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Unformatted text preview: General Equilibrium without Production Exchange (Chapter 31) May 19, 2009 Endowment Economy ◮ Suppose that there are Two consumers, A and B. and Two goods, goods 1 and 2. ◮ Their endowment of both goods are given by Endowment ω A = ( ω A 1 ,ω A 2 ) and ω B = ( ω B 1 ,ω B 2 ) ◮ For example, ω A = (6 , 4) and ω B = (2 , 2). ◮ This implies that the total endowment of good 1 is ω A 1 + ω B 1 = 6 + 2 = 8 and the total of good 2 is ω A 2 + ω B 2 = 4 + 2 = 6. ◮ Let x A = ( x A 1 , x A 2 ) and x B = ( x B 1 , x B 2 ) be the allocations or consumptions of A and B, respectively. Feasible Allocation ◮ ( x A , x B ) is feasible if Feasible Allocation x A 1 + x B 1 ≤ ω A 1 + ω B 1 and x A 2 + x B 2 ≤ ω A 2 + ω B 2 ◮ That is, the allocation is feasible if it use at most the aggregate endowment. ◮ We can depict all feasible allocations in so called Edgeworth Box. Edgeworth Box Z A ( , ) 6 4 Z B ( , ) 2 2 O A O B 6 8 4 6 2 2 The endowment allocation The Endowment Allocation Edgeworth Box Feasible Reallocations O A O B Z Z 1 1 A B . x A 2 Z Z 2 2 A B . x A 1 x B 1 x B 2 Preferences of A Adding Preferences to the Box Z 2 A Z 1 A x A 2 x A 1 M o r e p r e f e r r e d For consumer A. O A Preferences of B Adding Preferences to the Box x B 2 x B 1 M o r e p r e f e r r e d For consumer B. O B Z 2 B Z 1 B Preferences of B Adding Preferences to the Box Z 2 B Z 1 B x B 1 x B 2 M o r e p r e f e r r e d For consumer B. O B Putting both of them together Edgeworth’s Box Z 2 A Z 1 A x A 2 x A 1 O A Z 2 B Z 1 B x B 1 x B 2 O B Feasible Allocation ◮ Paretoimproving allocation = a feasible allocation that improves the welfare of a consumer without reducing the welfare of another ....
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This note was uploaded on 12/26/2011 for the course ECON 100B taught by Professor Kilenthong during the Fall '08 term at UCSB.
 Fall '08
 KILENTHONG

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