Economic Growth 3rd Edition by David Weil Solution manual

Chapter 1
The Facts to Be Explained

Note:   Special icons in the margin identify problems requiring a computer or calculator     .

n 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  So g8%.

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.