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 = $\surd k$ to Y = 2$\surd k $
.What is the new steady-state level of K?
A) 100
B) 256
C) 400
D) 1,600

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 = $\surd k$  to Y = 2$\surd k $
.What is the new steady-state level of K?
A) 100
B) 256
C) 400
D) 1,600

Quizplus · Accepted Answer

In the steady state, investment equals depreciation, so we have:
0.5Y = 0.05K 
Substituting the new production level Y = 2, we get:
K = 20Y 
K = 20 x 2 = 40 
The new steady-state level of capital is 400 units.

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

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