NotesECN741-page39

NotesECN741-page39 - ECN 741: Public Economics Fall 2008...

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ECN 741: Public Economics Fall 2008 discussion above implies that T 0 ( y ( θ L )) > 0 ,T 0 ( y ( θ H )) = 0 3.1 The New Dynamic Public Finance So far we have characterized the set of achievable allocations by any mechanism. The goal of the planner is to find the best achievable allocation. T X t =1 β t - 1 X θ T D π ( θ T ) ω ( θ 1 ) ± u ( c t ( θ T )) - v ² y t ( θ T ) θ t ³´ (43) sub. to. T X t =1 X θ T π ( θ T ) ± u ( c t ( θ T )) - v ² y t ( θ T ) θ t ³´ T X t =1 X θ T π ( θ T ) ± u ( c t ( α 0 t ( θ T ))) - v ² y t ( α 0 t ( θ T )) θ t ³´ for all α 0 : D -→ D ( α 0 t is θ t - measurable). X Θ D T X t =1 c t ( θ T ) π ( θ T ) /R t - 1 X Θ D T X t =1 y t ( θ T ) π ( θ T ) /R t - 1 ( c t ,y t ) are θ T -measurable c t ( θ T ) ,y t ( θ T ) 0 t,θ T D Note that we allow for allocation to depend on date on realization of θ . The goal of this section is to characterize the properties of constraint efficient allocation (i.e.
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