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 output?

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 output?

Quizplus · Accepted Answer

In the new steady state, the production function is Y = 2√K. The steady-state condition is when investment equals depreciation: γY = δK. Substituting the values, 0.5(2√K) = 0.05K. Solving for K gives K = 400. The new steady-state output is Y = 2√400 = 40.

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

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