1. [10 points] Consider the following optimal growth model with quadratic util- ity and full depreciation: 00 t a 2 max ( ) 1 {Ctakt+1} ;6 Ct 201: ( ) subject to the resource constraint kt+1 = 241% Ct + gt: (2) and k0 is given, Assume that B 6 (0,1), A > 1, y, is a given bounded deter- ministic labor income process, and a > 0 is set to be a value such that the utility function is always increasing in consumption. (a) [3 points] Derive the lifetime resource constraint using (2) and the non- Ponzi game condition. What restriction do we need to impose on the model parameters such that optimal consumption is constant over time. (b) [7 points] Assume that yt = y > O. Formulate this maximization problem as a dynamic programming problem and solve explicitly for the value function and the consumption function