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Unformatted text preview: ECO 475 PS5 Solution Yu LIU November 30, 2010 Question 1 Assume ≤ y 1 < y 2 ≤ 1 . Considering that the endowment process is i.i.d., let Prob ( y 1 ) = π , then Prob ( y 2 ) = 1- π . Since rst best allocation is not sustainable, then c 1 < c 2 . From (20.6.4) in LS, the ergodic consumption set for person 1 is c 1 , c 2 . So, in steady state, person 1's consumption is ( c 1 = c 1 c 2 = c 2 , and net continuation value is ( x 1 = x 1 x 2 = 0 , where Q 1 ( x 1 ) = 0 De ne the continuation value: v s = x s + deviation utility in the state y s . Then the steady state distribution of continuation value v is given by ( v 1 = x 1 + u ( y 1 ) + β 1- β [ πu ( y 1 ) + (1- π ) u ( y 2 )] v 2 = u ( y 2 ) + β 1- β [ πu ( y 1 ) + (1- π ) u ( y 2 )] with probability Prob ( v 1 ) = π , Prob ( v 2 ) = 1- π . Since consumption and continuation value depend only on the current state (which is given by the endowment realization), then history becomes irrelevant, and the allocation displays full amnesia re- garding previous promised utilities. Question 2 [Reference: Krueger and Perri (2006), Does Income Inequality Lead to Consumption Inequality? Evi- dence and Theory , Review of Economic Studies .] The relationship is ambiguous. On the one hand, from LS Chap 20.4.1 - 20.4.3, since market is incomplete, the consumption process weakly tracks the endowment realization. When the endowment process is more volatile, the volatility of consumption may also increase. A simple example: Environment 1: (question 1) V ar ( y ) > , V ar ( c ) > ....
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- Fall '07
- Constraint, endowment process, Review of Economic Studies, participation constraints bind, Qj xj