Derive the law of motion for the capital stock. Show that it satisfies = , where is a constant that depends only on exogenous parameters.

Given:

Y = AKG¹

K = (1)sYK

G = Y

Resolved:

K = (1)sYK

K = (1)sAKG¹K

K = (1)sAKY¹K

K = sAK(1)Y¹K

K = sAK(1-)A¹K¹G⁽¹⁾⁽¹⁾

K = K⁽¹⁾K

Can anyone help me check my answer for this question? Many thanks!