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ECON201B 2006 PS7 - Economics 201B 2nd Half Spring 2006 Due...

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Problem Set 7 Economics 201B 2nd Half - Spring 2006 Due Thursday, 11 May in Ryan°s 5th ±oor mailbox 1. Consider a consumer with the following preferences and endowment: u ( x 1 ; x 2 ) = max f min f 2 x 1 ; x 2 g ; min f x 1 ; 4 x 2 gg ; ( ! 1 ; ! 2 ) = (2 + 2 °; 4 ° 3 ° ) ; ° 2 (0 ; 1) (a) Draw the indi/erence curves for this consumer. Are this consumer°s preferences convex? (b) Now suppose we have an economy of I 2 N identical consumers with I ± 2 , each of which has the same preferences and endowment as the consumer described above. Find a necessary and su¢ cient condition for ° that must be satis²ed for there to exist a Walrasian equilibrium of this economy. Show that as I increases, the set of a 2 (0 ; 1) that satisfy the condition you found increases in size. (c) Explain in a few sentences how these results relate to Theorem 5 in the (revised) Lecture Notes 12. That is, relate your above results to the fact that, in this economy, we can show that 8 a 2 (0 ; 1) , 9 p ° >> 0 and x ° i 2 D i ( p ° ) such that 1 I X l max f ( X i x ° i ° X i !
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