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Unformatted text preview: Chapter ThirtyOne 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 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? 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 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. Which allocations will be blocked by one or both consumers? Which allocations make both consumers better off? Adding Preferences to the Box 2 A 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 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 2 B 1 B Adding Preferences to the Box 2 B 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 Adding Preferences to the Box 2 A 1 A x A 2 x A 1 O A 2 B 1 B x B 1 x B 2 O B Edgeworths Box 2 A 1 A x A 2 x A 1 O A 2 B 1 B x B 1 x B 2 O B ParetoImprovement An allocation of the endowment that improves the welfare of a consumer without reducing the welfare of another is a Paretoimproving allocation ....
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 Spring '10
 IOANADAN

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