Suppose that the real GDP per capita in country j ∈ {A,B} follows this equation:
yj(t) = yj(0) · egjt
Show that lnyj(t + 1) - lnyj(t) = gj;
Suppose that yA(0) = 1 and gA = 2%. How long it takes for the (log of) real GDP per capita to double?
Suppose that yA(0) = 1 and gA = 7%. How long it takes for the (log of) real GDP per capita to double?
Suppose that yA(0) = yB(0) = 1, gA = 2% and gB = 4%. What is the (log) difference in real GDP per capita between country A and B when t = 50?
Suppose that lnyA(T) - lnyB(T) = 2, gA = 2% and gB = 4%. Calculate lnyA(0) - lnyB(0) when T = 50 and T = 100.