question 4

4. [20 points total] Consider an economy characterized with the following equations. Yt = AtK. Lut AKt+1 = syt - dKt At+1 = zAtLat Lyt + Lat = L Lat = IL (a) [10 points] Let gr,t denote the growth rate of a in period t. Prove the following conditions. JK,t = s Yt d gY,t = gA,t + agk,t (b) [10 points] Find # on the balanced growth path in this economy