Question

Suppose an economy is described by the following production function:

Y = K1/2 (EL)1/2

The savings rate in the economy is 0.40, population is growing at a rate of 0.01, technological progress is growing at a rate of 0.01, and the depreciation rate is 0.02.

What is the Golden Rule level of capital per effective worker? (Use two decimal places)

Answer 1

Golden rule level of capital per effective worker is that level of steady state level of capital per effective worker where consumption per effective worker maximizes.

Formula :

Golden rule level of capital per effective worker is that level of steady state level of capital per effective worker where :

MPk = d + n + g

where d = depreciation rate = 0.02, n = population growth rate = 0.01 and g = technological progress growth rate = 0.01

=> MPk = 0.02 + 0.01 + 0.01 = 0.04

Y = K^1/2(EL)^1/2

=> (Y/(EL)) = (K^1/2(EL)^1/2)/(EL) = (K/(EL))^1/2

=> y = k^1/2 where y = Y/(EL) and k = K/(EL)

MPk(Marginal product of capital per effective worker) = dy/dk = 0.5/k^1/2

Thus, MPk = 0.04

=> 0.5/k^1/2 = 0.04

=> k^1/2 = 12.5

=> k = 156.25

Hence, Golden Rule level of capital per effective worker = 156.25