Question

xt Problem 9 Suppose that the economy's production function is given by where Y is output, K is capital, and N is the number of workers. The steady-state level of capital per worker in terms of the saving rate, s, and the depreciation rate, 8, is ON=□ Property format your oxpression using the too sinthe palette Hover over tools t see keyboard shortcuts. E character) as person t can be Enter your arawer in the answer box and then click Check Answer parts Ciedr All Check Answer MacBook Air 3 4 5 7 K.

Answer 1

Y/N =

Y/N = squareroot K squareroot N Y/N = squareroot K/N squareroot N/N Y/N = squareroot K/N The following equation shows capital per worker from year t to year (t + 1) K_t + 1/N-K_t/N = (s)f(K*/N)-(delta)(K*/N) = 0 (s) f(K*/N) = (delta)(K*/N) s* squareroot K/N = delta(K/N) Squaring both sides, s^2(K/N) = delta^2(K/N)^2 s^2/delta^2 = (K/N).

Y/N = $\sqrt{K/N}\sqrt{N/N}$

Y/N = $\sqrt{K/N}$ .

The following equation shows capital per worker from year t to year (t+1)

K_t+1/N - K_t/N = (s) f(K*/N) - ( $\delta$ ) (K*/N)

Under steady state, the capital stock does not change, so K_t+1/N - K_t/N = 0.

(s) f(K*/N) - ( $\delta$ ) (K*/N) = 0

(s) f(K*/N) = ( $\delta$ ) (K*/N)

s * $\sqrt{K/N}$ = $\delta$ (K/N)

Squaring both sides,

s² (K/N) = $\delta$ ² (K/N)²

s^2/ $\delta$ ² = (K/N).