1. Chapter 10
General Equilibrium and Economic Welfare

2. Topics General Equilibrium. Trading Between Two People.
Competitive Exchange.
Production and Trading.
Efficiency and Equity.

3. General Equilibrium
Partial-equilibrium analysis - an examination of equilibrium and changes in equilibrium in one market in isolation.eg.??
General-equilibrium analysis - the study of how equilibrium is determined in all markets simultaneously.eg. ??

4. Pareto Principle
A value criterion used in evaluating welfare in general equilibrium.
Used to rank different allocations of goods and services for which no interpersonal comparisons need to be made.
Pareto efficient - describing an allocation of goods or services such that any reallocation harms at least one person.

5. Feedback Between Competitive Markets
Markets are closely related if an increase in the price in one market causes the demand /supply curve in another market to shift measurably. Egs dd/ss??.
An event in one market may have a spillover effect on other related markets for various reasons.
Corn and soybean markets using supply and demand curves estimated by Holt (1992).

6. if demand for corn decreased ….
Ret
(a) Co r
n Ma k et S c
ushel S 3 c b e c
, $ per
$2.15 D c
Price e 1 c e 3 c
$1.9171
$1.9057 D 1 c
8.227
8.2613
8.44 Co r
n, Billion b
ushels per y
ear
(b) S o
ybean Ma r k et
if demand for corn decreased …. S s
ushel b e s
, $ per
$4.12 D s
Price S 2 s S 4 s e 2 s
$3.8325
$3.8180 e 4 s D 2 s D 4 s
2.0505
2.0514
2.07 S o
ybean s
, Billion b
ushels per y
ear

7. Table 10.1 Adjustment in the Corn and Soybean Markets

8. Minimum Wages with Incomplete Coverage
Result of partial-equilibrium analysis in Chapter 2:
The minimum wage causes the quantity of labor demanded to be less than the quantity of labor supplied.
Workers who lose their jobs cannot find work elsewhere, so they become unemployed.

9. Minimum Wages with Incomplete Coverage (cont.)
The story changes substantially if the minimum wage law covers workers in only some sectors of the economy.
When the U.S. minimum wage law was first passed in 1938 it drove workers out of manufacturing and other covered industries into agriculture, which the law did not cover. Why?

10. Figure 10.2 Minimum Wage with Incomplete Coverage
(a) C o v
ered Sector
(b) Unc o v
ered Sector
(c) T
otal Labor Ma r k et
age per hour
age per hour
age per hour W W W , , , S w w w w – S u w w w 1 1 1 w 2 D c D u D L c 2 L 1 L 1 L u 2 L = L 1 + L 1 c u 1 c u L , An n
ual hours L , An n
ual hours L
, An n
ual hours c u

11. Solved Problem 10.1
After the government starts taxing the cost of labor by t per hour in a covered sector only, the wage that workers in both sectors receive is w, but the wage paid by firms in the covered sector is w + τ. What effect does the subsidy have on the wages, total employment, and employment in the covered and uncovered sectors of the economy?

12. Solved Problem 10.1

13. Trading Between Two People: Scenario
Using GEM, we show that free trade is Pareto efficient. Two pp/many pp using….
Jane and Denise live near each other in the wilds of Sarbah Hall when a snowstorm strikes, isolating them from the rest of the world.
They must either trade with each other or consume only what they have at hand.
Collectively, they have 50 cords of firewood and 80 bars of candy and no way of producing more of either good.

14. Trading Between Two People: Endowments
Endowment - an initial allocation of goods.
Jane’s endowment is 30 cords of firewood and 20 candy bars.
Denise’s endowment is 20 (= 50 − 30) cords of firewood and 60 (= 80 − 20) candy bars.
So Jane has relatively more wood, and Denise has relatively more candy.

15. Figure 10.3(a) Endowments in an Edgeworth Box

16. Figure 10.3(b) Endowments in an Edgeworth Box

17. Figure 10.3(c) Endowments in an Edgeworth Box

18. We use the Edgeworth box to illustrate a GEM in which we examine simultaneous trade in firewood and candy.

19. Mutually Beneficial Trades
Should Jane and Denise trade?
Four assumptions about their tastes and behavior:
Utility maximization.
Usual-shaped indifference curve ‘[Each person IC …..convex shape]
Nonsatiation [strictly positive MU for each good……].
No interdependence..[utility & harm…]

20. Figure 10.4 Contract Curve

21. Mutually Beneficial Trades
We can make four equivalent statements about allocation f:
The indifference curves of the two parties are tangent at f.
The parties’ marginal rates of substitution are equal at f.
No further mutually beneficial trades are possible at f.
The allocation at f is Pareto efficient: One party cannot be made better off without harming the other.

22. Contract Curve
Contract curve - the set of all Pareto-efficient bundles.
Trade may not be mutually beneficial but bundles are Pareto efficient

23. Bargaining Ability
Where on the contract curve between points b and c and Jane and Denise end up?
It depends on their respective bargaining abilities.

24. Solved Problem 10.2
Are allocations a and g in Figure 10.4 part of the contract curve?
Answer:
By showing that no mutually beneficial trades are possible at those points, demonstrate that those bundles are Pareto efficient.

25. Competitive Exchange Two desirable properties:
The competitive equilibrium is efficient. [ competition results in a Pareto-efficient allocation]
First Theorem of Welfare Economics
Any efficient allocations can be achieved by competition. [all possible efficient allocations can be obtained by competitive exchange]
Second Theorem of Welfare Economics

26. Competitive Equilibrium
If there were a large number of people with tastes and endowments like Jane’s and a large number of people with tastes and endowments like Denise’s, each person would be a price taker in the two goods.
Have you ever bargained at SHOPRITE!
How would the price takers trade?

27. Each person considers the relative price of the 2 goods when deciding to trade
Pw=2; pc=1
Sell 1 wood to buy 2 candys
e, Jane has goods worth 80;
slope of price line = -pc/pw = -1/2
Px line is all the combinations of goods Jane could get by trading given her endowment.

28. Jane max her utility by picking the bundle where one of her IC is tangent to her pline
Note, in PC markets, px adjust until Qd=Qs

29. Figure 10.5(a) Competitive Equilibrium

30. Figure 10.5(b) Competitive Equilibrium

31. Competitive Equilibrium (cont.)
Pc=1; pw= 1.33
In a competitive market, prices adjust until the quantity supplied equals the quantity demanded.
Px ratio does not result in competitive eqm.

32. The Efficiency of Competition
ICs are tangent at the same bundle on the PL
In a competitive equilibrium:
Thus, we have demonstrated the First Theorem of Welfare Economics:
Any competitive equilibrium is Pareto efficient.

33. Obtaining Any Efficient Allocation Using Competition
Any Pareto-efficient bundle x can be obtained as a competitive equilibrium if the initial endowment is x.
That allocation can also be obtained as a competitive equilibrium if the endowment lies on a price line through x, where the slope of the price line equals the marginal rate of substitution of the indifference curves that are tangent at x.
Thus, …..

34. Obtaining Any Efficient Allocation Using Competition
We’ve demonstrated the Second Theorem of Welfare Economics:
Any Pareto-efficient equilibrium can be obtained by competition, given an appropriate endowment.
So…..

35. Society can achieve efficiency by allowing competition
Society can obtain the particular efficiency allocation it prefers……..

36. Production and Trading
Scenario: Jane and Denise can produce candy or chop firewood using their own labor. They differ, however, in how much of each good they produce from a day’s work.

37. Production Possibility Frontier
Jane can produce either 3 candy bars or 6 cords of firewood in a day.
Denise can produce up to 3 cords of wood or 6 candy bars in a day.
α is the fraction of day she spends in making candys- 3α
1- α fraction………- 6(1- α)

38. Production Possibility Frontier (cont.)
Production Possibility Frontier - shows the maximum combinations of two goods that can be produced from a given amount of input.
The slope of the production possibility frontier is the marginal rate of transformation (MRT).
Tells us how much more wood can be produced if the production of candy is reduced by one bar

39. Jane – MRT=-2 which means 2 more wood
Denise-MRT= -1/2………
MRT also shows how much it cost to produce one good in terms of the forgone prodxn of the other good.
Someone with the ability to produce a good at a lower cost than someone else has a comparative advantage in produ…

40. Denise has CA in producing candy( she forgoes less in wood prodxn to produce a given amount of candy). Jane…….

41. Figure 10.6 Comparative Advantage and Production Possibility Frontiers

42. Production Possibility Frontier (cont.)
Comparative advantage - the ability to produce a good at a lower opportunity cost than someone else.
Because of the difference in their marginal rates of transformation, Jane and Denise can benefit from a trade.

43. Solved Problem 10.3
How does the joint production possibility frontier in panel c of Figure 10.6 change if Jane and Denise can also trade with Harvey, who can produce 5 cords of wood, 5 candy bars, or any linear combination of wood and candy in a day?

44. Solved Problem 10.3

45. The Number of Producers
With many producers the PPF is a smooth concave curve.
Because the PPF is concave, the marginal rate of transformation decreases (in absolute value) as we move up the PPF.
Also,
where MCc and MCw are the marginal costs of producing candy and wood respectively.

46. Figure 10.7 Optimal Product Mix

47. Efficient Product Mix
Which combination of prdts along the PPF should society choose.
If a single person were to decide on the product mix, that person would pick the allocation of wood and candy along the PPF that maximized his or her utility.
For each consumer:
MRS = MRT,
if the economy is to produce the optimal mix of goods for each consumer.

48. Competition The competitive equilibrium lies on the contract curve.
Each consumer picks a bundle of goods so,
Consumption efficiency - we can’t redistribute goods among consumers to make one consumer better off without harming another one.
The competitive equilibrium lies on the contract curve.
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49. Competition (cont.) If candy and wood are sold by competitive firms,
pc = MCc
pw = MCw
Therefore,

50. Competition (cont.) Since, A competitive equilibrium achieves an:
efficient product mix - the rate at which firms can transform one good into another equals the rate at which consumers are willing to substitute between the goods, as reflected by their willingness to pay for the two goods.
The relative pxs firms and consumers face are the same. Px lines are parrallel so MRS=PX ratios=MRT

51. Figure 10.8 Competitive Equilibrium

52. Competitive eqm in both consumption and production

53. Efficiency and Equity
How well various members of society live depends on how society deals with efficiency (the size of the pie) and equity (how the pie is divided).
The actual outcome depends on choices by individuals and on government actions.

54. Role of the Government
By altering the efficiency with which goods are produced and distributed and the endowment of resources, governments help determine how much is produced and how goods are allocated.

55. Application Wealth Inequality

56. Application Wealth Distribution in the United States (a)

57. Application Wealth Distribution in the United States (b)

58. Efficiency
The Pareto criterion ranks allocation x over allocation y if some people are better off at x and no one else is harmed.
If that condition is met, we say that x is Pareto superior to y.
Any policy change that leads to a Pareto-superior allocation must increase W (welfare).
However, some policy changes that increase W are not Pareto superior: There are both winners and losers.

59. Equity
Social welfare function - combines various consumers’ utilities to provide a collective ranking of allocations.
Sort of like a utility function for society.
Utility possibility frontier (UPF): the set of utility levels corresponding to the Pareto efficient allocations along the contract curve.

60. Figure 10.9 Welfare Maximization

61. Voting
Sometimes voting does not work well, and the resulting social ordering of allocations is not transitive.

62. Table 10.2 Preferences over Allocations of Three People

63. Arrow’s Impossibility Theorem
A social welfare function should satisfy the following criteria:
Social preferences should be complete and transitive, like individual preferences.
If everyone prefers Allocation a to Allocation b, a should be socially preferred to b.
Society’s ranking of a and b should depend only on individuals’ ordering of these two allocations, not on how they rank other alternatives.
Dictatorship is not allowed; social preferences must not reflect the preferences of only a single individual.

64. Arrow’s Impossibility Theorem (cont.)
It is impossible to find a social decision-making rule that always satisfies all of these criteria.
Result indicates that democratic decision making may fail—not that democracy must fail.

65. Social Welfare Functions
Utilitarian philosophers: suggested that society should maximize the sum of the utilities of all members of society.
Their social welfare function is the sum of the utilities of every member of society.
If Ui is the utility of Individual i and there are n people, the utilitarian welfare function is:
W = U1 + U Un.

66. Social Welfare Functions (cont.)
The Rawlsian welfare function is:
W = min {U1, U2, , Un}.
Rawls’ rule leads to a relatively egalitarian distribution of goods.

67. Efficiency versus Equity
Given a particular social welfare function, society might prefer an inefficient allocation to an efficient one.
By most of the well-known social welfare functions, but not all, there is an efficient allocation that is socially preferred to an inefficient allocation.
Competitive equilibrium may not be very equitable even though it is Pareto efficient.

68. Figure 10.10 Anti-Price Gouging Law