1. General Equilibrium and Economic Welfare
Chapter Ten
General Equilibrium and Economic Welfare

2. Topics General Equilibrium. Trading Between Two People.
Competitive Exchange.
Production and Trading.
Efficiency and Equity.
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3. General Equilibrium
partial-equilibrium analysis - an examination of equilibrium and changes in equilibrium in one market in isolation.
general-equilibrium analysis - the study of how equilibrium is determined in all markets simultaneously
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4. Feedback Between Competitive Markets
Corn and soybean markets using supply and demand curves estimated by Holt (1992).
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5. Figure 10.1 Relationship Between the Corn and Soybean Markets
(a) Co r
n Ma r k et
Figure 10.1 Relationship Between the Corn and Soybean Markets S c
ushel b S 3 c
, $ per e c
$2.15 e ic r D c P 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
if demand for corn decreased ….
(b) S o
ybean Ma r k et S s
ushel b e s
, $ per
$4.12 e ic D s r P 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
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6. Table 10.1 Adjustment in the Corn and Soybean Markets
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7. 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.
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8. 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?
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9. 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
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10. Solved Problem 10.1
After the government starts taxing the cost of labor by τ 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?
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11. Solved Problem 10.1
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12. Trading Between Two People: Scenario
Jane and Denise live near each other in the wilds of Massachusetts 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.
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13. 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.
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14. Figure 10.3a Endowments in an Edgeworth Box
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15. Figure 10.3b Endowments in an Edgeworth Box
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16. Figure 10.3c Endowments in an Edgeworth Box
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17. Mutually Beneficial Trades
Four assumptions about their tastes and behavior:
Utility maximization.
Usual-shaped indifference curves.
Nonsatiation.
No interdependence.
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18. Figure 10.4 Contract Curve
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19. 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.
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20. Contract Curve
contract curve - the set of all Pareto-efficient bundles
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21. Solved Problem 10.2
Are allocations a and g in Figure 10.4 part of the contract curve?
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22. Competitive Exchange Two desirable properties:
The competitive equilibrium is efficient.
First Theorem of Welfare Economics
Any efficient allocations can be achieved by competition.
Second Theorem of Welfare Economics
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23. 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.
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24. Figure 10.5a Competitive Equilibrium
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25. Figure 10.5b Competitive Equilibrium
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26. Competitive Equilibrium (cont).
In a competitive market, prices adjust until the quantity supplied equals the quantity demanded.
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27. The Efficiency of Competition
In a competitive equilibrium:
Thus, we have demonstrated the First Theorem of Welfare Economics:
Any competitive equilibrium is Pareto efficient.
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28. 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, …..
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29. Obtaining Any Efficient Allocation Using Competition
we’ve demonstrated the Second Theorem of Welfare Economics:
Any Pareto-efficient equilibrium can b obtained by competition, given an appropriate endowment.
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30. Comparative Advantage
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.
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31. 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.
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32. 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).
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33. Figure 10.6 Comparative Advantage and Production Possibility Frontiers
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34. 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.
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35. 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?
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36. Solved Problem 10.3
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37. Figure 10.7 Optimal Product Mix
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38. The Number of Producers
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.
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39. Efficient Product Mix
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.
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40. Competition 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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41. Competition (cont) If candy and wood are sold by competitive firms,
pc = MCc
pw = MCw
Therefore,
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42. 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.
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43. Figure 10.8 Competitive Equilibrium
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44. 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.
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45. Application Wealth Distribution in the United States
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46. Application Wealth Distribution in the United States (a)
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47. Application Wealth Distribution in the United States (b)
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48. 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.
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49. 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.
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50. Figure 10.9 Welfare Maximization
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51. Application An Unequal World
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52. Voting
Sometimes voting does not work well, and the resulting social ordering of allocations is not transitive.
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53. Table 10.2 Preferences over Allocations of Three People
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54. 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.
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55. 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.
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56. 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.
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57. Social Welfare Functions (cont).
The Rawlsian welfare function is:
W = min {U1, U2, , Un}.
Rawls’ rule leads to a relatively egalitarian distribution of goods.
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58. Cross-Chapter Analysis: Outsourcing and the World Trade Organization
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