If country A had four times the initial level of real GDP per capita of Country B and it was growing at 1.4 percent a year, while real GDP was growing at 2.3 percent in country B, how long would it take before the two countries had the same level of real GDP per capita?
Ans: Let country B's initial GDP be x. Then country A's initial GDP will be 4x
Let time taken when they have same gdp be t
thus, x*(1.023)^t = 4x*(1.014)^t
(1.023)^t = 4*(1.014)^t
taking log on both sides
t log 1.023 = log 4 + t log 1.014
0.00987 t = 0.60206 + 0.00604t
1.
0.00987t - 0.00604t = 0.60206
0.00383t = 0.60206
t = 0.60206/0.00383 = 156.88 years
Thus, it will take 156.88 or aproximately 157 years for the GDP to be same
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