Problem 1. Per Capita GDP in Six Countries. The file pwt90.xlsx posted on Blackboard
contains version 9.0 of the “Penn World Table” database. Use the file to extract the data
for the following six countries: United States, United Kingdom, Japan, Brazil, China, and
Ethiopia. Specifically, we are interested in two series: “rgdpe” for PPP-adjusted chainweighted GDP (in millions of 2011 dollars) and “pop” for population size (in millions). Use
the template file problem1.xlsx provided on Blackboard to place the relevant data and
generate per capita real GDP series for our six countries of interest.
1. Plot the resulting per capita real GDP series for the six countries over the time period
1960–2014 (on the same graph) on the standard scale and, separately, on a ratio scale
of your choice. Hint: to make a plot on a ratio scale in Excel first use the standard
scale, then right-click on the vertical axis, choose “Format Axis” and under the axis
options tab select logarithmic scale indicating a base of your choice (say, 3). To plot
all six trajectories on the same graph, select the six series and insert the line graph
based on your selection. Feel free to play around with the graph options to make them
look nice.
2. For each country, compute the average annual growth rate of real per capita GDP over
the time period 1960–2014.
Problem 2. (Midterm exam, Spring 2014). At the beginning of 2003, Mr. Pu, the president
of country Ru, set an ambitious goal: Ru’s real GDP must be doubled in 10 years, by 2013.
In 2003, Ru’s real GDP was equal to 20.
1. At what rate (let’s call it the “target” rate) did the economy of Ru have to grow in
order to achieve Mr. Pu’s goal? How long would it take for the economy of Ru to
double if it grew at 5% per year? Hint: use the rule of 70.
2. The economy of Ru was off to a good start and was growing at the target rate for 5
years, from 2003 until 2008, when the world economic crisis arrived. As a result of
the crisis, in 2008 and 2009 real GDP was growing at just 1% per year. Furthermore,
following the two crisis years the economy could only sustain the annual growth rate
of 2%. Write down the formula to calculate the level of Ru’s real GDP in 2013. Hint:
use the constant growth rule repeatedly. In case you are curious, if you evaluate that
formula, the answer will be roughly 30.
On a ratio scale of your choice, sketch two trajectories: the hypothetical evolution of
Ru’s real GDP according to the target rate and its actual evolution from 2003 until
2013.
Another ambitious goal set by Mr. Pu at the beginning of 2003 was to increase the
living standards of Ru’s people. Specifically, the goal was to catch up with country Po
in terms of the level of real GDP per capita by 2017. In 2003, the population of Ru
was 10. The real GDP per capita in Po was equal to 3 (measured in units comparable
to Ru’s GDP figure from part 1).
4. If Po’s real GDP grew at 6% per year and its population grew at 1% per year, what
would be its (approximate) level of real GDP per capita in 2017?
5. If Ru wants to catch up with Po in 2017, what would its annual growth rate of real
GDP per capita have to be? You do not have to calculate the exact value, just provide
the formula that allows to do it.
Problem 3. (Final exam, Spring 2013). Consider two countries, China and the United
States. In 2010, per capita GDP in China is equal to 5 thousand dollars, while in the U.S.
it is 40 thousand dollars. The annual growth rates of GDP per capita are 7% in China and
2% in the U.S.
1. Apply the rule of 70 to find the year in which China’s per capita GDP will reach the
U.S. initial level of 40 thousand dollars. Provide a formula to calculate the level of
U.S. GDP per capita in that year.
2. In what decade will China overtake the U.S. in terms of GDP per capita? Hint: use
the rule of 70 to track the GDP dynamics in both countries.
3. Sketch the paths of GDP per capita in China and the U.S. on the same graph. Be sure
to use the ratio scale.
Problem 4. Computing Levels. Suppose x grows at rate gx = 2% per year and y grows at
rate gy = 4% per year, with the initial values x0 = 2 and y0 = 1. Calculate the numerical
values of z for t = 3 and t = 10 for the cases below. Hint: You will need two ingredients: 1)
z0 that you can compute based on x0 and y0, and 2) gz that you can compute using shortcut
rules for growth rates based on gx and gy. Once you have these two ingredients, just apply
the constant growth rule to find the required future values of z.
1. z = xy 2. z = x/y 3. z = x
1/3
y
2/3
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