Answer to Question #251597 in Macroeconomics for Smiley

Question

The rate of economic growth per capita in France from 1996 to 2000 was 1.9% per year, while in Korea over the same period it was 4.2%. Per capita real GDP was $28,900 in France in 2003, and $12,700 in Korea. Assume the growth rates for each country remain the same.

1. Compute the doubling time for France’s per capita real GDP.
2. Compute the doubling time for Korea’s per capita real GDP.
3. What will France’s per capita real GDP be in 2045?
4. What will Korea’s per capita real GDP be in 2045?

Answer 1

(1) The number of years it takes for a country's economy to double in size is equal to 70 divided by the growth rate, in percent:

$$Number\ of\ Years\ to\ Double=\dfrac{70}{France_{per\ capita\ real\ GDP}}.$$ $$Number\ of\ Years\ to\ Double=\dfrac{70}{1.9\%}=36.8\ y.$$

(2)

$$Number\ of\ Years\ to\ Double=\dfrac{70}{Korea_{per\ capita\ real\ GDP}}.$$ $$Number\ of\ Years\ to\ Double=\dfrac{70}{4.2\%}=16.7\ y.$$

(3) France per capita real GDP in 2045 will be (the time period equals 2045-2003=42 years):

$France_{per\ capita\ real\ GDP,2045}=France_{per\ capita\ real\ GDP}\cdot(1+Number\ of\ Years\ to\ Double)^{time\ period},$

$$France_{per\ capita\ real\ GDP,2045}=\$28900\cdot(1+0.019)^{42}=\$63710.$$

(4) Korea per capita real GDP in 2045 will be:

$Korea_{per\ capita\ real\ GDP,2045}=Korea_{per\ capita\ real\ GDP}\cdot(1+Number\ of\ Years\ to\ Double)^{time\ period},$

$$Korea_{per\ capita\ real\ GDP,2045}=\$12700\cdot(1+0.042)^{42}=\$71490.$$