1. General Equilibrium, Efficiency, and Equity
Chapter 16
General Equilibrium, Efficiency, and Equity
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

2. Main Topics The nature of general equilibrium
Positive analysis of general equilibrium
Normative criteria for evaluating economic performance
General equilibrium and efficient exchange
Equity and redistribution
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3. The Nature of General Equilibrium
Already studied competitive equilibrium in a single isolated market: partial equilibrium analysis
Useful when supply and demand for a good are largely independent of activities in other markets
However, markets are often interdependent (e.g., if complements or substitutes)
General equilibrium analysis is the study of competitive equilibrium in many markets at the same time
Allows us to understand the consequences of interdependence among markets
Factors that affect supply and demand in one market can have ripple effects in other markets
Accounts for feedback between markets
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4. Figure 16.1: General Equilibrium
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5. Positive Analysis of General Equilibrium
General equilibrium analysis can provide more accurate answers than partial equilibrium analysis does to positive questions
Examine the effects of a sales tax on ice cream
Assume pie and ice cream are complements
Assume no supply linkages
General equilibrium effects of the tax include:
Demand curve for pie shifts downward, so price of pie falls
This produces a feedback effect on the ice cream market
Effects of the tax ripple back and forth between the markets
Need a new tool to determine the prices that will prevail in both markets in a general equilibrium
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6. Market-Clearing Curves
First step in identifying a general equilibrium is to find the market-clearing curve for each good
Shows the combinations of prices for that good and related goods that bring supply and demand for the good into balance
Prices of the goods are on the axes
For two goods that are complements, the market-clearing curves will be downward sloping
Example: an increase in the price of pie reduces the demand for ice cream, which lowers the partial equilibrium price of ice cream
For substitutes, the curves will be upward sloping
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7. Figure 16.2: A Market-Clearing Curve
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8. General Equilibrium in Two Markets
If a price combination lies on both market-clearing curves, then both markets are in equilibrium
This is a general equilibrium
Find a general equilibrium by plotting both market-clearing curves on the same graph
Horizontal axis shows the price of one good; vertical axis shows the price of the other good
Intersection of the two market-clearing curves reveals the general equilibrium prices
The two goods markets clear at these prices
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9. Figure 16.4: General Equilibrium Price Combination
General equilibrium prices are $12 per pie and $6 per gallon of ice cream
Pie and ice cream markets both clear at these prices
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10. Effects of a Sales Tax: Partial Equilibrium
Continue the ice cream example
Examine effects of $3 per gallon sales tax on ice cream
Begin from initial equilibrium price of $6 per gallon, 25 million gallons
Tax shifts supply curve upward by $3
New partial equilibrium is at intersection of new supply curve and initial demand curve
Price of pie held constant at $12 per pie
Price of ice cream rises by $1.67 per gallon, less than the amount of the tax
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11. Effect of a Sales Tax: General Equilibrium
Need new market-clearing curve for ice cream, to find general equilibrium effects of tax
Tax shifts market-clearing curve for ice cream upward
New curve lies exactly $1.67 above the old one
Magnitude of the shift equals partial equilibrium effect of the tax
Look for intersection of new market-clearing curve for ice cream and old market-clearing curve for pie
Shows new general equilibrium
Pie price is $11 per pie, ice cream price is $8 per gallon
These prices clear both markets
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12. Effect of a Sales Tax: General Equilibrium
As a result of the tax, demand curves for both goods shift
Sales tax on ice cream reduces the price of a pie by $1
Because pie and ice cream are complements
Partial equilibrium analysis understates the effect of the tax on the price of ice cream
Lower pie price leads to greater demand for ice cream
Reinforces pressure for ice cream price to rise
General equilibrium analysis accounts for this feedback; partial equilibrium analysis does not
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13. Figure 16.5: General Equilibrium Effect of a Tax
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14. Figure 16.6: Effects of a Tax, part 2
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15. Normative Criteria for Economic Performance
Economists have clear criteria for measuring efficiency
Equity and fairness are more difficult to determine and evaluate
An allocation of resources is Pareto efficient if it’s impossible to make any consumer better off without hurting someone else
Proposed by Italian economist Vilfredo Pareto
Assume each person knows what’s best for her
The utility possibility frontier shows the utility levels associated with all efficient allocations of resources
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16. Figure 16.7: Pareto Efficient Outcomes
Points on the boundary are Pareto efficient
Point A is inefficient
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17. Equity Equity is harder to define and measure than efficiency
A subjective concept
Process-oriented notions of equity focus on the procedures used to arrive at an allocation of resources
Is the free market a fair process?
Outcome-oriented notions focus on whether the process used to allocate resources yields fair results
Some focus on the distribution of well-being, e.g., utilitarianism
Others focus on the distribution of consumption, e.g., egalitarianism
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18. Social Welfare Functions
Economists use social welfare functions to summarize judgments about resource allocations
For each possible allocation, the function assigns a number that indicates the overall level of social welfare
Higher numbers reflect greater social well-being
First, assign utility levels to every consumer using utility functions
Second, apply a function that converts those utilities into social welfare
Higher levels of individual utility imply higher levels of social welfare
Can capture concerns for both efficiency and outcome-oriented notions of equity
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19. Figure 16.8: Applying Social Welfare Functions
Indifference curves farther from the origin correspond to higher levels of social welfare
Point A is the best possible outcome
Since Point A is on the utility possibility frontier, it is Pareto efficient
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20. General Equilibrium in Exchange Economies
In an exchange economy, people own and trade goods but no production takes place
An endowment is the bundle of goods an individual starts out with before trading
Simple example:
Humphrey and Lauren are the only consumers
Two goods: food and water
Humphrey’s initial endowment is 8 pounds of food and 3 gallons of water
Lauren’s initial endowment is 2 pounds of food and 7 gallons of water
If food sells for $1 per pound and water sells for $1 per gallon this is not a general equilibrium
Supply and demand match if food costs $2 per pound and water sells for $1 per gallon
This is a general equilibrium
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21. Figure 16.9: General Equilibrium in an Exchange Economy
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22. The Edgeworth Box
The Edgeworth box is a diagram that shows two consumers’ opportunities and choices in a single figure
Often used for a simple exchange economy
Introduced by British economist Francis Edgeworth in 1881
Each point describes an allocation of resources between the two consumers
Dimensions of the box are determined by the total amounts of each good available in the economy
When the economy is in general equilibrium the points representing the two consumers’ choices after trading coincide
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23. Figure 16.10: Equilibrium in an Edgeworth Box
Point A represents initial endowments
Point C is the general equilibrium resource allocation
Food costs $2 per pound
Water costs $1 per gallon
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24. The First Welfare Theorem
First welfare theorem: in a general equilibrium with perfect information the allocation of resources is Pareto efficient
Clarifies what Adam Smith mean by the “invisible hand”
Use Edgeworth box to understand first welfare theorem
At general equilibrium allocation, two consumers face the same equilibrium prices
Line representing these prices serves as the budget line for both consumers
Impossible to choose an allocation at equilibrium prices, other than equilibrium allocation, that helps one consumer without hurting the other
The general equilibrium is Pareto efficient
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25. Figure 16.11: First Welfare Theorem in an Exchange Economy
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26. Efficiency in Exchange
Whenever an allocation is inefficient there are gains from trade
Whenever an allocation is efficient there are no mutually beneficial trades
Exchange efficiency condition holds if every pair of individuals shares the same MRS for every pair of goods
Holds as long as consumers’ indifference curves are smooth and have declining MRS
A test for existence of potential gains from trade between consumers
When consumers’ MRS differ they can both gain by trading
Contract curve shows every efficient allocation of consumption goods in an Edgeworth box
Starts at the southwest corner and ends at the northeast corner
Every allocation on the contract curve corresponds to a point on the utility possibility frontier, and vice versa
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27. Figure 16.13: Contract Curve
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28. General Equilibrium and Efficient Production
If add production, competitive equilibria remain Pareto efficient
Exchange efficiency is not enough; production must also be efficient
Two requirements for production efficiency:
Input efficiency
Output efficiency
Input efficiency: there is no way to increase any firm’s output of one good without decreasing the output of another good
Holding constant the total amount of each input used in the economy
Pareto efficiency requires input efficiency
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29. Input Efficiency Example
Two inputs:
Labor, total of 50 workers
Capital, total of 25 machines
Two firms:
MunchieCo, produces food
CribCo, produces housing
Use an Edgeworth box to illustrate allocations of inputs between firms
Allocations where two isoquants cross are inefficient
At points where the two firms’ isoquants touch but do not cross, the two inputs are allocated efficiently
There is no way to increase the output of one good without decreasing the output of the other
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30. Figure 16.15: Input Efficiency
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31. A Condition for Input Efficiency
Production contract curve shows every efficient allocation of inputs between two firms in an Edgeworth box
At efficient allocations, on firm’s MRTSLK is the same as the other’s
The firms’ isoquants lie tangent to the same straight line
Slope of this line shows the rate at which both firms can substitute labor for capital without changing their output
Input efficiency criterion holds if every pair of firms shares the MRTS between every pair of inputs
As long as the firms’ isoquants are smooth and have declining MRTS
Allocations that satisfy this condition are efficient
A test for existence of potential gains from trade between firms
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32. Production Possibilities
Production possibility frontier shows the combinations of outputs that firms can produce when inputs are allocated efficiently among them
Given their technologies and the total inputs available
Relationship between the PPF and the production contract curve is the same as the relationship between the utility possibility frontier and the contract curve
Each input allocation on the production contract curve is associated with a point on the PPF and vice versa
PPF always slopes downward
Upward slope would imply that, starting on the frontier, it’s possible to increase the production of both goods without changing the total amount of any input
But this would mean that the allocation of inputs on the frontier is inefficient and, by definition, the PPF includes only efficient combinations
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33. Figure 16.16: Production Possibility Frontier
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34. Marginal Rate of Transformation
Downward slope of the PPF reflects tradeoffs involved in production
If we choose to produce more of one good, we must produce less of another
Marginal rate of transformation from good X to good Y is the additional amount of Y that can be produced by sacrificing one unit of X
At any point on the PPF, the marginal rate of transformation is equal to the slope of a straight line drawn tangent to the frontier at the point, times negative one
Marginal rate of transformation is also related to the firms’ marginal products
Frontier gets steeper moving from left to right
Marginal rate of transformation from X to Y rises
Reflects decreasing returns to scale in the production technologies
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35. Output Efficiency
Output efficiency means there is no way to make all consumers better off by shifting production from one good to another
Among allocations satisfying exchange efficiency and input efficiency
Achieve input efficiency by picking a point on the production contract curve
Equivalent to picking a point on the PPF
To achieve output efficiency, need to pick the right point
Allocation satisfies the output efficiency condition if, for every pair of goods, every consumer’s MRS equals the marginal rate of transformation
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36. Figure 16.17: Output Efficiency
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37. First Welfare Theorem, Again
The general equilibrium of a competitive economy with production is Pareto efficient
Check the three efficiency conditions
Exchange efficiency condition holds for the same reasons as in the exchange economy
Input efficiency condition:
If firms use a positive amount of every input in equilibrium
From Chapter 8, MRTSLK=W/R for each firm
All firms faces the same prices so MRTSLK are equal across firms
Input efficiency criterion holds
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38. First Welfare Theorem, Again
Output efficiency criterion:
If every individual consumes a positive amount of each good in equilibrium
From Chapter 5, MRSXY=Px/PY
Competitive firms will produce so that price equals MC
Recall that So
And the output efficiency condition holds
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39. Justification for Free Markets
Advocates of free markets argue that government should not play a significant role in overseeing, directing, or conducting economic activity
Doctrine of laissez-faire holds that the government should adopt a “hands off” approach to private commerce
First welfare theorem provides some support for this position
Says a perfectly competitive economy would produce an efficient outcome
Opponents have two main reservations
Few economists describe the real economy as perfectly competitive
A market failure is a source of inefficiency in an imperfectly competitive economy
Many people express concerns that free markets can produce inequitable outcomes
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40. Equity and Redistribution
First welfare theorem says that a competitive equilibrium is Pareto efficient
May not convince you that competitive markets are desirable
Efficient allocations can be extremely inequitable
Even if the competitive equilibrium is on the contract curve, may be other points on that curve that are more equitable
Second welfare theorem says that every Pareto efficient allocation is a competitive allocation for some initial allocation of resources
If the initial allocation of resources heavily favors certain individuals, the equilibrium will favor them as well
In principle, societies can use competitive markets to achieve both efficiency and equity
If society can redistribute the initial allocation of resources appropriately, then competitive markets will deliver the most equitable Pareto efficient allocation
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41. Figure 16.20: Second Welfare Theorem
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42. Conflict Between Equity and Efficiency
Second welfare theorem suggests societies can use competitive markets and lump-sum transfers to achieve both efficiency and equity
Lump-sum transfer: amount of resources received or surrendered by each consumer is fixed
Doesn’t depend on consumer’s choices
Achieve an equitable outcome by transferring resources among consumers
Assumes we can observe consumers’ endowments so we know who to tax and who to subsidize
Achieve an efficient outcome by allowing competitive markets to operate
As a practical matter, transfers are linked to criteria that reflect choices
Brings equity and efficiency into direct conflict
May have to put up with a less efficient outcome to achieve a more equitable one
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43. Figure 16.21: Equity vs. Efficiency
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