NotesECN741-page42

NotesECN741-page42 - Note that at the ecient allocation the...

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ECN 741: Public Economics Fall 2008 Note: The Intertemporal condition only depends on consumption which is observable. Note: The additive separability assumption was key in deriving this result. Look at Farhi and Werning ( 2008 ) for a version of this result that is derived for more general class of utility functions. Note: This result does not hold if private information affect the marginal utility of consump- tion (for example in Atkeson and Lucas ( 1992 ) taste shock model). This result implies that it is not desirable for planer to allow access to saving. To see this look at the following Euler equation (which has to hold if there is access to saving) u 0 ( c t ( θ T )) = βR X θ t +1 | θ t π ( θ t +1 ) π ( θ t ) u 0 ( c t +1 ( θ T )) (45) But let’s look back at Inverse Euler Equation ( 44 ) u 0 ( c t ( θ T )) = βR 1 θ t +1 | θ t π ( θ t +1 ) π ( θ t ) 1 u 0 ( c * t +1 ( θ T )) > βR 1 1 P θ t +1 | θ t π ( θ t +1 ) π ( θ t ) u 0 ( c * t +1 ( θ T )) = βR X θ t +1 | θ t π ( θ t +1 ) π ( θ t ) u 0 ( c * t +1 ( θ T ))
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Unformatted text preview: Note that at the ecient allocation the individuals are saving constrained. In other words, if individuals can privately save, they will choose to do so and it is desirable for planer to prevent them from doing that. Another way of seeing this is the following: suppose ( 45 ) holds. Then we must have R u ( c * t ( T )) < X t +1 | t ( t +1 ) ( t ) 1 u ( c * t +1 ( T )) Now suppose the planer wants to increase utility at time t by and decrease it at time t + 1 by -1 . The cost of increase of utility in period t is u ( c t ( T )) / . On the other hand planer hands in u ( c t +1 ( T )) / less at each t +1 that follows t . Therefore it can free up resources. 42...
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