3. Consider an economy in which the equilibrium solves the optimal growth problem max 3" B (0log(C,) +(1- O) log(N,h L,)) S1.: Cr.r * KH[ = (1 = 5)Kr it \"IGK::{?!L;' )I_ C =0 K,.>0 K, 1s given N, =n'N, a) Define a balanced growth path for this economy. Write down conditions that characterize this balanced growth path. Verify that the balanced growth path exhibits characteristics consistent with Kaldor's stylized facts on economic growth