Problem Set 1 (Due October 7 Thursday before class)
Econ 100B, Fall 2021
1. What counts as GDP (II)?: By how much does GDP rise in each of the following
scenarios? Explain.
(a) A computer company buys parts from a local distributor for $1 million, assembles the
parts, and sells the resulting computers for $2 million.
(b) 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.
(c) During a recession, the government raises unemployment benefits by $100 million.
(d) A new U.S. airline purchases and imports $50 million worth of airplanes from the
European company Airbus.
(e) A new European airline purchases $50 million worth of airplanes from the American
company Boeing.
(f) A store buys $100,000 of chocolate from Belgium and sells it to consumers in the United
States for $125,000.
2. National accounting over time (I): Look back at Table 2.4. Some missing entries are
labeled at question marks. Compute the values that belong in these positions.
3. How large is the economy of India?: Indian GDP in 2010 was 78.9 trillion rupees, while
U.S. GDP was $14.5 trillion. The exchange rate in 2010 was 45.7 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 0.368 in 2010.
(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?
4. The ratio scale: 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 need a calculator
or computer program. Use the Rule of 70 to label the value of per capita GDP on the graph
in the year listed below.
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(a) Per capita GDP grows at a constant rate of 5% per year between 2015 and 2085.
(b) Per capita GDP grows at 2% per year between 2015 and 2085, 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) Per capita GDP grows at 7% per year for 50 years and then slows down to 1% per year
for the next 140 years.
5. Computing growth rates (II): Suppose k, l, and m grow at constant rates given by ḡk , ḡl ,
and ḡm . What is the growth rate of y in each of the following cases?
(a) y = k 1/3
(b) y = k 1/3 l2/3
(c) y = mk 1/3 l2/3
(d) y = mk 1/4 l3/4
(e) y = mk 3/4 l1/4
(f) y = (klm)1/2
(g) y = (kl)1/4 (1/m)3/4
6. Computing levels: Suppose xt grows at 2% per year and yt grows at 5% per year, with
x0 = 2 and y0 = 1. Calculate the numerical values of zt for t = 0, t = 1, t = 2, t = 10, t = 17,
and t = 35 for the following cases:
(a) z = x
(b) z = y
(c) z = x3/4 y 1/4
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