3. The accompanying table provides approximate statistics on per capita income levels and growth rates for regions defined by income levels. According to the Rule of 70, starting in 2012 the high-income countries are projected to double their per capita GDP in approximately 78 years, in 2088. Throughout this question, assume constant growth rates for each of the regions that are equal to their average value between 2000 and 2012.
| Region | Real GDP per capita (2012) | Average annual growth rate of real GDP per capita (2000–2012) |
| High-income countries | $31,372 | 1.1% |
| Middle-income countries | 2,730 | 4.7 |
| Low-income countries | 422 | 3.2 |
Data from: World Bank.
Calculate the ratio of per capita GDP in 2012 of the following:
Middle-income to high-income countries
Low-income to high-income countries
Low-income to middle-income countries
Calculate the number of years it will take the low-income and middle-income countries to double their per capita GDP.
Calculate the per capita GDP of each of the regions in 2076. (Hint: How many times does their per capita GDP double in 64 years, the number of years from 2012 to 2076?)
Repeat part a with the projected per capita GDP in 2076.
Compare your answers to parts a and d. Comment on the change in economic inequality between the regions.