A country in a steady state invests 50% of its output in new capital ( $\gamma$ = 0.5) and depreciates 5% of its capital stock ( $\delta$ = .05) . With a capital stock of 100 units, labor remains constant. Because of technological innovation, production improves from Y = $\sqrt { K }$ to Y = 2 $\sqrt { K }$
. What is the new steady-state level of K?

Question

A country in a steady state invests 50% of its output in new capital (

\gamma

= 0.5) and depreciates 5% of its capital stock (

\delta

= .05) . With a capital stock of 100 units, labor remains constant. Because of technological innovation, production improves from Y =

\sqrt { K }

to Y = 2

\sqrt { K }

. What is the new steady-state level of K?

Quizplus · Accepted Answer

In the new steady state, the investment ($\gamma Y$) must equal depreciation ($\delta K$). With the new production function Y = 2$\sqrt{K}$, investment is 0.5 * 2$\sqrt{K}$ = $\sqrt{K}$. Setting $\sqrt{K}$ = 0.05K, solving gives K = 400.

A Country in a Steady State Invests 50% of Its γ\gammaγ

A Country in a Steady State Invests 50% of Its $\gamma$