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 output per effective worker?

Answer 1

Y=K1/2(EL)1/2

Savings rate in the economy(s)= 0.40, population is growing at a rate(n)= 0.01, technological progress is growing at a rate(t)= 0.01, and the depreciation rate(d)= 0.02.

Divide both side by EL

Y/EL= K1/2/(EL)1/2= (k)1/2

y=k1/2

Here y is output per effective worker and k is the capital per effective worker

At steady state:

Change in k=0

sy-(n+d+t)k=0

0.40k1/2-(0.01+0.01+0.02)k=0

0.40k1/2 = 0.04k

0.40/0.04= k/k1/2

10= k1/2

k= 100

y= k1/2 = 1001/2 = 10

The steady state level of output per effective worker is y=10.