Edgeworth Box and Feasible Allocations for Two Consumers A and B

1. Chapter Twenty-Nine Exchange

2. Exchange • Two consumers, A and B. • Their endowments of goods 1 and 2 are • E.g. • The total quantities available and and units of good 1 are units of good 2. and

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.

4. Starting an Edgeworth Box

5. Starting an Edgeworth Box Width =

6. Starting an Edgeworth Box Height = Width =

7. Starting an Edgeworth Box Height = The dimensions ofthe box are thequantities availableof the goods. Width =

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.

10. The Endowment Allocation The endowmentallocation is Height = and Width =

11. The Endowment Allocation Height = Width =

12. The Endowment Allocation OB 6 OA 8

13. The Endowment Allocation OB 6 4 OA 6 8

14. The Endowment Allocation 2 OB 2 6 4 OA 6 8

15. The Endowment Allocation 2 OB 2 6 Theendowmentallocation 4 OA 6 8

16. The Endowment Allocation More generally, …

17. The Endowment Allocation OB Theendowmentallocation OA

18. Other Feasible Allocations • denotes an allocation to consumer A. • denotes an allocation to consumer B. • An allocation is feasible if and only if and

19. Feasible Reallocations OB OA

20. Feasible Reallocations OB OA

21. Feasible Reallocations • All points in the box, including the boundary, represent feasible allocations of the combined endowments.

22. 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?

23. There are two goods, bread and fish, and two traders Alice and Bob. Alice’s initial endowment is 5 units of fish and 2 units of bread. Bob has 3 units of fish and 8 units of bread. For these traders, an Edgeworth box with bread on the horizontal axis and fish on the vertical will be • 5 units wide and 8 units tall. • 13 units wide and 5 units tall. • 10 units wide and 8 units tall. • 8 units wide and 6 units tall. • 18 units wide and 18 units tall.

24. Adding Preferences to the Box For consumer A. OA

25. Adding Preferences to the Box For consumer A. More preferred OA

26. Adding Preferences to the Box For consumer B. OB

27. Adding Preferences to the Box For consumer B. More preferred OB

28. Adding Preferences to the Box For consumer B. OB More preferred

29. Adding Preferences to the Box For consumer A. OA

30. Adding Preferences to the Box OB OA

31. Edgeworth’s Box OB OA

32. 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?

33. Edgeworth’s Box OB OA

34. Pareto-Improvements OB OA The set of Pareto-improving allocations

35. Pareto-Improvements • Since each consumer can refuse to trade, the only possible outcomes from exchange are Pareto-improving allocations. • But which particular Pareto-improving allocation will be the outcome of trade?

36. The white area shows allocations that are better for both consumers than the initial allocation. OB OA A) True B) False A) A

37. Pareto-Improvements OB OA The set of Pareto-improving reallocations

38. Pareto-Improvements

39. Pareto-Improvements

40. Pareto-Improvements Tradeimproves bothA’s and B’s welfares.This is a Pareto-improvementover the endowment allocation.

41. Pareto-Improvements New mutual gains-to-trade region is the set of all further Pareto- improving reallocations. Tradeimproves bothA’s and B’s welfares.This is a Pareto-improvementover the endowment allocation.

42. Pareto-Improvements Further trade cannot improve both A and B’s welfares.

43. Pareto-Optimality Better forconsumer A Better forconsumer B

44. Pareto-Optimality A is strictly better off but B is strictly worse off

45. Pareto-Optimality A is strictly better off but B is strictly worse off B is strictly betteroff but A is strictlyworse off

46. Pareto-Optimality Both A andB are worseoff A is strictly better off but B is strictly worse off B is strictly betteroff but A is strictlyworse off

47. Pareto-Optimality Both A andB are worseoff A is strictly better off but B is strictly worse off B is strictly betteroff but A is strictlyworse off Both Aand B are worse off

48. Pareto-Optimality The allocation isPareto-optimal since theonly way one consumer’s welfare can be increased is todecrease the welfare of the otherconsumer.

49. Pareto-Optimality An allocation where convexindifference curves are “only just back-to-back” is Pareto-optimal. The allocation isPareto-optimal since theonly way one consumer’s welfare can be increased is todecrease the welfare of the otherconsumer.

50. Pareto-Optimality • Where are all of the Pareto-optimal allocations of the endowment?