Question

If the production function is equal to y=√k, the rate of depreciation is equal to 3 percent and the savings rate is 30 percent, show how to solve for the steady state of capital. There are currently 20 units of capital in the economy. Calculate the steady state of capital. Show your work. Will the capital stock increase or decrease over time?

Answer 1

Steady State occurs when change in k = 0

change in k = sy - dk

where s = saving rate = 30% = 0.30 and d = depreciation rate = 3% = 0.03

So, change in k = 0 => sy - dk = 0 => 0.3k^0.5 - 0.03k = 0 => k^0.5 = 10 => k = 100

Thus, Steady state level of capital = 100 units.

Currently there is 20 units of capital which is lesser than steady state level of capital. Thus, Steady state level of Capital will increase over time but once it reaches 100, then it stops increasing and became constant.