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HW5ans - Alejandro Badel Macro II Jonathan Heatchote...

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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 0 ) where n are hours worked and a 0 are end of period bond holdings. feasible set: ° ( a; w ) = f ( n; a 0 ) : wn + (1 + r ) a ° a 0 ± 0 ; a 0 ± 0 g Bellman Equation: V ( a; w ) = max a 0 2 °( a;w ) ( 1 1 ° ° ° wn + (1 + r ) a ° a 0 ° n 1+1 =" 1 + 1 =" ± 1 ° ° + ±E [ V ( a 0 ; w 0 ) j w ] ) w 0 random draw from ² ( w 0 j w ) 2) First order conditions Intertemporal u c ± ± (1 + r ) E [ u 0 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: State: p current fraction of agents with high wages ( w h ) .
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