(Answered) Suppose that the real gdp per capita in country j isin ab

Engineering

Suppose that the real GDP per capita in country j ∈ {A,B} follows this equation:

y_j(t) = y_j(0) · e^g^jt

Show that lny_j(t + 1) - lny_j(t) = g_j;

Suppose that y_A(0) = 1 and g_A= 2%. How long it takes for the (log of) real GDP per capita to double?

Suppose that y_A(0) = 1 and g_A= 7%. How long it takes for the (log of) real GDP per capita to double?

Suppose that y_A(0) = y_B(0) = 1, g_A= 2% and g_B= 4%. What is the (log) difference in real GDP per capita between country A and B when t = 50?

Suppose that lny_A(T) - lny_B(T) = 2, g_A= 2% and g_B= 4%. Calculate lny_A(0) - lny_B(0) when T = 50 and T = 100.

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