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**

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