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 steady state level of investment per effective worker?

Answer 1

Production function is given by :

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

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

Steady state occurs when Change in k = sy - (d + n + g)k = 0

where, s = savings rate = 0.40, n = population growth rate = 0.01, g = technological progress growth rate = 0.01, and d = depreciation rate = 0.02.

Thus at steady state, 0.4k^1/2 - (0.02 + 0.01 + 0.01)k = 0 => k = 100

=> Investment per worker = sy = 0.4*100^1/2 = 4

Hence, Investment per worker = 4