Aggregation_SL

Aggregation_SL - Aggregation Prof Lutz Hendricks August 7...

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Aggregation Prof. Lutz Hendricks August 7, 2009 L. Hendricks () Aggregation August 7, 2009 1 / 20

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Notes on Aggregation We have assumed a representative household. How restrictive is this assumption? If households are not identical, do they "aggregate" into a representative household? L. Hendricks () Aggregation August 7, 2009 2 / 20
Example with Heterogeneity L. Hendricks () Aggregation August 7, 2009 3 / 20

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Example with Heterogeneity Consider a Cass-Koopmans model with two types of households, i = 1, 2 . Demographics: The population of each type is constant ( N i ). Preferences are identical: R 0 e ρ t c 1 σ 1 1 σ dt . Endowments: Each household starts with capital k i 0 . Each has one unit of type i time at any moment. L. Hendricks () Aggregation August 7, 2009 4 / 20
Example with Heterogeneity Technology: Y t = K θ t [( L 1 t ) 1 θ + ( L 2 t ) 1 θ ] = ˙ K t + δ K t + C t . Note: Each household supplies a di/erent type of labor. L. Hendricks () Aggregation August 7, 2009 5 ± 20

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The household problem is entirely standard. Solution is k i t and c i t which satisfy Euler equation g c i t ± = ( r ρ ) / σ (1) and budget constraint: ˙ k i = rk i + w i c i (2) Boundary conditions: k i 0 given and TVC. L. Hendricks ()
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Aggregation_SL - Aggregation Prof Lutz Hendricks August 7...

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