Lec 18 Chapter Thirty-One

1. Lec 18Chapter Thirty-One 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. Example Imagine two people (Amy and Bob) with a fixed amount of resources between the two of them — say, 8 liters of water and 6 hamburgers. If Amy takes 5 hamburgers and 4 liters of water, then Bob is left with 1 hamburgers and 4 liters of water. The Edgeworth box is a rectangular diagram with Amy's Origi on one corner (represented by the Oa) and Bob’s origin on the opposite corner (represented by the Ob). The width of the box is the total amount of one good, and the height is the total amount of the other good. Thus, every possible division of the goods between the two people can be represented as a point in the box.

5. Starting an Edgeworth Box

6. Starting an Edgeworth Box Width =

7. Starting an Edgeworth Box Height = Width =

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

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?

10. 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.

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

12. The Endowment Allocation Height = Width =

13. The Endowment Allocation OB 6 OA 8

14. The Endowment Allocation OB 6 4 OA 6 8

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

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

17. The Endowment Allocation More generally, …

18. The Endowment Allocation OB Theendowmentallocation OA

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

20. Feasible Reallocations OB OA

21. Feasible Reallocations OB OA

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

23. 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?

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

37. Pareto-Improvements

38. Pareto-Improvements

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

40. 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.

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

42. Pareto-Optimality Better forconsumer A Better forconsumer B

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

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

45. 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

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 Both Aand B are worse off

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

48. 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.

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

50. Pareto-Optimality OB OA