Economics F320L, Summer 2025 Instructor: Dr.

Trenton Herriford
Macroeconomic Theory

Problem Set #1
(due Monday, June 16 at 9:30 am)

Show your work and explain your reasoning in your answers. It should be clear how you
arrived at your conclusions in each answer. The quality of your explanations can determine
your grade on exams, so it helps to practice this in your problem sets.

Your answers should be handwritten and graphs drawn by hand. You are free to work with
others, but your answers should be written in your own words.

Part 1: Defining and Measuring GDP

1.1 [Textbook Ch. 2 Question #3 modified]

By how much does GDP rise in each of the following scenarios? Explain.
a. A computer company buys parts from a local distributor for $2 million, assembles the
parts, and sells the resulting computers for $5 million.
b. A real estate agent sells a house for $300,000 that the previous owners had bought 10
years earlier for $150,000. The agent earns a commission of $11,000.
c. During a recession, the government raises unemployment benefits by $200 million.
d. A new U.S. airline purchases and imports $70 million worth of airplanes from the
European company Airbus.
e. A new European airline purchases $40 million worth of airplanes from the American
company Boeing.
f. A store buys $110,000 of chocolate from Belgium and sells it to consumers in the
United States for $130,000.

1.2 [Textbook Question Ch. 2 #5]

Consider an economy that produces oranges and boomerangs. The prices and quantities of
these goods in two different years are reported in the following table. Fill in the missing
entries.

Percentage Change
2025 2026
2025-2026

Quantity of oranges 100 105 ?

Quantity of boomerangs 20 22 ?

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 Price of oranges (dollars) 1 1.10 ?

Price of boomerangs (dollars) 3 3.10 ?

Nominal GDP ? ? ?

Real GDP in 2025 prices ? ? ?

Real GDP in 2026 prices ? ? ?

Real GDP in chained prices,

benchmarked to 2026 ? ? ?

1.3 [Textbook Ch. 2 Question #6 modified]

Consider the economy from the previous question. Calculate the inflation rate for the 2025–
2026 period using the GDP deflator based on the chain-weighted index of GDP.

1.4 [Textbook Ch. 2 Question #7]

Indian GDP in 2017 was 152 trillion rupees, while U.S. GDP was $17.7 trillion. The exchange
rate in 2017 was 65.1 rupees per dollar. India turns out to have lower prices than the United
States (this is true more generally for poor countries): the price level in India (converted to
dollars) divided by the price level in the United States was 0.277 in 2017.
a. What is the ratio of Indian GDP to U.S. GDP if we don’t take into account the
differences in relative prices and simply use the exchange rate to make the conversion?
b. What is the ratio of real GDP in India to real GDP in the United States in common
prices?
c. Why are these two numbers different?

Part 2: Price Indexes and Measuring Inflation

2.1 [Textbook Ch. 8 Question #1 modified]

The following table converts the data in Table 8.1 of the textbook using more recent values
of the CPI index.

Year Consumer Price Index (2023=100)

1900 2.67

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 1930 5.48

1950 7.90

1960 9.72

1970 12.75

1980 27.04

1990 42.89

2000 56.52

2010 71.56

2023 100.00

Calculate the value in 2023 dollars of the following items using the CPI values above (refer to
the nearest year in the table to do your calculations):
a. Babe Ruth’s salary in 1932: $80,000.
b. A bottle of Coke or Pepsi in the late 1940s: one nickel.

2.2

Use the data on the CPI in the table given in the previous question to answer the following.
a. Compute the average annual rate of inflation that prevailed between 1980 and 2010.
b. Compute the average annual inflation rate between 1970 and 1980.
c. Compare these two rates.
Note: Average growth rates are covered in the next part of the problem set, so you may benefit
from solving this question with that part of the problem set.

Part 3: Details on Growth Rates

3.1 [Textbook Ch. 3 Question #1 modified]

In 2017, Ethiopia had a per capita income of approximately $1,900 (or about $5.20 per day).
Compute per capita income in Ethiopia for the year 2050 assuming average annual growth is
a. 1% per year.
b. 2.5% per year.

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3.2 [Textbook Ch. 3 Question #7 modified]

Compute the average annual growth rate of per capita GDP in each of the cases below. The
levels are provided for 1980 and 2019, measured in 2017 U.S. dollars. When doing this problem,
show and explain your work for just one country; you do not need to show your work for other
countries. (Note: the data in this table comes from the Penn World Tables.)

Per capita GDP (in 2017 U.S. dollars)

Country 1980 2019
United States 30,788 63,393
Canada 27,694 49,359
China 1,680 13,988

3.3 [Textbook Ch. 3 Question #5]

Plot the following scenarios for per capita GDP on a ratio scale. Specifically, use the rule of
70 to label the value of per capita GDP on the graph in the years listed below. Assume that
per capita GDP in the year 2025 is equal to $10,000.
a. Per capita GDP grows at a constant rate of 5% per year between 2025 and 2095.
b. Per capita GDP grows at 2% per year between 2025 and 2095, speeds up to 7% per
year for the next 20 years, and then slows down to 5% per year for the next 28
years.
c. Starting in 2025, per capita GDP grows at 7% per year for 50 years and then slows
down to 1% per year for the next 140 years.

Part 4: Aggregate Production

4.1 [Textbook Ch. 4 Question #5 modified]

The table below reports per capita GDP and capital per person in the year 2019 for 10
countries. Your task is to fill in the missing columns of the table. When filling in these columns,
show and explain your work for one country; you do not need to show your work for other
countries. (Note: the data in this table comes from the Penn World Tables.)
a. Given the values in columns 1 and 2, fill in columns 3 and 4. That is, compute per
capita GDP and capital per person relative to the U.S. values.
b. In column 5, use the production function 𝐹(𝐾, 𝐿) = 𝐴𝐾 𝛼 𝐿1−𝛼 (with a capital exponent
of 𝛼 =1/3) to compute predicted per capita GDP for each country relative to the United
States, assuming there are no TFP differences.
c. In column 6, compute the level of TFP for each country that is needed to match up the
model (that is, the production function) and the data.
d. Which country has the highest TFP? Which has the lowest?

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 In 2017 U.S. dollars Relative to U.S. values (U.S. values = 1)
(1) (2) (3) (4) (5) (6)
Capital Per Capital Per Implied TFP
Predicted
Country per capita per capita (to match
y*
person GDP person GDP data)

United States 209,865 63,393 1.000 1.000 1.000 1.000

Canada 233,116 49,359

China 70,823 13,988

Mexico 85,703 19,308

Ethiopia 5,788 2,552

4.2 [Textbook Ch. 5 Question #9 modified]

Use the production function in per capita terms (which is 𝑦𝑡 = 𝐴𝑘𝑡𝛼 , where 𝑦𝑡 is per capita
GDP and 𝑘𝑡 is capital stock per person) and also the rules for computing growth rates to write
the growth rate of per capita GDP as a function of the growth rate of capital stock per person.
Assume 𝛼 = 1/3.

Part 5: The Basic Solow Growth Model

Note: Please see the “Solow Diagram Guide” posted in the Notes on Canvas for instructions
on drawing Solow diagrams.

5.1 [Textbook Ch. 5 Question #2 modified]

One explanation for China’s rapid economic growth during the past several decades is its
expansion of policies that encourage “technology transfer.” By this, we mean policies—such
as opening up to international trade and attracting multinational corporations through
various incentives—that encourage the use and adoption in China of new ideas and new
technologies. This question asks you to use the Solow model to study this scenario.

Suppose China begins in steady state. To keep the problem simple, let’s assume the sole result
of these technology transfer policies is to increase A̅ by a large and permanent amount, one
time. To help you label the time-series graphs, you can assume that this change occurred at
the start of 1990.

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 a. Analyze this change using a Solow diagram. This graph should include the
investment and depreciation curves and how they change in response to the
economic change described above.
b. Draw a time series graph showing what happens to output in China over time. Start
the graph in 1990. Label any steady state value(s) of output per person on the vertical
axis and ensure that the size of the changes illustrated over time are qualitatively
consistent with the Solow model.
c. Draw a time series graph showing what happens to the growth rate of output in
China over time.

5.2 [Textbook Ch. 5 Question #5 modified]

Consider a basic Solow economy (with no productivity or labor/population growth) that

begins with a capital stock equal to $200 billion, and suppose its steady-state level of capital is
$600 billion. To its pleasant surprise, the economy receives a generous gift of foreign aid in
the form of $150 billion worth of capital.
a. Use the Solow diagram to explain what happens to the economy, both immediately
and over time. By what proportion does consumption per person initially increase?
What happens to steady-state consumption assuming consumption is some constant
fraction of GDP?
b. Suppose instead of starting below its steady state, the economy begins in steady state,
with a capital stock equal to $600 billion. Answer part (a) for this case.
c. Summarize what this exercise teaches you about the possible consequences of
foreign aid. In this example, does foreign aid exert a steady-state effect on the welfare
of poor countries? What is the benefit of foreign aid (in the form of capital) according
to the Solow model?

5.3 [Textbook Ch. 5 Question #8 modified]

According to the Solow model, by what proportion does steady-state real GDP per capita
change in the in response to each of the following changes?
a. The depreciation rate falls by 20%.
b. The productivity level rises by 5%.
c. An earthquake destroys 25% of the capital stock.
d. A more generous immigration policy leads the population to triple.

5.4

Repeat part (d) from the previous question except comparing total GDP in steady state before
and after the change. Explain why or why not the proportion you find for total GDP is different
than it is for per capita GDP.

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Part 6: Productivity (and Population) Growth in the Solow Model

6.1

Make one change to the Solow model with productivity growth (which is covered in the
slides): let the production function for output be 𝑌𝑡 = 𝐴𝑡 𝐾𝑡1/4 𝐿3/4
𝑡 (that is, change the exponent
on capital in the production function to 𝛼 = 1/4).
a. Solve for the growth rate of output per person along a balanced growth path.
b. Solve for the level of output per person along a balanced growth path.

6.2

Suppose this year, a country experiences a decline in the growth rate of its labor/population.
Draw a plot using a ratio (log) scale of this country’s output per capita on its old balanced
growth path versus output per capita on its new one in the same graph. Start the graph in this
year. Note that while you do not have specific numbers, you should still be able sketch this.

6.3

Especially in the mid-2010s, many forecasted that productivity growth would be lower in the
coming century for developed countries. Assume that productivity growth goes from 2% to
1%. Use the Solow model with productivity growth to answer the following questions.
a. What is the growth rate of GDP per capita on the balanced growth path before and
after this change?
b. By what factor would incomes increase in a century on the balanced growth path
under the old growth rates and under the new growth rates? Compare the two.
Assume that 𝛼 = 1/3; population growth rate is 1%; the depreciation rate is 10%; and
the saving rate is 30%.

Note: The model with productivity growth we discuss in class is different than the one
discussed in the course textbook, which is discussed in its Chapter 6. However, I have still
asked questions similar to those in textbook, except just applied to the model we discuss in
class. The questions I have loosely based these on are Chapter 6 questions #9 and appendix
question #5, as well as the ratio scale plotting asked for in questions #7 and #10.