ECON201B 2006 PS4

ECON201B 2006 PS4 - Economics 201B 2nd Half - Spring 2006...

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Problem Set 4 Economics 201B 2nd Half - Spring 2006 Due Thursday, 20 April in Lecture 1. In this problem, you are asked to prove in detail some of the steps from the Second Welfare Theorem in a production economy. Let ( x ; y ) be a P.O. allocation, let pref- set Y j to produce goods in such a way that strictly positive total consumption is possible. That is, 9 y j 2 Y j such that ! + P j y j >> 0 if 0 2 Y j 8 j and ! >> 0 ). A i = f x 0 i : x 0 i i x i g A = P i A i . Show that A is convex. (b) In the proof, we show that 9 p 6 = 0 s.t. sup p ± ( Y + f ! g ) ² inf p ± A . Show that inf p ± A = P i inf p ± A i . (c) Later in the proof, we establish that p ³ 0 , and that ( p ; x ; y ; T ) is a Walrasian quasi-equilibrium with transfers. That is, x i is in the quasi-demand set for each agent and y j Show that ( p ; x ; y ; T ) is a
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ECON201B 2006 PS4 - Economics 201B 2nd Half - Spring 2006...

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