Download Ch 16

Chapter 16
General Equilibrium, Efficiency,
and Equity
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
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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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
 Markets can be linked because the price or production of one
good affects the demand or cost of another….think substitutes
or complements.
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Figure 16.1: General Equilibrium
Above is the general equilibrium in the markets for Pie
and Ice cream. Both equilibriums take the other product
(and product price) into account in identifying its own
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product clearing price and quantity.
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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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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Figure 16.2: A Market-Clearing Curve
Slide A shows the ice cream curve with 3 different
demand curves that correspond to different prices for
pie. Slide B is the general equil. market-clearing curve for
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both products.
Figure 16.2: A Market-Clearing Curve
Slide A shows the pie curve with 3 different demand
curves that correspond to different prices for ice cream.
Slide B is the general equil. market-clearing curve for
both products.
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General Equilibrium in
Two Markets
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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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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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 the
new supply curve and initial demand curve
Price of pie held constant at $12 per pie
(Consumer) Price of ice cream rises by $1.67
per gallon, less than the amount of the tax
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Effect of a Sales Tax:
Gen. 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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Effect of a Sales Tax:
Gen. Equilibrium
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Sales Tax Effect : 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
Based on partial anal., ice cream prices rise only by
$1.67, but based on general equil, prices rise by $2.
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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Figure 16.6: Effects of a Tax, part 2
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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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Figure 16.7: Pareto Efficient
Outcomes
Points on the
boundary are Pareto
efficient
Point A is inefficient
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Equity
 Equity is harder to define and measure than efficiency
 Process-oriented notions of equity focus on the
procedures used to arrive at an allocation of resources
 Focus on what could be chosen instead of what is chosen.
 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
(equal weight on w-b of every person)
 Rawlsianism – focus should be on the w-b of the worst-off member
of society
 Others focus on the distribution of consumption, e.g.,
egalitarianism (equal division of resources to every member of
society)
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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 outcomeoriented notions of equity
Social Welfare  W U1 ,U 2 ,,U N 
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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
 The social welfare
function reflects a
preference for efficiency
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General Equilibrium in
Exchange Economies
 In an exchange economy, people own and trade goods but no
production takes place. This is a starting model to explain the
concept.
 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 for the two people match if food costs $2 per
pound and water sells for $1 per gallon
 This is a general equilibrium
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Figure 16.9: General Equilibrium
in an Exchange Economy
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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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Equilibrium in an Edgeworth Box
 Point A represents initial
endowment
 Point C is the general
equilibrium resource
allocation
 Food costs $2 per pound
 Water costs $1 per gallon
 Notice how they coincide.
 Also, the curves are
opposite due to the
inverse nature of the graph.
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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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Figure 16.11: First Welfare Theorem
in an Exchange Economy
They like points on the budget line equally. But the points of D and E
are not as well liked as choosing either of them would hurt the other
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party.
Efficiency in Exchange
16-27
Efficiency in Exchange
 Whenever an allocation is inefficient, there are gains
from trade
 Whenever an allocation is efficient there are no mutually
beneficial trades
 The 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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Figure 16.13: Contract Curve
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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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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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Figure 16.15: Input Efficiency
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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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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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Figure 16.16: Production
Possibility Frontier
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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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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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Figure 16.17: Output Efficiency
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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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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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Figure 16.20: Second Welfare
Theorem
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