NotesECN741-page59

# NotesECN741-page59 - θ t 1(1-δ F K K t 1,Y t ² ² θ t 1...

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ECN 741: Public Economics Fall 2008 in deriving the inverse Euler equation depends crucially on additive separability. If the preferences are of the form u ( c, l ) = c 1 - σ 1 - σ v ( l ) then the proof presented will not work. See Farhi and Werning ( 2008 ) for derivation of the inter-temporal optimality condition for larger class of preferences (including those that are consistent with balanced growth). 3.2 Implementing Efficient Allocations 3.2.1 Wedges and Taxes So far we have shown that efficient allocations must satisfy a condition like the following (if there is no aggregate shock) β (1 - δ + F K ( K * t +1 , Y * t )) u 0 ( c * t ( θ t )) = E 1 u 0 ( c * t +1 ( θ t +1 )) θ t +1 . We also showed that this implies the following u 0 ( c * t ( θ t )) < β
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Unformatted text preview: ( θ t +1 ))(1-δ + F K ( K * t +1 ,Y * t )) ² ² θ t +1 µ . In other words there is an inter-temporal wedge 1-τ t = u ( c * t ( θ t )) β E ´ u ( c * t +1 ( θ t +1 ))(1-δ + F K ( K * t +1 ,Y * t )) ² ² θ t +1 µ < 1 . But does this mean that the eﬃcient allocations can be implemented by a positive tax on capital? Two period example Consider the following example: • T = 2 . • Θ = { , 1 } , π ( θ 1 = 1) = 1 , π ( θ 2 = (1 , 1)) = 0 . 5 and π ( θ 2 = (1 , 0)) = 0 . 5 . (Note that this implies y 2 h = y 2 ((1 , 1)) = l 2 h (1 , 1) and y 2 l = y 2 ((1 , 0)) = 0 ) 59...
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