GE_exchange_CH10 - 1 General Equilibrium: Exchange Economy...

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Unformatted text preview: 1 General Equilibrium: Exchange Economy 2 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 3 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. 2 4 Starting an Edgeworth Box 5 Starting an Edgeworth Box Width = 1 1 6 2 8 A B 6 Starting an Edgeworth Box Width = 1 1 6 2 8 A B Height = 2 2 4 2 6 A B 3 7 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. 8 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? 9 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 . 4 10 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 11 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 12 A ( , ) 6 4 O A O B 6 8 B ( , ) 2 2 The Endowment Allocation 5 13 A ( , ) 6 4 O A O B 6 8 4 6 The Endowment Allocation 14 B ( , ) 2 2 O A O B 6 8 4 6 2 2 The Endowment Allocation 15 A ( , ) 6 4 B ( , ) 2 2 O A O B 6 8 4 6 2 2 The endowment allocation The Endowment Allocation 6 16 More generally, … The Endowment Allocation 17 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 18 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 7 19 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 20 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 21 Feasible Reallocations All points in the box, including the boundary, represent feasible allocations of the combined endowments. 8 22 Feasible Reallocations...
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GE_exchange_CH10 - 1 General Equilibrium: Exchange Economy...

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