pr3ec702

# pr3ec702 - Homework 3 Spring 2004, Econ 702 Problem 1 We...

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Spring 2004, Econ 702 Problem 1 We have de f ned the Sequence of Markets Equilibrium (SME) as an allocation { c t ,k t +1 ,n t ,b t +1 } t =0 and a sequence of prices { R t , w t ,i t } t =0 such that: · Given { R t ,w t ,i t } t =0 , { c t ,k t +1 ,n t , 0 } t =0 solves the following representa- tive consumer’s problem: max { b t +1 } , { c t ,k t +1 } 0 X t =0 β t u ( c t , 1 n t ) (1) subject to c t + k t +1 + b t +1 = R t k t + w t n t +(1+ i t ) b t t (2) n t [0 , 1] t (3) and k 0 given, b 0 =0 (4) and No-ponzi condition lim T →∞ T Y s =1 b T +1 (1 + i s ) =0 (5) · Given { R t ,w t } , { k t ,n t } solves the following representative f rm’s prob- lem: for t max { y t ,k t ,n t } { y t w t n t ( R t 1+ δ ) k t } (6) subject to y t F ( k t ,n t ) (7) · Goods market clear: y t + k t (1 δ )= c t + k t +1 t (8) We have also de f ned the Valuation (Arrow-Debreu) Equilibrium (VE) as an allocation { x it ,y it } t =0 ,i =1 , 2 , 3 and a valuation function (assuming it has an inner product representation) b p ( x )= P t =0 3 P i =1 p it x it such that given b p ( x ) , 1

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## This note was uploaded on 11/12/2010 for the course ECON 8108 taught by Professor Staff during the Spring '08 term at Minnesota.

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pr3ec702 - Homework 3 Spring 2004, Econ 702 Problem 1 We...

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