Download Due Date: Thursday, September 8th (at the beginning of class)

Problem Set 1
FE411 Spring 2006
Rahman
INSTRUCTIONS: Use your own paper to answer the questions. Please turn in your
problem sets with your name clearly marked on the front page and all pages stapled
together. You are encouraged to work together, but you must hand in your own work.
You must show your work for credit and answer in complete sentences when appropriate
(such as when the question asks you to “describe” or “explain”).
Comparing GDP Using Purchasing Power Parity
1. Consider two economies, Richania and Pooristan, which produce and “consume” only
bread and buildings. The following table contains price and production data for each
country:
Country
Richania
Pooristan
Bread
Produced
per Capita
90
15
Buildings
Produced per
Capita
30
5
Price of Bread
in Local
Currency
4
2
Price of Buildings
in Local
Currency
100
10
a. Calculate the level of GDP per capita in each country, measured in its own
currency.
Richania: 90 bread * $R4 + 30 buildings * $R100 = $R 3360
Pooristan: 15 bread * $P2 + 5 buildings * $P10 = $P 80
b. Calculate the market exchange rate between the currencies of the two
countries.
Bread should be treated as the traded good. $R4/ $P2 = $R2/ $P . We
consider the price ratio of bread as our market exchange rate because this is
where arbitrage can occur. Since bread is traded, we expect bread to be the
same price across countries when converted to the local currency.
c. What is the ratio of GDP per capita in Richania to GDP per capita in
Pooristan, using the market exchange rate?
$P 80 * ($R2/ $P) = $R 160. Thus, measured in Richanian dollars, it looks
like Richania is 3360/160 = 21 times richer than Pooristan.
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Problem Set 1
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d. Calculate the purchasing power parity (PPP) exchange rate between the two
currencies.
Basket should be 3 loaves of bread and 1 building. This costs $R112 in
Richania and $P16 in Pooristan. $R112/ $P16 = $R7 / $P . Why does this
exchange rate make Richanian dollars appear more “cheap” (since for just
1 Pooristanian buck you can get a whopping 7 Richanian dollars)? When
we compare what things actually cost in each country, the Pooristanian
dollar can simply buy more in Pooristan (because buildings are so much
cheaper).
e. What is the ratio of GDP per capita in Richania to GDP per capita in
Pooristan, using the PPP exchange rate?
$P 80 * ($R7/ $P) = $R 560. Thus, measured in Richanian dollars, it looks
like Richania is 3360/560 = 6 times richer than Pooristan. Indeed, this is
reality!
Calculating Growth Rates
2. In 1900 GDP per capita in Japan (measured in year 2000 dollars) was $1433. In 2000
it was $26,375. Calculate the annual growth rate of income per capita in Japan over this
period. Now suppose that Japan grows at the same rate for the century following 2000.
What will Japanese GDP per capita be in the year 2100?
(Y1900)*(1+g)100 = Y2000. Rearrange to solve for g: ($26,375/$1,433)(1/100) – 1.
g ≈ 0.0296.
To find the income per capita of Japan 100 years from now in 2100, we solve
(Y2000)*(1+g)100 = Y2100. ($26,375)*(1.0296)100 = Y2100. Y2100 = $485,443.60.
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Problem Set 1
FE411 Spring 2006
Rahman
3. In 2000 GDP per capita in the United States was $35,587 while GDP per capita in Sri
Lanka was $3,527. Suppose that income per capita in the United States has been growing
at a constant rate of 1.9% per year. Calculate the year in which income per capita in the
United States was equal to year 2000 income per capita in Sri Lanka.
(YUS,2000-t)*(1+g)t = YUS,2000. Note that YUS,2000-t = YSri Lanka,2000 .
($3527)*(1.019)t = $35,587. Solve for t.
t * ln(1.019) = ln($35,587/$3527). t = 122.8.
Issues with Inference
4. For each of the following scenarios, discuss what statistical problem might make the
inference incorrect:
a. People who vote for right-wing political parties tend to live longer than those who
vote for left-wing parties. Therefore, being a political conservative is good for
you.
Although the majority of right-winged voters may live longer, the inference that
being a political conservative is good for you is incorrect because correlation
does not imply causation. A majority of right-winged voters may live longer,
not because they are conservative but rather, because they lead healthier
lifestyles that right-wing policies promote. Thus, we have an omitted third
variable affecting both the choice of party affiliation and the length of life.
b. People in hospitals are generally less healthy than those outside of hospitals.
Therefore, it is best to avoid hospitals.
Although people in hospitals are generally less healthy than those outside
hospitals, the inference that one should avoid hospitals is incorrect because of
reverse causation. Majority of people go to the hospital because they are
unhealthy.
Cobb-Douglas and Payments to the Factors of Production
5. Suppose that the production function is Cobb-Douglas with parameter α = 0.3.
a. What fractions of income do capital and labor receive?
Note that MPL = (1-α)*Y/L, and MPK = α*Y/L. Given that profit-maximizing
firms hire factors of production until their marginal products equal their costs,
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MPL = W/P, and MPK = R/P. And since α = 0.3, we see that 30% of Y is paid
to capital, while the rest is paid to labor.
b. Suppose that immigration raises the labor force by 10 percent. What happens to
total output (in percent)? The real rental price of capital (in percent)? The real
wage (in percent)?
Y1 = AK0.3L0.7,
Y2 = AK0.3(1.1L0.7)
Y2 / Y1 = (1.1)0.7 = 1.069
(R/P)1 = MPK = 0.3AK-0.7L0.7,
(R/P)2 = 0.3AK-0.7(1.1L0.7)
(R/P)2 / (R/P)1 = 1.069
(W/P)1 = MPL = 0.7AK0.3L-0.3,
(W/P)2 = 0.7AK-0.7(1.1L-0.7)
(W/P)2 / (W/P)1 = 0.972
Thus we see that while output and the rental rate of capital each rise by 6.9%,
the wage falls by 2.8%.
c. Suppose that a gift of capital from abroad raises the capital stock by 10 percent.
What happens to total output (in percent)? The real rental price of capital (in
percent)? The real wage (in percent)?
Y1 = AK0.3L0.7,
Y2 = A(1.1K0.3)L0.7
Y2 / Y1 = (1.1)0.3 = 1.029
(R/P)1 = MPK = 0.3AK-0.7L0.7,
(R/P)2 = 0.3A(1.1K-0.7)L0.7
(R/P)2 / (R/P)1 = 0.935
(W/P)1 = MPL = 0.7AK0.3L-0.3,
(W/P)2 = 0.7A(1.1K-0.7)L-0.7
(W/P)2 / (W/P)1 = 1.029
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Problem Set 1
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Thus output rises by 2.9%, rental rates fall by 6.5%, and wages rise by 2.9%
d. Suppose that a technological advance raises the value of the parameter A by 10
percent. What happens to total output (in percent)? The real rental price of
capital (in percent)? The real wage (in percent)?
So the same thing for A, and you’ll see that everything rises by 10%.
Aid for Investment
6. Read Chapter 2 of “The Elusive Quest for Growth.” In two or three sentences, explain
what the financing gap approach is for development economists. Is Easterly a fan of this
approach? Why or why not?
Direct quote from pp. 29: “The difference between the required investment and
the country’s own savings is called the financing gap. Private financing is assumed to
be unavailable to fill the gap, so donors fill the gap with foreign aid to attain target
growth. This is a model that promised poor countries growth right away through aidfinanced investment.”
As you might be able to tell from the words above dripping in sarcasm, he’s not
a big fan of this approach. It gives too much credit to capital, and does not account for
diminishing returns to that investment.
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