The accompanying table provides approximate statistics on...

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 . a. Calculate the ratio of per capita GDP in 2012 of the following: i. Middle-income to high-income countries ii. Low-income to high-income countries iii. Low-income to middle-income countries b. Calculate the number of years it will take the lowincome and middle-income countries to double their per capita GDP. c. 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?) d. Repeat part a with the projected per capita GDP in $2076 .$ e. Compare your answers to parts a and d. Comment on the change in economic inequality between the regions.

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 .
a. Calculate the ratio of per capita GDP in 2012 of the following:
i. Middle-income to high-income countries
ii. Low-income to high-income countries
iii. Low-income to middle-income countries
b. Calculate the number of years it will take the lowincome and middle-income countries to double their per capita GDP.
c. 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?)
d. Repeat part a with the projected per capita GDP in $2076 .$
e. Compare your answers to parts a and d. Comment on the change in economic inequality between the regions.

Key Concepts

Rule of 70

The Rule of 70 provides a quick method to estimate the number of years it takes for a quantity growing at a fixed percentage rate to double. It is calculated by dividing 70 by the annual growth rate, offering an intuitive gauge of how fast economies or investments can grow over time.

Doubling Time

Doubling time is a concept that refers to the period required for a variable, such as GDP per capita, to double in size at a consistent growth rate. It emphasizes the exponential nature of growth and is directly related to the Rule of 70 in various economic projections.

GDP per Capita

GDP per capita is a measure of a region's economic output that is calculated by dividing the total Gross Domestic Product by the population. It is used as an indicator of average living standards and economic well-being, providing a basis for comparing different economies.

Compound Growth

Compound growth describes a process in which a quantity increases at a constant rate, and each period's increase builds upon the previous period's total. This type of growth leads to exponential increases over time, making it useful for forecasting long-term economic developments.

Ratios

Ratios are mathematical comparisons between two quantities, illustrating their relative sizes. In economic contexts, ratios such as those comparing GDP per capita across regions are essential for understanding and analyzing disparities and relative economic performance.

Economic Inequality

Economic inequality pertains to the differences in income, wealth, and economic opportunities among various groups or regions. By examining the ratios of GDP per capita and changes over time, economists can assess the extent and evolution of disparities within and between economies.

Transcript

00:01 The company table provides approximate statistics on per capita income levels and growth rates for regions defined by income levels.

00:08 According to the rule of 70s, starting in 2012, the high income countries are projected to double their per capita gdp in approximately 78 years in 2088.

00:17 Throughout this question is some constant growth rates for each of the reasons that are regions that are equal to their average value between 2000 and 2012.

00:27 So here we have the high income countries with a real gdp per capita in 2012 with 31.

00:33 1 ,372.

00:35 Middle income countries, their real gdp per capita in the same year is only $2 ,730.

00:41 Low income countries, their real gdp per capita is 422.

00:46 Average annual rate of growth of real gdp per capita, high income countries is 1 .1%.

00:52 Middle income countries is 4 .7 % and low income countries is 3 .2%.

00:57 Calculate the ratio of per capita gdp in 2012 for middle income to high income countries, low income to high income countries and low income to middle income countries.

01:08 Middle income to high income countries is $2 ,730 divided by $31 ,372 and we get $0 .087.

01:18 Low income to high income countries, 422 divided by 31 ,372.

01:24 We get a ratio of 0 .013.

01:27 Low income to middle income is 422 divided by 2 ,730.

01:32 We get a ratio of 0 .155.

01:36 Calculate the number of years it'll take the low income and middle income countries to double their per capita gdp.

01:42 Doubling period equals 70 divided by the annual growth rate.

01:46 Low income, 70 divided by 3 .2.

01:49 We get 21 .88 years...