Question

A country is described by the Solow model with a production function of y=k^(1/2). Suppose that k is equal to 400. The fraction of output invested is 50%. The depreciation rate is 5%.

a. How does k change at this level?
b. What is the steady state level of k?
c. Suppose the level of k is 900. How does this change affect the rate of change of k to the steady state?

Answer 1

(a) Change in k = sy - dk

Where k=400

y= k^1/2 = 400^1/2 = 20

d = deprecation rate = 0.05

s = saving rate= 0.50

change in k = (0.50)20 - (0.05)(400)

= 10 - 20

= -10.

So, when k=400, k decreases.

(b) At steady state level , change in k = 0.

change in k = sy - dk

0 = (0.50)(k)^1/2 - (0.05)(k)

0.50/ 0.05 = k^1/2

10 = k^1/2

k = 100 [ Steady state level of k]

(c) k= 900

Because k=900 and at steady state k =100. Therefore, change in k =sy - dk

y = (900)^1/2 = 30

change in k = (0.50)(30) - (0.05)(900)

= 15 - 45

= -30.

There is increase in the rate of change of k to the steady state.