You know the Cobb-Douglas production function in per-worker terms is: f(k)=Ak. And the steady-state

level of output per worker given the effect of population growth is: A(1²)( :)(1-a). Suppose there are

two countries of i and j that have the same values for A (productivity parameters), y (which measures the

fraction of output that is invested), and 8 (which measures depreciation). Let n; and n; denote their growth

rates of population (n; + nj).

1) Write the equation for the steady state levels of output per worker in each country.

2) Write the expression for the ratio of steady-state income in country i to steady state income in country

j.

3) If = 5%, α= 1/3, n₁ = 0% and n; = 4%, then calculate the ratio of steady-state income in country i to

steady-state income in country j.

Fig: 1