1. 1 Exchange

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

3. 3 Exchange Edgeworth and Bowley devised a diagram, called an …………………………, to show all possible allocations of the available quantities of goods 1 and 2 between the two consumers.

4. 4 Starting an Edgeworth Box Width = Height = The dimensions of the box are the quantities available of the goods.

5. 5 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.

6. 6 If the endowment allocation is and The Endowment Allocation How can we represent it in the Edgeworth box?

7. 7 The Endowment Allocation OAOA OBOB The endowment allocation

8. 8 Other Feasible Allocations denotes an allocation to consumer A. denotes an allocation to consumer B. An allocation is feasible if and only if and

9. 9 Feasible Reallocations: example OAOA OBOB

10. 10 Feasible Reallocations All points in the box, including the boundary, represent of the combined endowments. Which allocations will be blocked by one or both consumers? Which allocations make both consumers better off? ……………………………

11. 11 Adding Preferences to the Box More preferred For consumer A. OAOA

12. 12 Adding Preferences to the Box More preferred For consumer B. OBOB

13. 13 Adding Preferences to the Box More preferred For consumer B. OBOB

14. 14 OAOA OBOB Adding Preferences to the Box

15. 15 Pareto-Improvement An allocation of the endowment that the welfare of a consumer the welfare of another is a Pareto-improving allocation. Where are the Pareto-improving allocations? ……………………………..… ………………

16. 16 Pareto-Improvements OAOA OBOB The set of ………………. ……………………..

17. 17 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?

18. 18 Pareto-Improvements In the following diagrams, we show only the Pareto-improving allocations for clearer illustration Trade to improves both A’s and B’s welfares. This is a Pareto-improvement over the endowment allocation.

19. 19 Pareto-Improvements New mutual gains-to-trade region is the set of all further Pareto-improving reallocations.

20. 20 Pareto-Improvements At point, ……. ……………..

21. 21 Pareto-Optimality Better for consumer B Better for consumer A

22. 22 Pareto-Optimality A is strictly better off but B is strictly worse off B is strictly better off but A is strictly worse off Both A and B are worse off

23. 23 Pareto-Optimality The allocation is Pareto-optimal since the only way one consumer’s welfare can be increased is to ……………….. the welfare of the other consumer. An allocation where convex indifference curves are “only just back-to-back” is Pareto-optimal.

24. 24 Pareto-Optimality Where are all of the Pareto-optimal allocations of the endowment? Ans. In normal cases, they are all the tangency points of the consumers’ indifferent curves.

25. 25 Pareto-Optimality OAOA OBOB All the allocations marked by a are ……………………..

26. 26 Pareto-Optimality The ……………………. is the set of all Pareto- optimal allocations.

27. 27 Pareto-Optimality OAOA OBOB All the allocations marked by a are Pareto-optimal. The contract curve

28. 28 Pareto-Optimality But to which of the many allocations on the contract curve will consumers trade? That depends upon how trade is conducted. In perfectly competitive markets? By one- on-one bargaining?

29. 29 The Core OAOA OBOB The set of Pareto- improving reallocations

30. 30 The Core OAOA OBOB Pareto-optimal trades

31. 31 The Core OAOA OBOB Pareto-optimal trades blocked by …. Pareto-optimal trades blocked by …..

32. 32 The Core OAOA OBOB Pareto-optimal trades not blocked by A or B are called the core.

33. 33 The Core The core is the set of all Pareto-optimal allocations that are welfare-improving for both consumers relative to their own endowments. Rational trade should achieve a core allocation. But which core allocation? Again, that depends upon the manner in which trade is conducted.

34. 34 Trade in Competitive Markets Consider trade in perfectly competitive markets. Each consumer is a price-taker trying to maximize her own utility given p 1, p 2 and her own endowment. That is,

35. 35 Trade in Competitive Markets For Consumer A Max Subject to

36. 36 Trade in Competitive Markets OAOA A’s Constraint ………………………

37. 37 Trade in Competitive Markets So given p 1 and p 2, consumer A’s net demands for commodities 1 and 2 are And, similarly, for consumer B. and

38. 38 Trade in Competitive Markets For Consumer B Max Subject to

39. 39 Trade in Competitive Markets OBOB B’s constraint ………………………

40. 40 Trade in Competitive Markets So given p 1 and p 2, consumer B’s net demands for commodities 1 and 2 are and

41. 41 Trade in Competitive Markets A general equilibrium occurs when prices p 1 and p 2 cause both the markets for commodities 1 and 2 to clear; i.e. and

42. 42 Trade in Competitive Markets OAOA OBOB Can this PO allocation be achieved?

43. 43 Trade in Competitive Markets OAOA OBOB Budget constraint for A Budget constraint for B

44. 44 Trade in Competitive Markets OAOA OBOB Consumer …’s consumption choice

45. 45 However, from previous diagram, and Trade in Competitive Markets

46. 46 Trade in Competitive Markets So at the given prices p 1 and p 2 there is an  excess ……….. of commodity 1  excess ………… for commodity 2. Neither market clears so the prices p 1 and p 2 do not cause a general equilibrium.

47. 47 Trade in Competitive Markets OAOA OBOB So this PO allocation cannot be achieved by competitive trading.

48. 48 Which PO allocations can be achieved by competitive trading? Trade in Competitive Markets

49. 49 Trade in Competitive Markets Since there is an excess demand for commodity 2, p 2 will rise. Since there is an excess supply of commodity 1, p 1 will fall. The slope of the budget constraints is - p 1 /p 2 so the budget constraints will pivot about the endowment point and become less steep.

50. 50 Trade in Competitive Markets OAOA OBOB Excess demand for x 2, p 2 will rise. Excess supply of x 1, p 1 will fall. Budget constraint pivots around the endowment point

51. 51 Trade in Competitive Markets OAOA OBOB Consumer A’s consumption choice Consumer B’s consumption choice

52. 52 Trade in Competitive Markets From the Edgeworth Box and

53. 53 Trade in Competitive Markets At the new prices p 1 and p 2 both markets clear; there is a general equilibrium. Trading in competitive markets achieves a particular Pareto-optimal allocation of the endowments. This is an example of the …………. …………………….

54. 54 First Fundamental Theorem of Welfare Economics Given that consumers’ preferences are well-behaved, trading in perfectly competitive markets implements a Pareto- optimal allocation of the economy’s endowment.

55. 55 Second Fundamental Theorem of Welfare Economics The First Theorem is followed by a ………………………….... that states that any Pareto-optimal allocation (i.e. any point on the contract curve) can be achieved by trading in competitive markets provided that endowments are first appropriately rearranged amongst the consumers.

56. 56 Given that consumers’ preferences are well-behaved, for any Pareto-optimal allocation there are prices and an allocation of the total endowment that makes the Pareto-optimal allocation implementable by trading in competitive markets. Second Fundamental Theorem of Welfare Economics

57. 57 Second Fundamental Theorem OAOA OBOB The contract curve

58. 58 Second Fundamental Theorem OAOA OBOB Implemented by competitive trading from the endowment . 

59. 59 Second Fundamental Theorem OAOA OBOB Can this allocation be implemented by competitive trading from  ? Ans. ……. 

60. 60 Second Fundamental Theorem OAOA OBOB But this allocation is implemented by competitive trading from . 

61. 61 Walras’ Law Walras’ Law is an identity; i.e. a statement that is true for any positive prices (p 1,p 2 ), whether these are equilibrium prices or not.

62. 62 Walras’ Law Every consumer’s preferences are well- behaved so, for any positive prices (p 1,p 2 ), each consumer spends all of his budget. For consumer A: For consumer B:

63. 63 Walras’ Law Rearranged, Value of excess demand of x 1 Summing up the two constraints gives Value of excess demand of x 2

64. 64 Walras’ Law Thus, the above equation says that the summed market value of excess demands is zero for any positive prices p 1 and p 2 → this is Walras’ Law.

65. 65 Implications of Walras’ Law Suppose the market for commodity A is in equilibrium; that is, Then, Walras Law implies that for x 2

66. 66 Implications of Walras’ Law So one implication of Walras’ Law for a two-commodity exchange economy is that …………… then the other market must also ……………

67. 67 Implications of Walras’ Law What if, for some positive prices p 1 and p 2, there is an excess quantity supplied of commodity 1? That is, Then, Walras Law implies

68. 68 Implications of Walras’ Law So a second implication of Walras’ Law for a two-commodity exchange economy is that an excess ……..….. in one market implies an excess …………… in the other market and vice versa.