Transcript Welfare Economics

Welfare
Economics
Chapter 20
Slides by Pamela L. Hall
Western Washington University
©2005, Southwestern
Introduction


To include society’s value of commodities under alternative
resource allocations directly involves welfare economics
 Study of all feasible allocations of resources for a society
 Establishment of criteria for selecting among these allocations
Public Choice Theory
 Attempts to understand and explain society’s actual choice for
resource allocation
• Choice is based on normative economics


Involves value judgments
 Since various agents have conflicting value judgments, it is difficult to
establish a socially optimal allocation
Even if these differing value judgments prevent a socially optimal allocation
 Theory of welfare economics provides a method for delineating
important conceptual issues facing all societies
2
Introduction

Aim in this chapter is to investigate how economic theory
attempts to reconcile individual decentralized resource
allocation with overall social values of a society
 May be accomplished with a social-welfare function
• Requires a cardinal measure of individual consumer preferences

We maximize welfare function subject to a utility possibilities
frontier based on individual consumers’ preferences
 Then we specify and compare alternative egalitarian social-welfare
functions

We discuss Arrow’s Impossibility Theorem
 Indicates that a social-welfare function is impossible given
consumers’ ordinal ranking of utility and based on some reasonable
assumptions concerning society’s social rankings
3
Introduction

Because we cannot determine a social ranking based on individual
consumers’ ordinal preferences
 We evaluate idea of majority voting as a second-best Pareto-optimal
allocation

We discuss causes of market failure
 Such as monopoly power, externalities, public goods, and asymmetric
information

• As potential constraints on improving social welfare
We demonstrate Theory of the Second Best by showing how any policy
designed for improving social welfare that only corrects some
constraints may not result in social welfare improvement
 Because economists are unable to specify a social-welfare function, an army
of applied economists is required to develop and direct mechanism designs
for filling in economic gaps resulting from missing markets
• Objective of each mechanism is to yield an incremental improvement in social
•
welfare
Tâtonnement process will move a society toward maximum social welfare
4
Social-Welfare Function

Using broad definition of social welfare as a level of happiness for
society as a whole
 Measurement for this happiness is needed to determine socially optimal
allocation of resources
• Such a measurement for determining how well off agents are in a society requires
a set of welfare criteria

Much of research on formulation of welfare criteria and their implications
for economic policy has relied on Pareto-allocation criterion
 A Pareto criterion is a value judgment based on unanimity rule
 If one agent could be made better off without reducing welfare of others
• Social welfare could be improved by allocation that makes this one agent better
off

Since no one agent is made worse off and at least one agent is made better off
 It is assumed, given independence of utility functions, that all agents would
support Pareto criterion
5
Social-Welfare Function

Pareto-optimal allocation yields an efficient allocation of resources and
thus is a necessary condition for a social optimum
 However, many decisions on allocation result in an improvement of one
agent’s utility at expense of other agents
• For example, a redistribution of endowments from taxing rich households and
providing subsidized housing for poor households may increase social welfare

But cannot be justified by Pareto criterion
 Fundamental inadequacy of Pareto criterion is its inability to yield a complete
ranking of all social states within an economy
• Pareto criterion is useless in context of many policy propositions, so additional
welfare criteria are necessary to determine if these policies will improve social
welfare

To investigate a social-welfare function, a comparison of individual
consumers’ utilities is generally required
 Assumed that utility functions can be measured on a cardinal scale
• Under this assumption, taking a monotonic transformation of utility function will
change preference relationships
6
Pure-exchange Economy



Consider pure-exchange economy developed in Chapter 6
Two-consumer (Friday and Robinson), two-commodity (q1
and q2) economy is illustrated in Figure 20.1
Only points on contract curve can be considered as possible
candidates for a social optimum
 For example, points P1, P2, and P3 represent tangencies of Friday’s
and Robinson’s indifference curves
• Any point off this contract curve is not Pareto efficient


Possible to increase welfare of one consumer without reducing welfare of
the other
From contract curve in Figure 20.1,we can derive a utility
possibilities frontier
 Theoretically similar in construction to production possibilities frontier
7
Figure 20.1 Contract curve for a twoconsumer, two-commodity pure-exchange
economy
8
Pure-exchange Economy

Utility possibilities frontier
 Mapping of Pareto-efficient utilities for Robinson, R, and Friday, F,
corresponding to each point on contract curve
 For P1, P2, and P3, in Figure 20.1, corresponding utility levels for
Robinson and Friday are plotted on horizontal and vertical axes,
respectively, in Figure 20.2
 Points on utility possibilities frontier correspond to tangency of
indifference curves along contract curve in Figure 20.1
• Utility combinations associated with P1, P2, and P3 are same for both
figures


Every point inside this utility possibilities frontier is a feasible allocation
 Corresponding to points inside Edgeworth box of Figure 20.1
Boundary of utility possibilities frontier represents efficiency locus (contract
curve) in Figure 20.1
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Pure-exchange Economy

For a given amount of q1 and q2, utility possibilities frontier
indicates combination of UR and UF that can be obtained
 An increase in amount of q1 and q2 will result in utility possibilities
frontier shifting outward

With increasing opportunity cost (which yields a concave
utility possibilities frontier)
 Sacrifice in Friday’s utility increases for an additional unit increase in
Robinson’s utility
• However, although a monotonic transformation of an agent’s utility
function preserves preference ordering


It can result in opportunity cost switching from increasing to decreasing
One basis for assumption of measuring utility on a cardinal
scale
10
Figure 20.2 Utility possibilities
frontier
11
Production and Exchange Economy


We can also derive a utility possibilities frontier in a general-equilibrium context
by considering production
Efficiency condition is based on a given level of utility for Friday
 Illustrated in Figure 20.3


Changing this level of utility for Friday will result in alternative combinations of q1
and q2 produced and allocated between Robinson and Friday
As illustrated in Figure 20.4, maximizing Robinson’s utility given UFas Friday’s
level of satisfaction results in Pareto-efficient allocation of (qR1, qR2, qF1, qF2) with
q*1 and q*2 efficiently produced
 With an alternative level of satisfaction for Friday, say UF' maximizing Robin’s utility
will result in an alternative Pareto-efficient allocation, (qR'1, qR'2, qF'1, qF'2) with q*1 and
q*2 produced

In general, considering all possible Pareto-efficient allocations (MRSR = MRSF =
MRPT)
 We obtain a collection of Pareto-efficient utility levels for both Robinson and Friday
• By varying Friday’s utility from zero to level where Robinson’s utility would be zero
• Plotting these Pareto-efficient utility combinations yields utility possibilities frontier in Figure
20.2
12
Figure 20.3 Efficiency in production and
exchange for a two-consumer economy
13
Figure 20.4 Efficiency in production and
exchange for alternative utility levels
14
Production and Exchange Economy

For an economy with production, every utility bundle on this frontier
represents a Pareto-efficient allocation
 Where MRSR = MRSF and MRSR = MRSF = MRPT

A utility bundle in interior of frontier, say point A, is not Pareto optimal
 It is possible to increase either Robinson’s or Friday’s utility without
decreasing other’s utility

In contrast, on the frontier, say at point P1, Friday’s utility cannot be
increased without reducing Robinson’s utility
 At P1 utility combination and any other utility bundle on frontier are Pareto
optimal

Initial endowment of resources held by Robinson and Friday will
determine agent’s location on frontier
 If Robinson has a proportionally larger share of initial resources, utility

bundle P1 may result
A reversal of endowments may yield a higher utility level for Friday, such as
bundle P3
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Maximizing Social Welfare

Even after eliminating all Pareto-inefficient allocations, there remains an
infinite number of efficient allocations
 Represented by infinite number of points on utility possibilities frontier

First Fundamental Theorem of Welfare Economics
 A perfectly competitive equilibrium will result in a Pareto-efficient allocation
 Depending on initial distribution of endowments, a perfectly competitive

equilibrium can occur at any point on utility possibilities frontier
However, from a society’s point of view, allocation resulting from a perfectly
competitive equilibrium may not be equitable
• Society may redistribute income (initial endowments) among consumers in an
effort to achieve equity

May take form of redistributing income
 Taxing wealthy and giving tax revenue to poor
 Providing commodities to poor (for example, Medicare or surplus food from
agricultural support programs)
 Market regulation (for example, rent control or agricultural price supports)
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Maximizing Social Welfare

Efforts by governments to achieve a more equitable
allocation are costly in terms of possibly generating
inefficiencies within an economy
 For example, government playing Robin Hood dampens incentive to
work and invest
• Often directs resources toward tax avoidance

Can use concept of a social-welfare function as method for
determining socially optimal allocation among points on a
utility possibilities frontier
 With a social-welfare function, can determine point that maximizes
social welfare in terms of both equity and efficiency criteria
 Assuming government is not paternalistic, this function would
generally depend on welfare (utility) of agents within an economy
• Government would then maximize social welfare subject to utility
possibilities frontier
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Maximizing Social Welfare

For example, consider following social-welfare function, U, for an economy
consisting of two consumers (Robinson, R, and Friday, F)

Assuming a diminishing marginal rate of substitution between consumer utilities,
we can determine convex social indifference, or isowelfare, curves
 Assumption implies that society has inequality aversion
• Where (holding social welfare constant) the more satisfaction Robinson has the less society
is willing to give up Friday’s utility for one more unit of Robinson’s utility
 As illustrated in Figure 20.5, tangency between a social indifference curve and utility
possibilities frontier results in maximum level of social welfare
• Point P2 is only point on utility possibilities frontier where there is no other point preferred to it


For example, point P3 is Pareto efficient but there are points that are preferred to P3
Even though point A is Pareto inefficient, society prefers it over Pareto-efficient point P3
 Using maximum level of social welfare, point P2, we determine optimal allocation of
commodities in Edgeworth box (Figure 20.1) for a pure-exchange economy
• Or in production possibilities frontier (Figure 20.3) for a production and exchange economy
18
Figure 20.5 Maximizing social
welfare
19
Shapes of Isowelfare Curves

A social-welfare function represents society’s preferences
for particular Pareto-efficient points on a utility possibilities
frontier
 Various social preferences may be represented by social indifference
curves taking on various shapes
• These shapes (and thus social preferences) are generally based on
some equitable allocation among Pareto-efficient allocations


Comparison of alternative Pareto-efficient points requires
value judgments concerning trade-off among consumer
utilities
 Can be no one definition for equity
Social indifference curves will take on a number of forms
 Depending on which criterion (value judgment) is employed for
determining equitable allocation
• Two criteria—egalitarian and utilitarian
20
Egalitarian

Egalitarianism can take two forms
 Allocate each consumer an equal amount of each commodity


In terms of our Robinson and Friday two-commodity economy, this
egalitarian criterion sets qR1 = qF1 and qR2 = qF2
In a pure-exchange economy, Robinson and Friday would split total
endowment of each commodity in half
 Unless Robinson and Friday have identical utility functions, level of utility
achieved by them will not be the same

• But their utility levels are not a factor in this egalitarian equity
In terms of a social-welfare function, social preferences for Robinson’s
or Friday’s utilities are identical
 Are perfect substitutes as long as commodities are allocated equally
between them
• Maximizing welfare function with additional constraint that it be Pareto-efficient in
terms of a utility possibilities frontier will result in maximizing social welfare
21
Egalitarian

Second type of egalitarian criterion is an allocation of commodities
 Resulting in equality of utilities across all consumers


For Robinson and Friday, this criterion sets UR = UF
A social-welfare function resulting in equality of utilities is Rawlsian
criterion
 Most equitable allocation maximizes utility of least-well-off consumer in


society
For Robinson and Friday, Rawlsian criterion is
Maximum level of social welfare given a specific utility possibilities
frontier is on Pareto-efficient utility possibilities frontier (Figure 20.6)
 Unless Robinson and Friday have the same utility functions
• Equality of utilities will not result in Robinson and Friday each receiving the same
commodity allocation
22
Figure 20.6 Rawlsian socialwelfare function
23
Utilitarian



Maximizes sum of consumers’ utility
Criterion was formally developed by Bentham and provided initial impetus to
utility theory
For Robinson and Friday, criterion is
 Called classical utilitarian, or Benthamite welfare function
 Maximized subject to a utility possibilities frontier (Figure 20.7)

Under utilitarian criterion, increases or decreases in individual consumers’ utility
results in identical changes in social welfare
 Only total utility is relevant, so utilitarian criterion does not consider distribution of
utility
• As long as social gain is greater than social loss, it makes no difference that consumer who
gains in utility may already be happier than the other consumer

Unless utility functions of individual consumers are close to being identical
 Utilitarian criteria can result in substantial differences in consumers’ utility

Although ethics teaches that virtue is its own reward, classical utilitarian function
teaches that reward is its own virtue
 Only total level of utility is important
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Figure 20.7 Benthamite (classical
utilitarian) social welfare function
25
Utilitarian

By incorporating some virtue into classical utilitarian function, we get a
generalization of this function
 Weighted sum of utilities
• Weights (R, F) indicate how important each consumer’s utility is to overall social
welfare


For example, utility of an individual such as Mother Teresa will be weighted higher than that
of a child sex offender
In Figure 20.7, utilitarian social welfare optimal allocation is tangency
between social indifference curve and utility possibilities curve
 Depending on weights associated with individual consumers’ utility
• Any Pareto-efficient point on utility possibilities frontier could be a social-welfare
maximum

The more egalitarian a society is, the more its social indifference curves will
approach right angles
 Indicating society is concerned with equity issues of distribution
• For a utilitarian society that is indifferent to distribution, curves are more linear

Showing society simply maximizes output
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Arrow’s Impossibility Theorem

A problem in maximizing social welfare is how to establish this socialwelfare function
 A welfare function based on individual consumer preferences would be a
desirable
• Assuming social welfare is to reflect some aggregate consumer preferences
 However, because preference ranking by consumers is generally only
ordinal
• There is not sufficient information to determine a reasonable social preference
ranking of choices

Numerous examples where, due to ordinal preference ranking among
individuals, an aggregate ranking is impossible
 One example is Battle of the Sexes game discussed in Chapter 14
• Couple cannot jointly (socially) rank their preferences for opera or fights
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Arrow’s Impossibility Theorem

Arrow’s Impossibility Theorem
 Impossible to establish a reasonable social preference ranking
based solely on individual ordinal preference rankings

Suppose there are several feasible social states
 It is assumed each individual in society can ordinally rank these
states as to their desirability
 To derive a social-welfare function, there must exist a ranking of
these states on a society-wide scale that fairly considers these
individual preferences
• Let’s consider just three possible social states (A, B, and C)

For example, these states could be sending a human to Mars, building and
equipping a new aircraft carrier, or curing cancer
 Arrow’s Impossibility Theorem says a reasonable social ranking of
these three states cannot exist based only on how individual agents
ordinally rank these states
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Arrow’s Impossibility Theorem

A reasonable social ranking may be stated with the following axioms relating
individual consumers’ preferences
 Axiom 1: Completeness—Social ranking must rank all social states
• Either A > B, B > A, or A  B for any two states

Identical to Completeness Axiom for individual preference ordering
 Axiom 2: Transitivity—Society’s social ranking must be transitive
• Given three social states, A, B, and C, if A > B and B > C, then A > C

Identical to Transitivity Axiom for individual preference ordering
 Axiom 3: Pareto—If every consumer prefers A to B, then A is preferable in a social
ranking
• This also holds for the other two pairs (A, C) and (B, C)

Identical to a Pareto improvement
 Axiom 4: Nondictatorial—One consumer’s preferences should not determine
society’s preferences
• No agent paternalism
 Axiom 5: Pairwise Independence—Society’s social ranking between A and B should
depend only on individual preferences between A and B
• Not on individual preferences for some other social state, say state C

Identical to Independence Axiom for individual preference ordering of states of nature
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Arrow’s Impossibility Theorem

Can now state Arrow’s Impossibility Theorem more formally
 A social preference ranking satisfying these five axioms is
impossible, given an ordinal ranking of individual agent preferences
• Implies that there is no way to aggregate agents’ ordinal preferences into
a social preference ranking without relaxing at least one of these axioms

Axioms may seem a reasonable set of conditions for
democratically choosing among social states
 However, Arrow demonstrated that it is impossible to socially choose
among all possible sets of alternatives without violating at least one
of the axioms

Thus, social choice must be unreasonable if it is based on
agents’ ordinal preference ranking
30
Majority Voting

To see that Arrow’s Impossibility Theorem holds, let’s consider majority
voting
 Important social preference mechanism design

• Set of rules governing procedures for social [collective] choice
Majority voting satisfies both Pareto Axiom and Nondictatorial Axiom
 Sensitive to each individual agent’s preferences

Majority voting is symmetric among agents
 Treats all agents the same and all agents have just one vote

It is also neutral among alternatives
 By not making a distinction among alternatives a priori

However, majority rule can lead to a pattern of social choices that is not
transitive
 Even though every voter has ordinal and transitive preferences
• Thus, it violates Axiom 2
31
Majority Voting

Consider ballot in Table 20.1 among three
voters, Robinson, Friday, and Simpson
 Voters’ preferences are as follows
• Robinson and Simpson prefer alternative A to B
• Robinson and Friday prefer alternative B to C
• Friday and Simpson prefer alternative C to A
Majority (two) prefers A to B and B to C, but majority also
prefers C to A
 Thus majority voting results in a cyclical pattern that is
intransitive
 Called Condorcet Paradox
 Presents a major problem for group decision making

32
Table 20.1 Condorcet Paradox
33
Majority Voting

Next let’s consider case in which each voter must
vote for just one alternative
 As illustrated in panel (a) of Table 20.2, ordinal

preference ranking in Table 20.1 results in a three-way tie
• All three alternatives receive equal votes
However, if one alternative is removed, a clear winner
results
• As illustrated in panel (b), when alternative C is removed,
alternative A receives majority vote


Here, Axiom 5 is violated
We see this violation of Axiom 5 often in U.S. presidential elections
 Where a third-party candidate has determined the outcome
34
Table 20.2 Pairwise Independence
35
Majority Voting

Development of a social-welfare function requires more than just an
ordinal ranking of individual consumer preferences
 Requires a comparison of utilities across consumers on a cardinal scale
• For example, one reason a third party can influence results of an election is that
no weight is given to intensity of voters’ desires


However, intensity of desires is a utility measure that can only be measured on at least
a cardinal scale
 Magnitude or intensity of an individual voter’s desires is not known when she
votes
However, allowing voters an ordinal preference ranking (Table 20.1)
instead of just one vote (Table 20.2) does elicit additional information on
voter’s preference
 May result in a social ranking more consistent with a majority of electorate
• New voting machines, being put into place after 2000 presidential election, have
capability to allow voters to ordinally rank candidates

Called instantaneous voting, procedure has not yet been widely adopted
 But offers potential of further revealing voters’ preferences and mitigating any
strategic voting
36
Strategic Voting

A problem with allowing ordinal ranking of candidates (or any other choices) is
possibility of strategic voting
 Where an agent does not reveal her true preferences but instead votes to enhance
outcome in her favor

A game-theory strategy
 Particularly effective when number of voters is relatively small or when a strategicvoting coalition can be formed

One form of strategic voting is for an agent, say Friday, to rank her first choice
highest
 Then rank other alternatives inversely to expected outcome
• Thus, Friday would rank alternative expected to be in close competition with her first choice
last, suppressing competitive threat

Strategic voting is illustrated in Table 20.3 for determining social ranking of four
alternatives
 In panel (a), alternative A, which was not Friday’s top choice, comes out on top
• However, as illustrated in panel (b), Friday can change outcome by ranking alternative A low
(strategic voting)

Now Friday’s top choice, alternative B, comes out on top as the social choice
 Judges in Olympic games have been accused of practicing this type of strategic voting
37
Table 20.3 Strategic Voting
38
Strategic Voting

A method for removing this potential of strategic voting is
sequential voting
 Lowest-ranking alternative after each vote is dropped and another
vote is then taken on remaining alternatives

In panel (b) of Table 20.3, alternative C only received a
rating of 5
 Dropping this alternative from list yields individual preference ranking
for the three alternatives listed in panel (a) of Table 20.4
• Now alternative D receives lowest ranking
• Dropping alternative D and re-voting on alternatives A and B yields
outcome in panel (b)

From panel (b), alternative A is still selected even given strategic voting by
Friday
39
Table 20.4 Sequential Voting
40
Strategic Voting



Sequential voting is used to elect Speaker of the House in
U.S. House of Representatives
Employing sequential voting also allows for a social ranking
of alternatives based on Pairwise Independence Axiom
Implementing such a process for U.S. presidential elections
would probably have changed a number of outcomes
 By adopting instantaneous voting, where voters rank their choices
• Low-ranking alternatives could be automatically dropped until only two
alternatives are left

Given these two remaining alternatives, a president with majority of support
would then be elected
41
Strategic Voting

Illustrates that a confederation of individuals forming a
society should not be expected to behave with same
coherence as would be expected from an individual
 Arrow’s Theorem implies that institutional detail and procedures of a
political process (mechanism design) cannot be neglected
• Thus, it is not surprising that academic disciplines that complement
economics, such as political science and psychology


Have evolved to address process of group choice
 Attempt to determine intensities of individual and group desires
 Formulate policies and rules for group choice and actions
As demonstrated by Condorcet Paradox and quid pro quo
example in Chapter 14
 An agenda that determines which alternatives are first considered
will affect social choice
42
Market Failure

Suppose some process for group decision does exist for
determining optimal social choice
 A naive solution, based on Second Fundamental Theorem of Welfare
Economics
• Would advocate allowing markets freedom to obtain this social optimal
given a reallocation of endowments
 Unfortunately, this solution is based on properties of a perfectly
competitive equilibrium
• Extreme theoretical case of resource allocation


Does not generally hold for any society
When properties of a perfectly-competitive equilibrium do
not hold
 Resulting equilibrium is not efficient, so market failure exists
43
Market Failure

In general, conditions causing market failure are classified into four categories
 Monopoly power
• Exists when one or a number of agents (suppliers or demanders of a commodity) exert some
market power in determining prices
 Externalities
• An interaction among agents that are not adequately reflected in market prices—effects on
agents are external to market

Air pollution is classic example of an externality
 Public goods
• One individual’s consumption of a commodity does not decrease ability of another individual
to consume it

Examples are national defense, income distribution, and street lights
 Asymmetric information
• When perfectly competitive assumption of all agents having complete information about
commodities offered in market does not hold

Incomplete information can exist when cost of verifying information about a commodity may not be
universal across all buyers and sellers
 For example, sellers of used automobiles may have information about quality of various
automobiles that may be difficult (costly) for potential buyers to acquire
• When there is asymmetry in information buyers may purchase a product in excess of a given
quality
44
Market Failure

Existence of monopoly power, externalities, public goods,
and asymmetric information are justification for
establishment of governments to provide mechanisms to
address resulting market failures
 Governments can regulate firms with objectives of mitigating
monopoly power and negative externalities
 Governments can provide for public goods either by direct production
or private incentives
 Governments can generate information, aid in its dissemination, and
mandate that information be provided in an effort to reduce
asymmetric information
• The more a government must intervene in marketplace to correct these
failures

The less dependent will the economy be on freely operating markets
45
Market Failure

In some societies these market failures appear
quite large and, thus, freely operating markets are
severely limited
 True in many centrally-planned economies
• Where government determines what and how to produce as well
as who should receive commodities produced
 Even within U.S., which generally relies on free markets
to allocate resources and outputs, there is always the
question concerning level of government intervention
• For example, many environmental regulations directly limit inputs
firms can use in their production decisions

For example, local zoning ordinances may restrict a firm’s use of
inputs that generate noise, smoke, or odors
46