Transcript 슬라이드 1 - Konkuk

Public Choice
Chapter 6
Market Failures and Government
Intervention

How do governments and state
bureaucrats actually behave?

Efficiency of providing the public goods

Government failures leading to an
inefficient level of government
expenditure
Efficient Provision of Public Goods

A trade-off between private and public goods is just like a
tradeoff between two private goods

The indifference curves for the public goods are also
downward-sloping (more of one good must be obtained to
compensate for a reduction in the availability of the other good
for the consumer to remain indifferent)

Indifference curves are also strictly convex to the origin (as
more private goods are consumed, the household is willing to
give up fewer and fewer units of the public good to obtain
successive additional units of the private good)

The further away from the origin the indifference curve is
located, the higher overall utility it represents
Existence Value

An individual may derive satisfaction from the
provision of a public good even if he or she
himself or herself does not consume the
good

Examples include charity, contributions for
preserving wild nature

Some people attribute value just to the fact
that something exists: the existence value
Compensating Variation

Suppose the household is only consuming the private good: in
the space of the private and public goods the price of the public
good is zero so that the budget line is a horizontal line

Suppose the government provides a certain amount of public
good

What is the most the household is willing to pay for the
opportunity to consume that amount of public good?

The reduction in quantity of the previously consumed private
good that leaves the household on the same indifference curve
is called compensating variation
Compensating
Variation
Private good
C
A
Initial budget line
CV
B
Public good
Marginal Willingness to Pay
Private good
Marginal willingness to pay
for the public good
CV
Public good
Adding MWTP Curves for Public Goods

Re-cap: one individual’s consumption
of a public good does not reduce the
other person’s ability to consume the
public good

Therefore, we add MWTP-s for a public
good vertically rather than horizontally,
to obtain the aggregate MWTP
$
Aggregate MWTP
MWTP2
Aggregate MWTP
MWTP1
Public good
How Large Should the Provision
of the Public Good Be?

Re-cap: one individual’s consumption of a public good does not
reduce the other person’s ability to consume the public good

Therefore, we add MWTP-s for a public good vertically rather than

Suppose the marginal cost curve (MC) of producing an extra unit of a
public good is increasing upwards

The optimal supply is obtained when the sum of the marginal
willingness to pay over all households is equal to the marginal cost of
provision

Since both households can consume the unit simultaneously, we just
add up the households’ marginal willingness to pay for the public good
in order to obtain total (aggregate) MWTP
horizontally
Adding MWTP for Public Goods
$
Hshld 2
Aggregate MWTP
Hshld 1
MWTP
household 1
Public
good
Adding up MWTP for Public Goods
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For a supply less than the equilibrium amount, the
sum of the marginal willingness to pay over all
households is greater than the marginal cost of
producing an extra unit of a public good

For levels above the equilibrium amount households
are not willing to give up a sufficient amount of
consumption of other goods (or their income) to
cover the cost of producing the final unit of the
public good, so that reduction in supply adds to
social welfare
Provision of Public Goods and
Pareto Efficiency

A pure public good is efficiently supplied when the
sum of each individual’s marginal willingness to pay
is equal to the marginal cost of supplying the good

Pareto efficiency in private markets requires that an
individual’s MWTP is equal to the marginal cost
(p=MC)

The difference arises because public goods can be
consumed simultaneously by many individuals
Public Goods Provision and
Pareto Efficiency
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Private goods:
MRS1=MRS2=p1/p2=MRT

Public goods: MRS1+MRS2=MRT
How can Pareto Efficient Provision of
Public Goods can be Attained?

Assume the voter is paying a tax price to cover the provision of
public goods (the individual’s share of a dollar of government
expenditure)

With uniform taxation of H individuals the uniform tax price is
$1/H

The tax paid by the individual is p*z, where z is the amount of
the public good

In this case the budget constraint for a particular individual is
given by y=qx+pz, where qx is price times quantity of the private
good, y is income and pz is price times quantity of the public
good
Deriving the Demand Curve for
Public Goods

By varying the tax price for the public good provision we can
derive the demand curve for a public good

If the public good is normal as opposed to inferior an increase
in the voter’s income shifts the demand curve to the northeast

Therefore, individuals with different incomes will vote for
different levels of public goods (lower income people will vote
for a smaller amount of public goods)

If taxation is proportional, the tax price is an increasing function
of income so that in this case we cannot be sure whether higher
incomes will lead to an increase of decrease of the demand for
a public good
Deriving the Demand Curve for a
Public Good
A
B
Budget Line with a
Smaller Tax Price
Budget Line with a
Higher Tax Price
Income and Demand for
a Public Good
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
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An increase in income shifts demand
curve for a public good rightwards
Various income groups will vote for
different levels of public good
Higher income does not necessarily
mean higher demand for a public good!
It does under uniform taxation
 It does not necessarily under progressive
taxation

Lindahl Equilibrium

Assume there are only two individuals in the economy

Let those individuals pay for the public goods
according to their respective demand curves

Obtain equality between the sum of their tax prices
and the marginal cost of producing the public good

In the Lindahl equilibrium P1+P2=MC, and the two
individuals are consuming the same amount of the
public good
Lindahl Equilibrium and Pareto
Efficiency

Lindahl equilibrium is Pareto efficient in the sense that price (i.e.
the sum of individual tax prices) is equal to the marginal cost

However, because individuals realize their tax prices depend on
their willingness to pay for the public goods provision may try to
cheat by under- or over-stating their true willingness to pay for
the public good

This problem may be seen as a special case of the free rider
problem illustrated by means of the prisoners’ dilemma

In general, it is necessary to reveal individual preferences in
order to arrive at Lindahl equilibrium, but it is not clear how to
do that
Revealing Preferences for Optimal
Taxation

In general, it is necessary to reveal individual preferences in
order to arrive at Lindahl equilibrium, but it is not clear how to
do that

In the case of private goods, individuals reveal their preferences
in market place

In the case of public goods there is no similar market
mechanism so we need to reveal preferences

Possibilities



Ask people about their willingness to pay for public goods
Hypothetical payment experiments (contingent valuation
methodology)
Use some voting mechanism
The Majority Voting Rule

Majority voting rule: the alternative (among two
alternatives) that receives the majority of votes wins

Does the majority voting rule produce a Paretoefficient allocation?

Each level of the public good provision results in
different levels of utility so we can plot utility
schedules against the various levels of public good
provision
Classes of Individuals according
to their Most Preferred Level of
Public Good Provision
Utility
The Rich
Middle Class
The Poor
Public Good
The Median Voter

The median voter is the one for whom the number of individuals
preferring more expenditure is exactly equal to the number of
individuals preferring less expenditure

In the example before, the median voter’s most preferred level of public
good provision gets adopted according to the majority voting rule

Under uniform taxation, majority voting results in the Pareto efficient
level of public good provision since the median voter prefers an
expenditure level such that his MWTP is equal to the marginal costs

If taxation is proportional and the median voter’s income is smaller than
the average income in the society, his tax price will be small and he will
vote for a greater amount of public good compared to the one where
price is equal to marginal costs
Proportional Taxation

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
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Suppose taxation is proportional to income
Let median voter’s income fall short of the
average income
Median voter’s tax price is relatively low
Median voter will vote for too much of a
public good
Expenditure on public goods will be
excessive
Majority Voting and Pareto Efficiency

Majority-voting can, but need not be
Pareto efficient

Sometimes majority-voting equilibrium
will not exist
Majority Voting



Majority-voting equilibrium can be, but
is not necessarily, Pareto-efficient
Paradox of voting: the order is
important
Multiple-peaked preferences
Why do Voters Vote?

With millions of voters in the society, each
individual’s impact on the voting outcome is
negligible

Why do people continue to vote?


Interdependent utilities (e.g. some people may
care about the poor or clean environment)
In democratic societies, children are taught that
voting is a duty
Bureaucrats and Voters

Bureaucrats seek to maximize the size of their agencies so they choose
the level of public good provision that is too high compared to the
efficient one

Bureaucrats might choose the level of public good provision for which
the society is willing to pay a positive price

This maximum level of public good provision will be given by the
intersection of the aggregate demand curve for the public good and
the horizontal axis

Such excessive provision of a public good will be incurring social
welfare loss
Excessive Provision
of Public Goods
Public good amount that
maximizes the size of the
bureaucracy
Socially efficient
level of public
good provision
Avoiding Being Detected

Lack of competition among
bureaucratic agencies

Must be difficult to ascertain costs and
benefits of public good provision

Another possibility: voted budgets
Voted Budgets

Forcing the voters to choose between too little and too much of the
public good, the bureaucrats have a good chance of getting the
permission to produce too much of the public good (e.g. police force
in a criminal city)

The economic policy may reflect interests of those in power


Size of agricultural sector is way too large in most industrialized powers
In short, government intervention into public goods provision does not
necessarily move the economy closer to the Pareto efficient allocation
Reversion Level


Public good provision maximizing utility
of the median voter is disadvantageous
to the bureaucrat
Design a voting scheme that has two
options:
A little public good at the reversion level
(utility U1 for the median voter)
 A lot of public good (utility U2 a little more
than U1)

Reversion Level Voting
The voting scheme (scam?) will result
in the size of the budget that
maximizes the bureaucrats’ utility
A utility a little bit
higher than the
one obtained at
the reversion level
Median voter
prefererence
Reversion
Level
Same utility with
reversion level
Political Business Cycle



Nordhaus (1975)
Politicians increase probability of
reelection
Voters dislike inflation and
unemployment
Let’s manipulate business cycles to make
sure the minima of both are at the time of
election!
 Reinforcing the size of troughs may be
then an objective

Market Failures

Sometimes governments can correct for
them
Externalities
 Monopolies


Often government intervention produces
Pareto inefficiency
Voting paradoxes
 Public good provision
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