Unformatted text preview: c be consumption and l be the hours worked. Individual with skill θ who works l hours produce y = θl eﬃciency labor unit. If period utility over hours worked and consumption is U ( c,l ) , then we can write it in terms of consumption and eﬃciency labor unit as U i ( c,y ) = U ( c,y/θ i ) . Suppose there are θ ∈ Θ = ± θ i ,...,θ N ² . We call the individual of type θ i , person i or type i . The fraction of type i is π i . Assume ∑ i π i θ i = 1 . Aggregate state of economy is s t ∈ S (ﬁnite set) and is publicly observable. Denote the history of aggregate shocks by s t = ( s ,...,s t ) . Probability of history s t is Pr ( s t ) . Consumer problem Individual of type i solves max X t,s t β t Pr ( s t ) U i ( c t ( s t ) ,y ( s t )) (28) 20...
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This note was uploaded on 12/10/2011 for the course MAT 121 taught by Professor Wong during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 wong
 Calculus

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