Question

An economy has a steady-state output level of 9. The economy's labor, technology, and education levels are constant and the economy is described by the production function Y= Square root(k). If the depreciation rate is 6%, what is the steady-state capital stock and what is the investment rate needed to maintain it?

Answer 1

The economy has a steady-state output level of 9 and its labor, technology and education levels are constant.

The economy is described by the production function

Now, at steady state, output is Y*=9. Hence, if we put the value of Y in the production function, we will get the steady state capital accumulation.

Hence, from the production function, we get

or,

or, K* = 81

Hence, steady state capital accumulation is K*=81.

Now, the change in capital is defined as the difference between investment and depriciation of capital. We will use the equation to find the investment level required to maintain the steady state.

Hence, ∆K=I - d.K, where I is investment and d is depriciation. It is given that, d=6% or 0.06.

Now, at steady state, there is no change in capital accumulation i.e.

∆K=0

or, I* = d.K*

or, I* = 0.06×81 (As, K*=81 and d=0.06)

or, I* = 4.86 ~ 5

Hence, investment required to maintain the steady state is I*=5.

Hope the solution is clear to you my friend.