Economic Growth
3rd Edition by David Weil
Complete Chapter Solutions Manual
are included (Ch 1 to 16)
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,Chapter 1
The Facts to Be Explained
Note: Special icons in the margin identify problems requiring a computer or calculator .
Solutions to Problems
1. A ratio scale transforms absolute differences in the variable of interest to proportional differences.
For instance, the GDP of Country X, whose GDP is 10 times greater than Country Y, will be the
same distance apart as a Country Z whose GDP is 10 times smaller than Country Y ’s GDP, i.e.,
the distance between X, Y, and Z will be the same. On a common linear scale, the distance between
X and Y would be 10 times greater than the distance between Y and Z. As a result, transforming
Figure 1.1 into a ratio scale would convert the absolute differences in the height of marchers into
proportional differences.
2. Let g be the rate of growth. The rule of 72 says that 72/g 9. So g 8%.
3. Using the rule of 72, we know that GDP per capita will double every 72/g years, where g is the
annual growth rate of GDP per capita. Working backwards, if we start in the year 1900 with a GDP
per capita of $1,000, to reach $4,000 by the year 1948, GDP per capita must have doubled twice.
To see this, note that after doubling once, GDP per capita would be $2,000 in some year, and
doubling again, GDP per capita would be $4,000, exactly the GDP per capita in year 1948. Using
the fact that GDP doubled twice within 48 years and assuming a constant annual growth rate, we
conclude that GDP per capita doubles every 24 years. Solving for the equation, 72/g 24, we get g,
the annual growth rate, to be three percent per year.
4. Between-country inequality is the inequality associated with average incomes of different countries.
Country A’s average income is given by adding Alfred’s Income and Doris’s Income and then
dividing by 2. This yields an average income of 2,500 for Country A. Similar calculations reveal that
Country B’s average income is 2,500. Because the average income for Country A is equal to that
of Country B, there is no between-country inequality in this world.
Within-country inequality is the inequality associated with incomes of people in the same country.
In Country A, Alfred earns 1,000 while Doris earns 4,000, making it an income disparity of 3,000.
In Country B, the income disparity is 1,000. Therefore, we see within-country income inequality in
both Country A and Country B. Because there is no between-country inequality, world inequality
can be entirely attributed to within-country inequality.
, 2 Weil • Economic Growth, Second Edition
5. We can solve for the average annual growth rate, g, by substituting the appropriate values into the
equation:
(Y1900) (1 g)100 Y2000.
Letting Y1900 $1,617, Y2000 $23,639, and rearranging to solve for g, we get:
g ($23,639/$1,617)(1/100) – 1,
g 0.0272.
Converting g into a percent, we conclude that the growth rate of income per capita in Japan over this
period was approximately 2.72 percent per year.
To find the income per capita of Japan 100 years from now, in 2100, we solve
(Y2000) (1 g)100 Y2100.
Letting Y2000 $23,639 and g 0.0272,
($23,971) (1 0.0272)100 Y2100,
Y2100 $346,043.09.
That is, if Japan grew at the average growth rate of 2.72 percent per year, we would find the income
per capita of Japan in 2100 to be about $346,043.09.
6. In order to calculate the year in which income per capita in the United States was equal to income per
capita in Sri Lanka, we need to find t, the number of years that passed between the year 2009 and the
year U.S. income per capita equaled that of 2009 Sri Lanka income per capita. Equating income per
capita of Sri Lanka in year 2009 to income per capita of the United States in year 2009 – t, we now
write an equation for the United States as
(YU.S., 2009 – t) (1 g)t YU.S., 2009.
Since YU.S., 2009 – t YSri Lanka, 2009 $4,034, YU.S., 2009 $41,099, and g 0.018, we then substitute in
these values and solve for t.
($4,034) (1 0.018)t $41,099.
(1 0.018)t ($41,099/$4,034).
One can solve for t by simply trying out different values on a calculator. Alternatively, taking the
natural log of both sides, and noting that ln(x y ) y ln(x), we get
t ln(1 0.018) ln($41,099/$4,034)
t 130.11.
That is, 130.11 years ago, the income per capita of the United States equaled that of Sri Lanka’s
income in the year 2009. This year was roughly 2009 – t, i.e., the year 1879.
7. In order to calculate the year in which income per capita in China will overtake the income per capita
in the United States, we first need to find t, the number of years it will take for the income per
capita in the two countries to be equal. That is,
(YU.S., 2009) (1 .018)t (YChina, 2009) (1 .079)t.
