# HW1 - equilibrium values for prices and allocations(c...

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Graduate Macro II, Homework 1 Jonathan Heathcote Due in class on Tuesday January 31st 2006 Recall the example economy we worked through following Chapter 2 in Dirk Krueger’s notes. 1. Consider the following alternative description of preferences and endow- ments. Period utility is given by u ( c i ) = ¡ c i ¢ 1 γ 1 γ Assume both individuals are in fi nitely-lived, and discount at rate β . Sup- pose the endowment stream is e 1 t = 1 . 5 if t is even, e 1 t = 1 if t is odd e 2 t = 0 . 5 if t is even, e 2 t = 2 if t is odd (a) Characterize the set of Pareto E cient allocations in this economy, assuming β = 0 . 9 and γ = 2 . (b) For these parameter values, use Negishi’s method to fi nd a candidate competitive equilibrium for this economy. Describe the candidate
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Unformatted text preview: equilibrium values for prices and allocations (c) Verify that the prices and allocations you solved for satisfy the nec-essary conditions for equilibrium (d) Which agent enjoys higher utility in the equilibrium, and why? 2. Now revert back to the original description of preferences and endowments. Consider a Pareto e ﬃ cient allocation indexed by the Pareto weight α. Show that for any α ∈ (0 , 1) this e ﬃ cient allocation can be decentralized as a competitive sequential markets equilibrium given an appropriate choice for a 1 (where a 1 is not necessarily equal to zero). 1...
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