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

ANS) GIVEN

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

now, GDP in n years can be calculated by exponentially growth formula, i.e. Ae^{r n}

i.e. GDP in n years = Ae^{r n}

where, r = rate of interest

n = number of years

A = initial GDP

SO,

(i) the doubling time for France’s per capita real GDP-

Doubling time refers to time taken by france to make his GDP double i.e. If initial gdp is A then time taken to make it 2A would be known as doubling time.

So,

2A = Ae^{r n}

2 = e^0.019n ( r = 1.9%)

taking ln both sides we get

ln 2 = 0.019n

0.693 = 0.019n

n = 36.47 ( approx , n = 37 years)

(ii)  the doubling time for Korea’s per capita real GDP

  2A = Ae^{r n}

2 = e^0.042n ( r= 4.2%)

   taking ln both sides we get

ln 2 = 0.042n

0.693 = 0.042n

n = 16.5     ( approx , n = 17 years)

(iii) France’s per capita real GDP be in 2045 will be given by

= Ae^{r n}

= 28900 e^0.019x42 ( A = 28900 , n = 42 years , r = 1.9 %)

= 28900 e ^0.798

= 28900 x 2.22

= 64158

(iv) Korea’s per capita real GDP be in 2045 will be given by

  

= Ae^{r n}

= 12700 e^0.042x42   ( A = 12700 , n = 42 years , r = 4.2%)

= 12700 e ^1.764

= 12700 x 5.857

= 74383.9