Recursive Macroeconomics, Sargent . Many thanks.

Al (25 points) Consider a two period (t=0,1) version of the neoclassical growth model with the choice of labour input: max In(co) - Bho + B (In(c1) - Bh1) co, c1,k1,k2,ho,h1 s.t.: co + k1 = koh-a C1 + K2 = kihl-a. where B E (0, 1), B > O, co, C1, K1, k2, ho, h1 2 0, a E (0, 1) and Ko is given. All variables have the usual meaning. (a) Formulate the optimization problem in the last period, t = 1. What is are the state variable(s) in period t = 1? Find the optimal decision rules for c1, K2 and h1, and the value function V1. [12.5] (b) Formulate the optimization problem in period t = 0 recursively, in terms of the value function in the last period, V1. Solve for the optimal decision rules for co, k1 and ho. [12.5]