Question

1. Consider the Solow model of economic growth, with no technological progress. Assume that δ=0.07 and n=0.03. The production function is given by Y=K^0.5 L^0.5. The savings rate s=0.5.
   

a) Calculate the steady state levels of capital per worker, output per worker and consumption per worker.

b) Now, suppose there is an exogenous change in n, which increases to n=0.055 (while δ, s and the production function remain identical). What are the new steady state levels of capital per worker, output per worker and consumption per worker?

c) Use the Solow diagram to depict the effects of the change in n on steady-state capital per worker

d) After the change in n, is it possible for the economy to go back to the level of steady-state consumption per worker that it had before the change in n by changing its savings rate?

Answer 1

Answer :-

Given :-

Assuming that = 0.07 and n = 0.03.

The production function :- Y = K^0.5L^0.5

K^1/2 L^1/2

The saving rate (s)= 0.5

(a​). Output per worker, y= Y/L

= K^0.5 L^0.5/L

= (K/L)^1/2

y = k^1/2 where k = K/L

At steady state ∆k=0

sf(k) - (+n)k = 0

Put value of and n

So sy = (0.07+0.03)k

Put value of s and y given above

0.5 k^1/2 = 0.1k

0.5/0.1 = k/k^1/2

k^1/2 = 5

[ k* = 25]

[ y*= 25^1/2 = 5]

Consumtion per worker :-

c* =(1-s)y*

= (1-0.5) x 5

= 0.5x5

= 2.5

(b) - given n = 0.055

  sf(k) - (+n)k = 0

sy = (0.07+0.055)k

0.5 k^1/2 = 0.125k

0.5/0.125 = k/k^1/2

k^1/2 = 4

[ k*(new) = 16]

[ y*(new) = 16^1/2= 4]

New consumtion per worker-

c*(new)= (1-s)y*(new)

c*(new) = (1-0.5)x4

= 0.5x 4

[ c*(new)= 2]

(c) -

Solow diagram to depict the effects of the change in n on steady-state capital per worker shown below:-

Due to increase in n, the straight line

( +n1)k increases to ( +n2)k.

The new steady state, k*(new) = 16

(d) -

After the change in n, it is possible to achieve the old consumtion per worker by reducing the savings rate in the economy. This will shift the investment curve downward and the difference between output and investment which is consumtion can be increased.