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Unformatted text preview: Alejandro Badel. Macro II, Jonathan Heatchote. Homework 5 Answers. 1) Recursive formulation of the individual&s maximization problem: state: ( a;w ) where a represents beggining of period bond holdings and w is the current realization of the wage process. control: ( n;a ) where n are hours worked and a are end of period bond holdings. feasible set: & ( a;w ) = f ( n;a ) : wn + (1 + r ) a & a ;a g Bellman Equation: V ( a;w ) = max a 2 &( a;w ) ( 1 1 & & & wn + (1 + r ) a & a & n 1+1 =" 1 + 1 =" 1 & & + E [ V ( a ;w ) j w ] ) w random draw from ( w j w ) 2) First order conditions Intertemporal u c (1 + r ) E [ u c j w ] Intratemporal wu c = & u n 3) From the Intratemporal FOC we have w = n 1 =" ln n = & " ln + " ln w We can see that the elasticity of worked hours with respect to wages is given by ": 4) We could assume for simplicity that the wage distribution starts o/ at its stationary value, this would make the planner&s problem invariant over time. Mantaining the assumption that the initial distribution is uniform (50 50), we can formulate the planner&s problem recursively as follows:...
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