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Unformatted text preview: Macroeconomics 2. Master APE. 20092010. Search models. PS4 Prof. Christian Haefke / T.A : Eric Monnet 1 Two o ers per period Consider an unemployed worker who each period can draw two independently and identically distributed wage o ers ( w 1 and w 2 ) from the cumulative probability distribution function F ( w ) (think for example that a worker is hesitating between 2 independent sectors in which wages have a similar distribution). Work is then an absorbing state. The notations are the same as in the class handout. The event max { w 1 ,w 2 } is the event ( w 1 < w ) ∩ ( w 2 < w ) . Therefore Prob { max ( w 1 ,w 2 <w = F(w) 2 . The worker will limit his choice to the larger of the two o ers each pe riod. So we can write the Bellman equation recursively v ( w ) = max w 1 β ,c + β Z B v ( w ) dF ( w ) 2 Thus, using the same method as with the simple McCall model (cf class handout) we nd that the reservation wage with 2 o ers (denoted ¯ w 2 ) obeys the following equation : ( ¯ w 2...
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 Spring '10
 J.Baran
 Macroeconomics, Dynamic Programming, Recursion, Probability distribution, Cumulative distribution function, Bellman equation

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