add - Algebraic Addendum to second part slide 36. The...

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Algebraic Addendum to second part slide 36 . The algebraic details are as follows: Take the expectation at t=1 of both right and left hand side of b.c. E 1 " T X t =1 C t # = E 1 " B 0 + T X t =1 Y t # Since B 0 is known at t=1, this can be rewritten as T X t =1 E 1 ( C t )= B 0 + T X t =1 E 1 ( Y t ) Now observe that the left hand side of this equality can be rewritten as E 1 ( C 1 )+ E 1 ( C 2 E 1 ( C 3 ..... + E 1 ( C T ) Observe that E 1 ( C 1 C 1 . Moreover, from the Euler condition C t = E t ( C t +1 ) , we can write E 1 ( C 2 C 1 . Consider now the terms E 1 ( C 3 ) ,E 1 ( C 4 ) 1 ( C T ) . For example, take E 1 ( C 3 ): we know that E 1 ( C 3 E 1 [ E 2 ( C 3 )] by the "Law of it- erated expectations". But
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This note was uploaded on 07/25/2008 for the course ECON 813A taught by Professor Minetti during the Spring '08 term at Michigan State University.

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