Question

Consider an economy characterized by the production y = k^1/2, a saving rate equal to s = 0.3, a population growth of n = 0.2 and a depreciation rate of capital of σ = 0.05.

a. Calculate the steady state values of capital per capita, GDP per capita and consumption per capita. Show the result on the appropriate graph.

b. Is the above steady state Dynamic Efficient or Inefficient? Why?

c. What saving rate would ensure a steady state level consistent with the Golden Rule one?

Answer 1

a)

i = (n+d)K

s = (n+d)k

0.3K^1/2 =(0.2+0.05)K

0.3K^1/2 = 0.25K

0.3/0.25 = K/K^1/2

1.3 = K^1/2

K = 1.69

y = (1.69)^1/2

=1.3

c = (1-s)Y

= (1-0.3)1.3

=0.91

i = y -c

= 1.3 -0.91

= 0.39

Following is diagram:

b)

System is inefficient where saving rate is greater than golden rule saving rate.

Golden rule:

MPK -Depreciation =N

(1/2)K^-1/2 = 0.25

1/K^1/2 = 0.5

2 = K^1/2

K = 1.41

Saving rate is larger than required, so it is dynamically inefficient.

c)

sf(k) = 0.25

s.1.41 = 0.25

s = 0.18

saving rate 0.18 is required.