Question

Consider the following numerical example using the Solow growth model. Suppose that

F(K,N) = K^(4/13)N^(9/13) , Y = zF(K,N):

Furthermore, assume that the capital depreciation rate is d = 0.04, the savings rate is s = 0.3,

the population growth rate is n = 0.035, and the productivity is z = 1.75. Suppose K0 = 200 and

N0 = 100.

Question 1: Find the steady state per-capita capital stock (k*), output per capita (y*), and consumption

per capita (c*).

Question 2: Assume the economy is in the steady state of Question 1 and n goes down by 5% while

z increases by 5% and s increases by 5%. Using the Taylor approximation, evaluate the

contribution of each variable to the total change in the steady state consumption c*.

Answer 1

Solow Model with the following information given :

Ans1

Dividing Both sides by N

Lets see How K changes over time:

Now lets take a look at per capita picture:

Now Lets see How per capita consumption changes over time

Lets compute per capita capital, income and consumtion for initial period:

per worker capital, output and consumption in period one is given by:

Hence,

Ans2

At Steady state level:

This is the steady state level per capita capital which is equal to 16.63

Ans3

Steady state per capita capital is:

Now if we increase it by 5% New Steady state level will be:

In the above equation to reach the k** level we need to change Z such that

We need to find that x:

Hence we need to increase Z by (1-x).100% ie. 3.5% to raise steady state level of per capita capital by 5%

Ans3

Here K* = 16.63

Now Z drops by 10%, we want to keep the percapita output unchanges means we want to keep the per capita capital unchanged. We need to find out new savings rate such that output doesnot change.

i.e.

Old savings rate was 30%, When Z declines by 10% to keep the output at the same steady level savings rate should increase to 33.5%