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Bewley_SL - Bewley Models Prof Lutz Hendricks L Hendricks...

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Bewley Models Prof. Lutz Hendricks August 10, 2009 L. Hendricks () Bewley Models August 10, 2009 1 / 17
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Bewley Models For many applications we need models with heterogeneous agents . In Bewley models, agents are ex ante identical. They are ex post heterogeneous because they are hit by idiosyncratic shocks. Incomplete markets prevents sharing these risks. L. Hendricks () Bewley Models August 10, 2009 2 / 17
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An Endowment Economy Demographics: There is a unit measure of households. Each lives forever. Preferences: E t = 0 β t u ( c t ) (1) Technology: Households receive random endowments y t 2 Y (°nite). Transition matrix: π ( y 0 j y ) . L. Hendricks () Bewley Models August 10, 2009 3 / 17
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No aggregate uncertainty Assume a "law of large numbers." Let Π ( y ) be the stationary distribution of y . Assume that the fraction of households with endowment y is Π ( y ) . The aggregate endowment ¯ y is constant over time. With complete markets, households would not face any uncertainty. L. Hendricks () Bewley Models August 10, 2009 4 / 17
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Household problem Flow budget constraint: a 0 = y + ( 1 + r ) a ° c (2) Borrowing constraint: a 0 ± ° b (3) L. Hendricks () Bewley Models August 10, 2009 5 / 17
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Household problem Focus on a stationary equilibrium .
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