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

 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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 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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 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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 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 marketclearing 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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 If a price combination lies on both marketclearing 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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 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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 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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 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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 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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 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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 Points on the boundary are Pareto efficient
 Point A is inefficient
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 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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 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 outcomeoriented notions of equity
Social Welfare

W

U
1
, U
2
,  , U
N

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 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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 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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 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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 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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 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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 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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 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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 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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 Production contract curve shows every efficient allocation of inputs between two firms in an Edgeworth box
 At efficient allocations, on firm’s MRTS as the other’s
LK is the same
 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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 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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 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
MRT
XY

MP
MP
K
Y
K
X

MP
L
Y
MP
L
X
 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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 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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 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, MRTS
LK
=W/R for each firm
 All firms faces the same prices so MRTS
LK firms are equal across
 Input efficiency criterion holds
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 Output efficiency criterion:
 If every individual consumes a positive amount of each good in equilibrium
 From Chapter 5, MRS
XY
=P x
/P
Y
 Competitive firms will produce so that price equals MC
 Recall that
MC
X
 W
MP
L
X and MC
Y
 W
MP
L
Y
 So
MRS
XY

MP
L
Y
MP
L
X

MRT
XY
 And the output efficiency condition holds
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 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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 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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 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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