Question

Problem 5 Suppose that Country A has per capita GDP of $2,000 with associated growth rate 1.5%, and that Country B has per capita GDP of $1,200 with associated growth rate 1.8%. As- suming that GDP per capita follows an exponential process with constant growth rates, what is the minimum number of years required for GDP per capita in Country B to exceed that of Country A?

Answer 1

GDP per capita country A = 2000. Growth rate = 1.5%

GDP per capita country B = 1200. Growth rate = 1.8%

Let the years be N

2000e^0.015*N = 1200e^0.018*N

5/3 = e^(0.018N - 0.015N)

ln (5/3) = ln e^0.003N

N = 170.27

Hence, after 171 years approx per capita GDP of B will exceed per capita GDP of A.