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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
3. Using the rule of 72, we know that GDP per capita will double every 72/g years, where g is the
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
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.
Converting g into a percent, we conclude that the growth rate of income per capita in Japan over this
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
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,
Chapter 1 The Facts to Be Explained 3
◼ Solutions to Appendix Problems
A.1. The number of people living on less than a dollar a day will be larger if we calculate it using market
exchange rates instead of purchasing power exchange rates because market exchange rates only
take into account the relative value of traded goods, which are relatively more expensive in poorer
A.2. a. The level of GDP per capita in each country, measured in its own currency is
b. The market exchange rate is determined by the law of one price. As CPUs are the only traded
c. To find the ratio of GDP per capita between Richland and Poorland, we must first convert GDP
denominations into the same currency. In the analysis that follows, I choose to convert GDP
d. A natural basket to use is 3 computers and 1 ice cream. The cost of this basket in Richland
e. To find the ratio of GDP per capita between Richland and Poorland, we must first convert GDP
denominations into the same currency. In the analysis that follows, I choose to convert GDP
