Question

# Suppose an economy is described by the following production function: Y = K1/2 (EL)1/2 The savings...

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)

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 = K1/2(EL)1/2

=> (Y/(EL)) = (K1/2(EL)1/2)/(EL) = (K/(EL))1/2

=> y = k1/2 where y = Y/(EL) and k = K/(EL)

MPk(Marginal product of capital per effective worker) = dy/dk = 0.5/k1/2

Thus, MPk = 0.04

=> 0.5/k1/2 = 0.04

=> k1/2 = 12.5

=> k = 156.25

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

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