Question

Assume that the following hold true for the US and China, and assume that the growth rate listed will remain the same over the next century and a half. (The numbers given are fairly close to the current values, but the assumption that the growth rates will remain constant for the next 150 years is pretty ridiculous. Still, go with it.)

	US	China
annual growth rate of nominal GDP	3.5%	6.5%
annual inflation rate	1.5%	2%
annual growth rate of pop	1%	.5%
current real GDP per capita	$57,000	$8,000

1. Given the data in the table, what is the annual growth rate of real GDP per capita in the US? Show your work.

2. Given the data in the table, what is the annual growth rate of real GDP per capita in China? Show your work.

3. According to the Rule of 70 and using your answer from part 1, approximately how many years would it take for the real GDP in the US to double? Show your work.

4. According to the Rule of 70 and using your answer from part 2, approximately how many years would it take for the real GDP in China to double? Show your work.

5. Given your answer to part 3, approximately what will the real GDP per capita be in the US in 2158: that is, 140 years from now? Show your work.

6. Given your answer to part 4, approximately what will the real GDP per capita be in China in 2158: that is, 140 years from now? Show your work.

Answer 1

1.Find the growth rate of real GDP as = growth rate of nominal GDP - growth rate of inflation = 3.5% - 1.5% = 2%. Now find the annual growth rate of real GDP per capita = growth rate of real GDP - growth rate of population = 2% - 1% = 1%.

2. Using the same analogy, growth rate of real GDP = 6.5% - 2% = 4.5% and annual growth rate of real GDP per capita = 4.5% - 0.5% = 4%.

3. According to the Rule of 70 the required number of years would it take for the real GDP in the US to double is 70/2% = 35 years. This is because according to the rule of 70, growth is doubled after n years where n = 70/growth rate.

4. For China, the required number of years = 70/4.5% = 16 years (approx)

5. Find the real GDP per capita be in the US in 2158: that is, 140 years from now using the future worth formula

F = P(1 + r%)^n or 57000(1 + 1%)^140 = $229, 545.

6. Find the real GDP per capita be in China in 2158: that is, 140 years from now as

F = 8000(1+4%)^140 = $1,939,802