Question

Assume a = . Use the Solow Model to answer this question. If the saving rate increases by 10%, capital per capita in steady-state would increase by 15% 0% 5% 10%

Answer 1

The steady state condition is given by sf(k) = $\small \delta$ k, where s is the savings rate, k is the capital per capita, f(k) is the production function and $\small \delta$ is the depreciation rate.

Here f(k) = k^(1/3)
(because $\small \alpha$ = 1/3, therefore f(K,L) = K^(1/3)L^(2/3) is transformed into output per capita, i.e. f(K,L)/L = f(k) = k^(1/3)).

From the steady state condition we have, k/f(k) = s/$\small \delta$ or k/k^(1/3) = s/$\small \delta$ or k^(2/3) = s/$\small \delta$

Now suppose when savings rate increases by 10%, k becomes k* i.e. k*^(2/3) = 1.1s/$\small \delta$

From the above two equations, we have (k/k*)^(2/3) = 1/1.1
k*/k = (1.1)^(3/2)
k*/k = 1.1537
k* = 1.15k

Therefore, when savings rate increases by 10 percent, capital per capita increases by (1.15-1)*100 $\small \approx$ 15%.

Answer is 15%.