Question

2. Consumption per worker is 72, depreciation is 12.5%, and capital per worker is 64, the population growth rate is 2 percent. Given the production function y - 20k1/3, show that this economy is not in a steady state. If the saving rate should double, what is the new steady- state level of consumption per worker?

Answer 1

ANSWER:

Given that :

onsider the Willman economy, where consumption per worker is 72, depreciation is 12.5%, and capital per worker is 64.

C = (1-s) y

y= 20 k^1/3 = 20 (64)^1/3 = 80

72 = ( 1-6 ) 80

0.9 = 1- s

s= 1- 0.9=0.1

At steady state sy = dk

sy = 0.1 (80 ) = 8

dk 0.125(64) =8

sy=dk

the economy is at steady state .

Now s = 2 ( 0.1)=0.2

at steady state , 0.2y = o.125 k

o.2(20k^1/3 ) = 0.125k

k ^{2/3 =32}

^{y= 20 (181.02)1/3} = 113.14   

k = (32) ^3/2 = 181.02

consumption per worker = (1-s)y = ( 1-0.2) 113.14 = 90.51