Question

Country A has a production function per effective worker given by the following expression y = k^0.5. The savings rate of this country is 15 percent, the depreciation rate is 4 percent, the population growth rate is 4 percent, and the rate of technological change is 2 percent.

In the Golden-rule steady-state of this economy, what is the savings rate?

Answer 1

at the Golden Rule, the above calculated MP_K must equal (d+n+g),

MPK = 0.5k^-0.5

d = 0.04, n = 0.04, g = 0.02

0.5 / K^0.5 = 0.04 + 0.04 +0.02 = 0.1

0.5 / 0.1 = K^0.5

K** = 25

y** = 25^0.5 = 5

c** = y** - (d+n+g)k**

= 5 - 0.1*25 = 2.5

s** = 1- (c**/y**) = 1- 0.5 = 0.5

s** ( golden rule saving rate ) = 0.5 = 50%