Economic GDP?

Question

Suppose one country has a GDP that is one eighth the GDP of its richer neighbor. but the poorer country grows at 10% a year, while the richer country grows @ 2% a year. In 35 years, which country will have the higher GDP?

I am assuming it is the richer country but can't seem to get the problem accurate.

PLEASE HELP

Answer 1

wow,  good question.  I'm still tinkering with it.  

Any other factors?  Like population? density?  square mileage ?  resources or proximity to resources?

Answer 2

Country1 GDP=100

Country2 GDP=100/8=12.5

Year.Count1...Country2

0........100........12.5

1.......102.00......13.75

2.......104.04......15.13

3.......106.12......16.64

4.......108.24......18.30

5.......110.41......20.13

6.......112.62......22.14

7.......114.87......24.36

8.......117.17......26.79

9.......119.51......29.47

10......121.90......32.42

11......124.34......35.66

12......126.82......39.23

13......129.36......43.15

14......131.95......47.47

15......134.59......52.22

16......137.28......57.44

17......140.02......63.18

18......142.82......69.50

19......145.68......76.45

20......148.59......84.09

21......151.57......92.50

22......154.60......101.75

23......157.69......111.93

24......160.84......123.12

25......164.06......135.43

26......167.34......148.98

27......170.69......163.87

28......174.10......180.26

29......177.58......198.29

30......181.14......218.12

31......184.76......239.93

32......188.45......263.92

33......192.22......290.31

34......196.07......319.35

35......199.99......351.28 .<<<- Country2 is reacher

36......203.99......386.41

37......208.07......425.05

38......212.23......467.55

39......216.47......514.31

40......220.80......565.74

Or:

Country1=100*(1.02)^35=199.99

Country2=12.5*(1.08)^35=351.28

Answer 3

Set the initial GDP of the poor country = P.  The initial GDP of the rich country is then 8P.

From one year to the next, a country's GDP is multiplied by 1+r where r is the GDP growth rate.

In 35 years...

GDP of the initially poor country = P*1.1^35

GDP of the initially rich country = 8P*1.02^35

You'll find 1.1^35 > 8*1.02^35, so the initially poor country will have the higher GDP after 35 years.