Ch29 - Chapter Twenty-Nine Exchange Exchange Two consumers,...

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Unformatted text preview: Chapter Twenty-Nine Exchange Exchange Two consumers, A and B. Their endowments of goods 1 and 2 are E.g. The total quantities available A A A = ( , ) 1 2 B B B = ( , ). 1 2 and A = ( , ) 6 4 B = ( , ). 2 2 and 1 1 6 2 8 A B + = + = 2 2 4 2 6 A B + = + = units of good 1 units of good 2. and are Exchange Edgeworth and Bowley devised a diagram, called an Edgeworth box , to show all possible allocations of the available quantities of goods 1 and 2 between the two consumers. Starting an Edgeworth Box Starting an Edgeworth Box Width = 1 1 6 2 8 A B + = + = Starting an Edgeworth Box Width = 1 1 6 2 8 A B + = + = Height = 2 2 4 2 6 A B + = + = Starting an Edgeworth Box Width = 1 1 6 2 8 A B + = + = Height = 2 2 4 2 6 A B + = + = The dimensions of the box are the quantities available of the goods. Feasible Allocations What allocations of the 8 units of good 1 and the 6 units of good 2 are feasible? How can all of the feasible allocations be depicted by the Edgeworth box diagram? Feasible Allocations What allocations of the 8 units of good 1 and the 6 units of good 2 are feasible? How can all of the feasible allocations be depicted by the Edgeworth box diagram? One feasible allocation is the before- trade allocation; i.e. the endowment allocation . Width = 1 1 6 2 8 A B + = + = Height = 2 2 4 2 6 A B + = + = The endowment allocation is A = ( , ) 6 4 B = ( , ). 2 2 and The Endowment Allocation Width = 1 1 6 2 8 A B + = + = Height = 2 2 4 2 6 A B + = + = A = ( , ) 6 4 B = ( , ) 2 2 The Endowment Allocation A = ( , ) 6 4 O A O B 6 8 B = ( , ) 2 2 The Endowment Allocation A = ( , ) 6 4 O A O B 6 8 4 6 The Endowment Allocation B = ( , ) 2 2 O A O B 6 8 4 6 2 2 The Endowment Allocation A = ( , ) 6 4 B = ( , ) 2 2 O A O B 6 8 4 6 2 2 The endowment allocation The Endowment Allocation More generally, The Endowment Allocation The Endowment Allocation O A O B The endowment allocation 1 1 A B + 2 A 2 2 A B + 1 A 1 B 2 B Other Feasible Allocations denotes an allocation to consumer A. denotes an allocation to consumer B. An allocation is feasible if and only if ( , ) x x A A 1 2 ( , ) x x B B 1 2 x x A B A B 1 1 1 1 + + x x A B A B 2 2 2 2 + + . and Feasible Reallocations O A O B 1 1 A B + x A 2 2 2 A B + x A 1 x B 1 x B 2 Feasible Reallocations O A O B 1 1 A B + x A 2 2 2 A B + x A 1 x B 1 x B 2 Feasible Reallocations All points in the box, including the boundary, represent feasible allocations of the combined endowments. Feasible Reallocations All points in the box, including the boundary, represent feasible allocations of the combined endowments....
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This note was uploaded on 01/06/2012 for the course ECON 102 taught by Professor Goodhart during the Spring '11 term at Abu Dhabi University.

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Ch29 - Chapter Twenty-Nine Exchange Exchange Two consumers,...

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