D01235-4 Macroeconomic Theory
Homework #2
Spring 2025
due on Thursday, April 11
Problem 1 By how much does GDP in the US rise in each of the following scenarios?
1. The US government raises unemployment benefits by $100 million.
2. A foreign graduate student works as a teaching assistant at a local university in the US
and earns $5,000.
3. A real estate agent sells a house for $200,000 that the previous owners had bought 10
years earlier for $100,000. The agent earns a commission of $6,000.
4. The US government spends $100 million to build a dam.
Problem 2 Imagine a simple economy in which there are two goods, apples and computers.
The following table shows the calculation of real and nominal GDP for our simple economy.
Quantity of apples
Quantity of computers
Price of apples (dollars)
Price of computers (dollars)
Nominal GDP
Real GDP in 2018 prices
Real GDP in 2019 prices
Real GDP in 2020 prices
Real GDP in chained prices,
benchmarked to 2020
2018
500
5
1
900
5,000
5,000
6,000
?
?
2019
500
5
2
1,000
6,000
5,000
6,000
6,500
6,483
2020
550
6
3
1,000
?
?
7,100
7,650
7,650
Percentage change
2019-2020
10.0
20.0
50.0
0.0
27.5
?
18.3
17.7
18.0
Some missing entries are labeled with question marks. Compute the values that belong in these
positions.
Problem 3 Indian GDP in 2014 was 119 trillion rupees, while US GDP was $16.5 trillion.
The exchange rate in 2014 was 61.0 rupees per dollar. India turns out to have lower prices than
the US: the price level in India (converted to dollars) divided by the price level in the US was
0.280 in 2014.
1. What is the ratio of Indian GDP to US GDP if we don’t take into account the differences
in relative prices and simply use the exchange rate to make the conversion?
2. What is the ratio of real GDP in India to real GDP in the US in common prices?
3. Why are these two numbers different?
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Problem 4 Plot the following scenarios for per capita GDP on a ratio scale. Assume that per
capita GDP in the year 2015 is equal to $10,000. You should not use a calculator or computer
program. Instead, use the Rule of 70 to label the value of per capita GDP on the graph in the
years listed below.
1. Per capital GDP grows at a constant rate of 5% per year between 2015 and 2085.
2. Per capita GDP grows at 7% per year for 50 years and then slows down to 1% per year
for the next 140 years.
Problem 5 Refer to the following figure when answering the next two questions.
1. (Multiple choice) The shape of this production function function suggests
(a) a diminishing marginal product of labor.
(b) a constant marginal product of capital.
(c) an increasing marginal product of capital.
(d) an increasing marginal product of labor.
(e) a diminishing marginal product of capital.
(f) None of these answers is correct.
2. (Multiple choice) Suppose the above figure illustrates the Cobb-Douglas production function Y = K α L1−α . The shape of this production function function suggests that α in the
Cobb-Douglas production function is
(a) equal to one.
(b) greater than one.
(c) equal to zero.
(d) less than one.
(e) Not enough information is given.
Problem 6 Consider the following Cobb-Douglas production function
Y = AK α L1−α ,
where Y is output, K is capital, and L is labor. Assume that A is TFP and the exponents on
capital and labor in the above production function is 1/3 and 2/3, respectively. Output per
person is denoted by y ≡ Y /L and capital per person is denoted by k ≡ K/L.
The table below reports per capita GDP and capital per person in the year 2014 for 4 countries.
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Country
US
France
Korea
Kenya
In 2011 dollars
(1)
(2)
Capital Per capita
per person
GDP
141,841
51,958
162,207
37,360
120,472
34,961
4,686
2,971
Relative to the US values (US=1)
(3)
(4)
(5)
(6)
Capital Per capita Predicted Implied TFP
per person
GDP
y to match data
Your task is to fill in the missing columns of the table, using the production function.
1. 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 US values.
2. In column 5, use the production function to compute predicted per capita GDP for each
country relative to the US, assuming there are no TFP differences.
3. In column 6, compute the level of TFP for each country that is needed to match up the
model and the data.
4. Fill in the blanks of the following statement.
According to the data, Korea’s per capita GDP was (
capital per person was (
)% of the US level.
)% of the US level and Korea’s
5. Fill in the blanks of the following statement.
According to the prediction of the model (with the assumption of no TFP differences
across countries), Korea’s per capita GDP was (
)% of the US level and Korea’s
capital per person was (
)% of the US level.
6. Fill in the blank of the following statement and answer the question below.
According to the data, the US is (
) times richer than Kenya; what fraction of this
factor is due to differences in capital per person and what fraction is due to differences in
TFP?
7. (Multiple choice) Comparing between the data (part 4) and the prediction of the model
(part 5) for Korea, you obverse that the model
(a) underestimates the level of per capita GDP.
(b) overestimates the level of per capita GDP.
(c) does a really good job of estimating the level of per capita GDP.
(d) clearly contains all factors that affect per capita GDP.
(e) None of these answers is correct.
8. (Multiple choice) One possible explanation for the difference between the data (part 4)
and the prediction of the model (part 5) for Korea is differences in
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(a) capital per person.
(b) misallocation of production factors.
(c) capital’s share of GDP.
(d) labor’s share of GDP.
(e) None of these answers is correct.
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