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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 ) = , then Prob ( y 2 ) = 1 . 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 ) + 1 [ u ( y 1 ) + (1 ) u ( y 2 )] v 2 = u ( y 2 ) + 1 [ u ( y 1 ) + (1 ) u ( y 2 )] with probability Prob ( v 1 ) = , Prob ( v 2 ) = 1 . 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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