NotesECN741-page48

NotesECN741-page48 - ECN 741 Public Economics Fall 2008 sub...

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ECN 741: Public Economics Fall 2008 sub. to. T X t =1 X θ t π ( θ t ) ± u ( c t ( θ t )) - ˆ 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 ))) - ˆ 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 t T X t =1 π ( θ t ) µ c t ( θ t ) - y t ( θ t ) /R t - 1 0 assume the following (in addition to the assumption mentioned at the beginning of the discussion) ˆ βR = 1 ˆ v ( y θ ) = v ( y ) θ u () is unbounded below, hence w = -∞ E µ 1 θ = 1 . Suppose the above problem has a solution and let ˆ λ be the multiplier on resources constraint. Then the solution to the above problem must also solve the following P ( w 0 ) = max T X t =1 ˆ β t - 1 X θ T D π ( θ t ) ± u ( c t ( θ t )) - v ( y t ( θ t )) θ t - ˆ λc t ( θ t ) + ˆ λy t ( θ t ) ´ (50) sub. to. T X t
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