Questions 7 to 9. Consider the following version of the deterministic [25] optimal growth model where output is produced using 2 inputs capital (k) and labor (or hours worked, h): max 00 25' (111(ct) ht) {Ciahtakt+l}t20 i=0 St: at + kt\" = kfhf\Consider a two-period (t=0,1 ) version of the neoclassical growth model: max(co,cj,kj,k>) { In co + B Inc1}, where B E (0, 1), subject to co + ki = ko, c1 + k2 = ka, and co, C1, k1, k2 2 0, where a E (0, 1) and ko is given. Notation is as usual. (a) Derive the optimal decision rules for the capital stock and con- sumption in period t = 0. [5] (b) Derive the value function in period t = 0. [5]' y I 9(25 points) Consider a two period (t=0,1) version of the neoclassical growth model with the choice of labour input: max 111(00) Bhg + 5011(01) Bhl) c0,c1,k1,k2,h0,h1 s.t.: c0 + k1 = kgh-a, 01 + k2 = kilhla. where 5' E (0,1), B > 0, co,cl,k1,k2,h0,h1 2 0, o: 6 (0,1) and k0 is given. All variables have the usual meaning. (a) Formulate the optimization problem H. What is/are the state variab|e(s) in period t = 1? Find the optimal decision rules for 01, kg and hl, 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 /he optimal decision rules for (:0, 14:1 and hg. [12.5]