Problem Set 1 Answers
Chapter 1 #2, 3, 4, 5, 6, 7 (on pages 24-25) and Appendix problems A.1 and A.2 (on
pages 28-29).
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 withincountry income inequality in both Country A and Country B. Because there is no betweencountry inequality, world inequality can be entirely attributed to within-country inequality.
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 = $1,433, Y2000 = $23,971, and rearranging to solve for g, we get:
g = ($23,971/$1,433)(1/100) – 1,
g ! 0.0286.
Converting g into a percent, we conclude that the growth rate of income per capita in Japan
over this period was approximately 2.86 percent per y