Varian_Chapter31_Exchange

# Varian_Chapter31_Exchange - Chapter Thirty-One Exchange...

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Chapter Thirty-One Exchange

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Exchange ± Two consumers, A and B. ± Their endowments of goods 1 and 2 are ± E.g. ± The total quantities available ω ωω A A A = (, ) 12 BB B = ) . and A = (,) 64 B = . 22 and 11 628 AB += + = 426 + = 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.

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Starting an Edgeworth Box
Starting an Edgeworth Box Width = ω 11 628 A B += + =

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Starting an Edgeworth Box Width = ω 11 628 A B += + = Height = 22 42 6 A B + =+ =
Starting an Edgeworth Box Width = ω 11 628 A B += + = Height = 22 42 6 A B + =+ = The dimensions of the box are the quantities available of the goods.

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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 .

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Width = ω 11 628 A B += + = Height = 22 42 6 A B + =+ = The endowment allocation is A = (,) 64 B = . and The Endowment Allocation
Width = ω 11 628 A B += + = Height = 22 42 6 A B + =+ = A = (,) 64 B = The Endowment Allocation

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ω A = (,) 64 O A O B 6 8 B = 22 The Endowment Allocation
ω A = (,) 64 O A O B 6 8 4 6 The Endowment Allocation

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ω B = (,) 22 O A O B 6 8 4 6 2 2 The Endowment Allocation
ω A = (,) 64 B = 22 O A O B 6 8 4 6 2 2 The endowment allocation The Endowment Allocation

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More generally, … The Endowment Allocation
The Endowment Allocation O A O B The endowment allocation ω 11 A B + 2 A 2 2 A B + 1 A 1 B 2 B

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Other Feasible Allocations ± denotes an allocation to consumer A. ± denotes an allocation to consumer B. ± An allocation is feasible if and only if (, ) xx AA 12 ) BB AB A B 11 1 1 +≤ + ωω A B 22 2 2 + . and
Feasible Reallocations O A O B ω 11 A B + x A 2 2 2 A B + x A 1 x B 1 x B 2

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Feasible Reallocations O A O B ω 11 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.

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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 ω 2 A 1 A x A 2 x A 1 O A For consumer A.

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Adding Preferences to the Box ω 2 A 1 A x A 2 x A 1 M o r e p f d For consumer A. O A
Adding Preferences to the Box ω 2 B 1 B x B 2 x B 1 For consumer B. O B

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Adding Preferences to the Box x B 2 x B 1 M o r e p f d For consumer B. O B ω 2 B 1 B
Adding Preferences to the Box ω 2 B 1 B x B 1 x B 2 M o r e p f d For consumer B.

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Varian_Chapter31_Exchange - Chapter Thirty-One Exchange...

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