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ch30lec

# ch30lec - Chapter 30 Exchange Exchange Two consumers A and...

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Chapter 30 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 Z Z Z A A A ( , ) 1 2 Z and Z Z B B B ( , ). 1 2 Z A ( , ) 6 4 Z B ( , ). 2 2 and Z Z 1 1 6 2 8 A B ± ± units of good 1 are Z and Z 2 2 4 2 6 A B ± ± units of good 2.
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 The dimensions of the box are the quantities available of the goods. Height = Z Z 2 2 4 2 6 A B ± ± Width = Z Z 1 1 6 2 8 A B ± ±
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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The Endowment Allocation The endowment allocation is Z A ( , ) 6 4 Z B ( , ). 2 2 and Height = Z Z 2 2 4 2 6 A B ± ± Width = Z Z 1 1 6 2 8 A B ± ±
The Endowment Allocation O A O B The endowment allocation Z Z 1 1 A B ± Z 2 A Z 1 A Z 1 B Z 2 B Z Z 2 2 A 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 ( , ) x x A A 1 2 ( , ) x x B B 1 2 x x A B A B 1 1 1 1 ± d ± Z Z x x A B A B 2 2 2 2 ± d ± Z Z . and
Feasible Reallocations O A O B Z Z 1 1 A B ± x A 2 x A 1 x B 1 x B 2 Z Z 2 2 A B ±

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Feasible Reallocations O A O B Z Z 1 1 A B ± x A 2 x A 1 x B 1 x B 2 Z Z 2 2 A B ±
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?

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Adding Preferences to the Box Z 2 A Z 1 A x A 2 x A 1 More preferred O A For consumer A.
Adding Preferences to the Box Z 2 B Z 1 B x B 1 x B 2 More preferred O B For consumer B.

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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
Pareto-Improvement An allocation of the endowment that improves the welfare of a consumer without reducing the welfare of another is a Pareto-improving allocation. Where are the Pareto-improving allocations? Since each consumer can refuse to trade, the only possible outcomes from exchange are Pareto-improving allocations.

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ch30lec - Chapter 30 Exchange Exchange Two consumers A and...

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