xls.” Download these files and save them. These data include information on income
tax returns filed for different income categories (under $20,000, $20,000-$30,000, etc.).
1. Calculate the proportion of all returns that are filed for each income class in both states. For
example, if a total of 100 returns were filed and 22 of then came from households with annual
income less than $20,000, this value would be 22%.
2. Create a well-labeled pie chart for Minnesota that shows the proportion of returns that come
from each income category.
3. Create a well-labeled pie chart for Mississippi that shows the proportion of returns that come
from each income category.
4. Create a well-labeled column chart for Minnesota and Mississippi that compares the proportion
of returns that come from each income category.
5. In no more than one brief paragraph, on the basis of this information, compare and contrast
Minnesota to Mississippi.
6. Calculate the proportion of all adjusted gross income attributable to each income class in both
states. For example, if total adjusted gross income for Minnesota were $12,000,000 and
$9,000,000 of this came from households with annual income more than $200,000 this value
would be 75%.
7. Create two columns of numbers for each state. The first column is the cumulative percentage of
households filing returns with adjusted gross income less than or equal to a specific income
category. The second column is the cumulative proportion of total adjusted gross income
attributable to households with adjusted gross income less than or equal to the specific income
category. Order the income categories so they go from lowest to highest. For example, suppose
that in Minnesota the values associated with part C-1 and the values associated with part C-5 are
as follows.
Income Category
Less than $20,000
$20,000-$30,000
$30,000-$50,000
$50,000-$75,000
$75,000-$100,000
$100,000-$200,000
Over $200,000
Percent of Returns
filed in Income
Category
20%
15%
25%
13%
12%
10%
5%
Percent of Total AGI
Attributable to Income
Category
3%
7%
15%
10%
15%
20%
30%
Then the answer to this question would be the following table.
Income Category
Less than $0
Less than $20,000
Less than $30,000
Less than $50,000
Less than $75,000
Less than $100,000
Less than $200,000
All
Percent of Returns
filed in Income
Category
0%
20%
35%
60%
73%
85%
95%
100%
Percent of Total AGI
Attributable to Income
Category
0%
3%
10%
25%
35%
50%
70%
100%
Plot the percent of the population with income less than a value in the income category against
the associated percent of total adjusted gross income for both states. I have plotted the pretend
data above. You should end up with two relationships, one for each state, on the same diagram
(properly labeled).
Example for Problem Set
100%
90%
% of Adjusted Gross Income
80%
70%
60%
50%
Pretend Data
40%
30%
20%
10%
0%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
% of Population
This relationship is called a Lorenz Curve and is commonly used as a way of summarizing the
distribution of income for some group of people.
8. What would a Lorenz Curve look like if there were a very equal distribution of income.
9. What would a Lorenz Curve look like for a very unequal distribution of income.
10. In no more than one short paragraph, compare the Lorenz Curve for Minnesota with the
Lorenz Curve for Mississippi.
PART D
1. Carefully identify the opportunity cost of each of the following activities.
a. What is the opportunity cost to you of purchasing a $50 U.S. Savings Bond?
b. What is the opportunity cost to the owner of the Guthrie Theater of letting a group of poor
children into a Guthrie Theater production for free?
c. What is the opportunity cost to you of attending Carleton College?
2. A foreign graduate student has just gotten her degree and is about to return home. The trade
regulations of her country allow her to bring back one new automobile from the U.S. without
having to pay the normal 50% tariff levied by her home country on U.S. imports (the effects of
the tariff are to raise the price of a U.S. automobile in her country 50% above the U.S. price). A
Ford Taurus sells in the U.S. for $15,000 and in the grad student’s home country for $22,500.
The student’s father asks the student to bring back a new Taurus for him and sends the student a
check for $17,000. The money, explains the student’s father, will cover the costs of the car
($15,000), the transportation costs of shipping the car ($1,000), and some generous compensation
for the time and trouble of handling the situation ($1000 for five hours work).
Is the graduate student happy to oblige? Explain (remember that there is an active market for
automobiles)! [hint: This is essentially a true false question with a fairly straightforward
explanation. The entire answer should be about three or four sentences.]
3. Suppose that the U.S. can convert 1 unit of "input" into 3 units of corn, and 1 unit of input into
5 units of electronics. Japan, on the other hand, can convert one unit of input into 6 units of corn,
and one unit of input into 15 units of electronics. The U.S. is currently endowed with 500 units of
input and Japan is endowed with 180 units of input.
a. Derive the production possibility frontier for the U.S.
b. Derive the production possibility frontier for Japan.
c. Derive the production possibility frontier for the U.S. and Japan.
d. Arbitrarily select one point on the U.S. production possibility frontier (not on one of the axes).
We will refer to this as CUS , EUS  . Arbitrarily select one point on Japan’s production possibility
frontier (not on one of the axes). We will refer to this as C J , E J  . Interpret these points as
production and consumption points for these two countries in the absence of trade.
Next, find all the points on the joint production possibility frontier that result in the production of
more of both goods than the sum of the two points you selected. That is, find all the points on the
joint production possibility frontier such that C  CUS  C J and E  EUS  E J .
e. Choose one of the points you identified in part d. and show how the U.S. and Japan collectively
produce that point.