Question

In the Solow growth model, the steady state value of capital per worker will surely increase if:

a. The saving rate decreases and population growth increases

b. The saving rate increases and population growth decreases

c. The saving rate decreases and population growth decreases

d. The saving rate increases and population growth increases

Answer 1

In general Production function for solow model is given by :

y = Ak^a where k = Capital per worker, y = Output per worker, A = Total factor productivity and a = constant such that 0 < a < 1.

For solow model steady state occurs when change in k = 0

As, change in k = sy - (d + n)k.

So at steady state change in k = sy - (d + n)k = 0 where s = saving rate, d = depreciation rate and n = population growth rate

=> sy = (d + n)k

=> sAk^a = (d + n)k

=> k^1-a = s/(d + n) where 0 < a < 1

=> k = (s/(d + n))^1-a where 1 - a > 0

Hence we can see that as n decreases, k will increases. Also as d decreases, k will increases and finally increase in saving rate will result in steady state value of capital per worker.

Hence, the correct answer is (b) The saving rate increases and population growth decreases