NotesECN741-page43

# NotesECN741-page43 - t has persistent eﬀect on period t 1...

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ECN 741: Public Economics Fall 2008 On dynamics of consumption Consider again the full information optimal allocation u 0 ( c t ( θ T )) β t - 1 ω ( θ 1 ) = λ/R t - 1 Suppose for simplicity βR = 1 . Then 1. Allocation is independent of history (expect possibility θ 1 ) 2. There is no mobility in short-run or long-run 3. Inequality is constant Now consider private information optimal allocations. Assume θ t is i.i.d. Consider two diﬀerent history θ t and ¯ θ t u 0 ( c t ( θ T | θ t )) = βR X θ t +1 | θ t π ( θ t +1 ) π ( θ t ) u 0 ( c t +1 ( θ T | θ t )) u 0 ( c t ( θ T | ¯ θ t )) = βR X θ t +1 | θ t π ( θ t +1 ) π ( θ t ) u 0 ( c t +1 ( θ T | ¯ θ t )) note that π ( θ T | ¯ θ t ) = π ( θ T | θ t ) . Now suppose u 0 ( c t ( θ T | θ t )) > u 0 ( c t ( θ T | ¯ θ t )) , then there exist a history θ t +1 such that π ( θ t +1 | θ t ) = π ( θ t +1 | ¯ θ t ) and u 0 ( c t +1 ( θ T | θ t )) > u 0 ( c t +1 ( θ T | ¯ θ t )) good shocks up to period
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Unformatted text preview: t has persistent eﬀect on period t + 1 allocations. Next we consider inequality. Assume, u ( c ) = log( c ) , then 1 u ( c ) = c . Start from inverse Euler equation ( βR = 1 ) 1 u ( c t ( θ T )) = E ± 1 u ( c t +1 ( θ T )) | θ t ² We want to know what happens to variance of consumption over time V ar ³ 1 u ( c t ( θ T )) ´ = V ar ³ E ± 1 u ( c t +1 ( θ T )) | θ t ²´ = V ar ³ 1 u ( c t +1 ( θ T )) ´-E ± V ar ³ 1 u ( c t +1 ( θ T )) | θ t ´² 43...
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## This note was uploaded on 12/10/2011 for the course MAT 121 taught by Professor Wong during the Fall '10 term at SUNY Stony Brook.

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