Lindahl pricing

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Chapter 9
Political Economy
Jonathan Gruber
Public Finance and Public Policy
Aaron S. Yelowitz - Copyright 2005 © Worth Publishers
Introduction
 In the real world, it is not always easy for the government to maximize
welfare.
 Politicians have considerations other than getting to the socially efficient
level or conducting cost-benefit analyses in order to approve a project.
Instead, such economic decisions are made in the context of a political
system.
 For example, a 2004 spending bill contained many projects of dubious
value. $200 million was allocated to build one bridge in Alaska that
would connect a small town with an island that housed 50 residents and
the area’s airport (offering 6 flights a day). The crossing is now made by
a ferry and takes 5 minutes.
 Alaska’s representative, Republican Don Young, chairman of the
Transportation and Infrastructure Committee, said “This is the time
to take advantage of the position I’m in …”
Introduction
 This lesson focuses on the fourth question of public
finance: Why do governments do what they do?
 We start by discussing the “best case scenario” in
which government appropriately measures and
aggregates the preferences of its citizens in deciding
what projects to undertake.
Introduction
 Then we examine both direct democracy and
representative democracy.
 Finally, we examine government failure, the inability
(or unwillingness) of government to appropriately
address market failures.
UNANIMOUS CONSENT ON PUBLIC
GOODS LEVELS: Lindahl Pricing
 Ideally, the government could provide public goods
through unanimous consent of its citizens.
 Lindahl pricing is a system where individuals
report their willingness-to-pay for each quantity of
the public good, and the government aggregates
preferences to form a measure of the social benefit.
Lindahl Pricing
 To illustrate Lindahl’s procedure, imagine that the
public good in question is fireworks for two people
(Ava and Jack).
 First, the government announces tax prices for the
public good, that is, the share of the cost that each
individual must bear.
Lindahl Pricing
 When a tax price is arrived at where both individuals
want the same amount of the public good, the
government has reached Lindahl equilibrium.
 The government produces the public good at that
level, and finances it by charging each person their
tax price.
Lindahl Pricing
 Each person announces how much of the public
good he or she wants at those tax prices.
 If the individual announcements differ, the
government raises the tax price for the person who
wants more of the good, and lowers it for the
person who wants less.
 Figure 1 illustrates this scenario.
Willingness
to pay
Adding up their individual
demands curves vertically
Jack’s
surplus
is this areademand.
gives
the
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While
Jack’s
Ava’s
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demand
curve
curve
forfor
$4
fireworks
fireworksisisfairly
fairlysteep.
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DJACK
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The
This
Andsocially
agenerates
With
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efficient
of 25¢
marginal
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Ava
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isof
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Ava’s surplus is this area 75¢
Lindahl
socially
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beneficial
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the good.
S=SMC
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$0.75
DAVA
$0.25
0
Figure 1
25
50
Lindahl pricing
75
100
Fireworks
Lindahl Pricing
 Fireworks production of 75 units is equilibrium for
two reasons.
 First, both Ava and Jack are happy to pay those tax
prices to get that quantity.
 Second, the government has covered the marginal
cost of producing the fireworks by charging each
person their marginal willingness-to-pay.
Lindahl Pricing
 Lindahl pricing corresponds to the concept of
benefit taxation, which occurs when individuals are
being taxed for a public good according to their
valuation of the benefit they receive.
 With Lindahl pricing, the government does not need
to know the utility functions of individual voters: it
gets the voters to reveal their preferences by stating their
willingness to pay for different levels of the public
good.
Problems with Lindahl Pricing
 Lindahl pricing is unlikely to work in practice,
however.



Preference revelation problem: Individuals may
behave strategically, and pretend their willingness to
pay is low in order to get others to bear a larger cost
of the public good.
Preference knowledge problem: It is hard for people
to properly value goods they do not shop for on a
regular basis.
Preference aggregation problem: Aggregating
millions of voters’ preferences is difficult in reality.
MECHANISMS FOR AGGREGATING
INDIVIDUAL PREFERENCES
 This section discusses how voting can serve to
aggregate individual preferences into a social
decision.
 For now, we focus on direct democracy, whereby voters
directly cast ballots in favor of or in opposition to
particular public projects.
Direct democracy in
the United States
 Direct democracy was very prominent in the news in 2003,
when the citizens of California voted to replace their
governor, Gray Davis, with Arnold Schwarzenegger in a recall
election.
 A recall election is a special election initiated by citizens with
the goal of replacing a sitting official.
 Only one sitting governor had been removed before. 18
states allow the recall of state officials, and 36 allow recall of
local officials.

About 5,000 recall elections have been held in the U.S., with
nearly half resulting in the removal of an elected official.
Direct democracy in
the United States
 Two other ways in which voters participate in direct
democracy are through referendum and voter initiative.
 A referendum is a measure placed on the ballot by the

government allowing citizens to vote on state laws or
constitutional amendments that have already been passed by
the state legislature.
A voter initiative is the placement of legislation on the ballot
by citizens.
 For example, on October 5, 2003 (two days before he was
recalled), Gray Davis signed a health insurance mandate on
employers. In a referendum on the November 2004 ballot–
Proposition 72–California voters narrowly overturned this
law by a 51% to 49% margin.
Majority Voting: When It Works
 The Lindahl pricing scheme had a very high
standard for coming to a consensus: only when
citizens were unanimously in agreement did the
government achieve Lindahl equilibrium.
 A common mechanism used to aggregate individual
votes into a social decision is majority voting, in
which individual policy options are put to a vote,
and the option that receives the majority of votes is
chosen.
Majority Voting: When It Works
 Majority voting does not always provide a consistent means
of aggregating preferences.
 To be consistent, an aggregation mechanism must satisfy
three goals:



Dominance: If one choice is preferred by all voters, then the
aggregation mechanism much be such that this choice is made
by society.
Transitivity: Choices must satisfy this mathematical property.
Independence of Irrelevant Alternatives: The introduction of a third
choice does not change the ranking of the first two choices.
Majority Voting: When It Works
 It turns out that with these three conditions,
majority voting can only produce a consistent
aggregation of individual preferences if preferences
are restricted to take a certain form.
 This is best illustrated with some examples.
 Table 1 shows a case when majority voting works.
A town is deciding on education taxes (and
Consider
pair-wise
High
Since
Medium
High
vs
Mvs
Medium:
vs
has
Low:
Low:
beaten
Parents
Parents
Parents
both
spending). There are 3 possibilities:
high,
voting:
High
vs
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Table 1
Hand
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&
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theare
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The preferences of While
parents
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not haveof
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then
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to M
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wins
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2-1.
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elderly
are exactlypay
opposite.
for high spending, then
medium
high taxes
high.
right now.
Types
of voters
spending, then low spending.
Preference
Parents
Elders
Young
rankings
Couples
First
H
L
M
Second
M
M
L
Third
L
H
H
Majority Voting: When It Doesn’t Work
 Table 2 shows a different scenario, where majority
voting does not work.
Table 2
Majority voting
AThus,
towntheir
is again
deciding
on
education
taxes
Private
Assuming
parents,
that
ordering
first
doesn’t
and
is low,
happen,
foremost,
then
high,
however,
want
then
low
High
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Medium
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vs
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Hmmm
Low:
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Low:
Only
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winner.
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pair-wise
voting:
(andsospending).
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elderly
have
been
taxes
private
they
parents
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to sent
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Young
private
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Marrieds
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assumption
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for
vote
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L
so
High
vs
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High
replaced with “private
parents.”
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other
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and
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isleads
M
so
preferred
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wins
H wins
to
2-1.
2-1.
cycling.
to
2-1.
M. vs
Medium,
and
Medium
groupsaare
the same
as
before.
doesn’t deliver
consistent
outcome
M is preferred
Low. to L.
Types of voters
Preference
rankings
Parents
Private
Parents
Young
Couples
First
H
L
M
Second
M
H
L
Third
L
M
H
Majority Voting: When It Doesn’t Work
 This set of outcomes is problematic because there is no clear
winner. These results violate the principle of transitivity
resulting in cycling–when majority voting does not deliver a
consistent aggregation of individual preferences.
 Note that the failure to get a consistent winner from majority
voting does not reflect a failure on the part of individuals–
each group has a sensible set of preferences.
 The problem is aggregation–we are unable to use voting to
aggregate these individual preferences into a consistent social
outcome.
Majority Voting: When It Doesn’t Work
 This creates the problem of the agenda setter, the
person who decides the sequencing of the votes.
 In the second situation, he can affect the outcome.


For low spending to win, for example, first set up a
vote between H and M. H wins. Then a vote
between L and H means L will win.
Any outcome can win with appropriate ordering.
Arrow’s Impossibility Theorem
 In fact, there is no voting system that will produce a
consistent outcome here.
 Arrow’s Impossibility Theorem states that there
is no social decision (voting) rule that converts
individual preferences into a consistent aggregate
function without either restricting preferences or
imposing a dictatorship.
Restricting Preferences to Solve the Impossibility
Theorem
 One way to solve this problem is to restrict preferences
to “single-peaked” preferences.


A “peak” in preferences is a point that is preferred to
all its immediate neighbors. Utility falls in any
direction away from this point.
Multi-peaked preferences means that utility may first
rise, then fall, then rise again.
 If preferences are single peaked, majority voting will
yield a consistent outcome.
 We can visualize our earlier examples. See Figure 2.
(a)
(b)
Utility
Utility
Elders
Young
marrieds
Private
parents
Parents
Young
marrieds
Public
parents
M
H
Private
Their utility
parents
goesare
in
indifferent
either direction
in the
second
from case.
M.
And young marrieds
The elderly
are single peaked
are single
at “M”.
peaked at “L”.
L
Figure 2
Parents are
single peaked
at “H”.
H
M
Voting rules
School
spending
L
School
spending
Restricting Preferences to Solve the Impossibility
Theorem
 The failure of these preferences for the “private
parents” in this second case is what leads to the
inability of majority voting to consistently aggregate
preferences.
 Fortunately, single-peakedness is a reasonable
assumption in most cases.
Median Voter Theory
 When preferences are single-peaked, then majority
voting will deliver a consistent aggregation of
preferences of the individual voters.
 Even stronger, the median voter theorem states
that majority voting will yield the outcome preferred
by the median voter if preferences are single peaked.

The median voter is the voter whose tastes are in the
middle of the set of voters, so an equal number of
other voters prefer more and prefer less of the
public good.
Potential Inefficiency of the Median Voter
Outcome
 Thus, the voting would suggest that the government
only needs to find the preferences of the median
voter, and implement that level of public goods.
 This does not account for intensity of preferences,
however, so it does not follow that the social
marginal benefits equal the social marginal cost.

For example, if small numbers of individuals derive
enormous benefits from the public good, this should
be accounted for in the total social marginal benefits.
Potential Inefficiency of the Median Voter
Outcome
 For example, imagine that there are 1,001 voters in a
town, who are considering building a monument
that costs $40,040 ($40/person).

Assume all 1,001 voters have single-peaked
preferences, so the median voter will determine the
outcome.
 If 500 citizens value the monument at $100 each,
and the other 501 value it at $0, then the social
marginal benefit is $50,000, far greater than the cost.
However, the monument doesn’t get built.
REPRESENTATIVE DEMOCRACY:
Vote-Maximizing Politicians
 In reality, voters elect representatives, who are
supposed to aggregate their preferences and take
them into account when they vote on the
appropriate level of public goods.
 If politicians care about maximizing the number of
votes they get, they choose the outcome preferred
by the median voter.
Vote-Maximizing Politicians
 The public good in question is defense; the key
question is what fraction of the budget (0% to 50%)
should be spent on defense? Voters are uniformly
distributed on this continuum.
 Two politicians, John and George, are running for
office and vying to maximize their votes.
 Figure 3 illustrates this.
In
this case, the
John
is
trying
to
appeal
to
Figure 3
candidates split the voteWhile George chooses a
those who don’t want
much higher level of
equally.
much defense, so he
defense, G1.
places
himself
at
J
.
1
Voters for John
Voters for George
By
But
doing
nowso
imagine
he gets
that
the
(a)
Defense
majority
John changes
of the votes.
his
spending
position
to
J
.
2 25%
J
G
50%
0%
1
1
Voters for George
ByIndoing
response,
so, George
George
now
Defense
lowers
gets ahis
majority
position
ofto
the
G 2.
spending
G1
50%
votes.
Voters for John
(b)
0%
J2
Voters for John
(c)
0%
J2
Voters for John
(d)
25%
Voters for George
This process will continue
until the median voter’s
G2are arrived at.
25%
preferences
Defense
spending
50%
Voters for George
Defense
spending
0%
J3 = G3 = 25%
50%
Assumptions of the Median Voter
Model
 The median voter model is a powerful tool, but relies on a number of
assumptions worth mentioning:
 Single-dimensional voting: Voters only care about one issue.
 Only two candidates: With a 3rd candidate, there is no stable
equilibrium.
 No ideology or influence: Assumes politicians only care about votes,
not ideological positions.
 No selective voting: All citizens actually vote.
 No money as a tool of influence.
 Perfect information along three dimensions: voter knowledge of the
issues, politician knowledge of the issues, and politician knowledge
of voter preferences.
Lobbying
 The issues of money and information make it likely
that elected officials will be lobbied by highly
interested and informed subgroups.
 Lobbying is the expending of resources by certain
individuals or groups in an attempt to influence a
politician.
Lobbying
 Lobbyists can:


Inform politicians
Reward politicians
 The problem with lobbying arises when an issue
benefits a small group and imposes small costs on a
larger (perhaps even a majority) group.

In this case, politicians might support socially
inefficient positions.
Lobbying
 The key point to remember is that large groups of
people with small individual interest on an issue
suffer from a free rider problem in trying to organize
politically.
 Small groups with large interest overcome the freerider problem.
Farm policy in the United States
 Even though only 2.5% of workers are employed on
farms, this sector receives $25 billion in direct
support from the federal government.
 This comes in direct subsidy payments to farmers, and
price supports (guaranteed minimum prices for crops).
 These subsidies costs each American household
about $360 per year on average, and the average
recipient of a subsidy receives $18,000 per year.
Farm policy in the United States
 The 2002 farm bill was estimated to cost $190
billion over the following decade. Although it
motivated by preserving “family farms,” this
motivation is completely at odds with the facts.



Only 8 of 400 crops are eligible for the subidy.
Subsidy increases with productions, so large farms
benefit more than small farms.
Two-thirds of all subsidies accrue to 10% of
recipients, most of who earn over $250,000 per year.
Farm policy in the United States
 How do such expensive, and poorly targeted
subsidies end up surviving?
 The total cost per American family is modest ($360),
and dwarfed by the enormous gain to the typical
farm ($18,000).
 The small group of farms are able to effectively
organize and lobby, while the much larger group of
taxpayers hurt by the programs are not able to do
so.
Evidence on the Median Voter Model
 While the median voter model is a potentially
powerful tool, does it have predictive power?

The empirical evidence is mixed. It certainly does
not completely explain legislator behavior. There is
strong evidence that legislators consider their own
ideology, and that of their core constituency, when
they vote on policies.
Testing the
median voter model
 Stratmann (2000) found that redistricting, which
changes the nature of the district’s median voter for
largely exogenous reasons, affected the voting
preferences of legislators.
 He asked: When districts become more conservative
through redistricting (as measured by the vote for
the Republican presidential candidate in 1988 and
1992), but were represented by the same politician,
did the politician start to vote more conservatively.

The answer: Yes.
Testing the
median voter model
 There is also evidence that “core constituencies” matter as
well.
 Levitt (1996) compared two senators from the same state but
different political parties. Median voter theory suggests they
should take the same position on legislation, yet he found
that the senators vote very differently.


The senators vote very similarly to senators from other states
who are in their party.
He found that legislators care roughly equally about the
median voter, voters in their own core constituencies, and the
“party line.” Yet most of the voting pattern is explained by
individual ideological differences.
Cycling in Representative Democracies
 An issue that arises in direct democracy, cycling, can
also arise in representative democracy if legislator
preferences are not single peaked.
 There is some evidence that such cycling has
occurred in Congress from time-to-time.
The Political Business Cycle
 Another issue that arises in representative
democracy is the “political business cycle.”
Pocketbook issues matter.

Bill Clinton’s mantra – “It’s the economy, stupid!”
 Ray Fair has developed models relating the fraction
of the vote for the incumbent to the economy’s
growth rate and inflation rate.
 Figure 4 shows the results.
Figure 4
The Political Business Cycle
 On average, predicted share of the vote for the
incumbent party is within 2.6 percentage points of
the actual vote received.
 It has done a pretty good job at predicting winners
in presidential elections.
The Political Business Cycle
 That fact that voters respond to economic
conditions close to the Presidential election has led
some to posit the existence of a political business
cycle, where politicians attempt to manipulate
economic conditions.
 Although the actual business cycle may or may not
exist, it is clear that incumbents do use government
powers of taxation and spending to try to win voter
favor.
PUBLIC CHOICE THEORY: THE
FOUNDATIONS OF GOVERNMENT
FAILURE
 The analysis in most of this course assumes a
benign government intent on maximizing social
welfare.
 Public choice theory questions this assumption by
noting that governments often do not behave in an
ideal manner, so that traditional assumption of a
benevolent social-welfare maximizing government
may be inappropriate.
PUBLIC CHOICE THEORY: THE
FOUNDATIONS OF GOVERNMENT
FAILURE
 Government failure is the inability or unwillingness
of the government to act primarily in the interest of
its citizens. Reasons include:



Size maximizing bureaucracy
Leviathan theory
Corruption
Size-Maximizing Bureaucracy
 Niskanen (1971) developed a model of the budget
maximizing bureaucrat. In this model, the bureaucrat
runs an agency that has a monopoly on the
government provision of some good or service.
 Bureaucrat’s salary typically unrelated to efficiency.
His compensation consists of salary, but also perks
like the size of his office and support staff.
 The larger government tries to rein in the
bureaucrat.
Size-Maximizing Bureaucracy
 A key question is then whether goods and services are more
efficiently provided by the public or private sector.


For most goods and services, it is abundantly clear that private
provision is more efficient.
In a review of the literature, Mueller (2003) finds that only 5
of 71 studies found state-owned companies outperformed
their private counterparts.
 For some goods, such as social services, public provision may
be superior, especially when there is a market failure.

Hart, Shliefer, and Vishny (1997) compared public and private
prisons. Private prisons were 10% cheaper, through lower
wages to guards. The low pay led to more violence, however.
Leviathan Theory
 Leviathan theory sees individual bureaucrats and the
larger government as one monopolist that simply
tries to maximize the size of the public sector.
 This view would help explain rules that explicitly tie
the government’s hands in terms of taxes and
spending.
Corruption
 Finally, corruption is where government officials
abuse their power in order to maximize their own
personal wealth or that of their associates.
Government
Corruption
 Former Illinois governor George Ryan was indicted in
December 2003 for selling state contracts to his friends in
exchange for cash, gifts, loans, and trips for his family. The
case is still pending.
 This was uncovered as part of “Operation Safe Road,” which
investigated bribes that many truck drivers had given to
officials at then Secretary of State Ryan’s office to obtain a
driver’s license.

At least 20 people had died in accidents involving drivers who
had bribed officials for their licenses.
 The investigation resulted in 70 indictments and over 60
convictions of many people who were close friends and
allies of the former governor.
The Implications of Government
Failure
 There is clear evidence that governments fail in
some instances to benevolently serve the interests
of their citizens.
 Can citizens “undo” these harms through actions
like direct democracy?
 Some evidence suggests that government failures
can have long-lasting negative impacts on economic
growth.
Government failures
and economic growth
 Acemoglu, Johnson, and Robinson (2001) examined two sets
of nations that were similar when they were colonized by
European powers, yet colonization took very different forms.


Treatment group: Nations in the Caribbean, Central America,
and Africa.
 The colonizers were focused solely on extracting natural
resources, and not interested in setting up institutions to
foster economic success.
Control group: Nations in North and South America,
Australia, and New Zealand.
 The colonizers moved to these nations in large numbers and
set up institutions to foster economic success.
Government failures
and economic growth
 Why the lack of “hands-on” governing in the
treatment group?

The odds of colonists dying from locally infectious
disease was much higher. This exogenously affected
settlement patterns of colonizers.
 Despite their precolonization similarity, the
treatment nations have grown much more slowly
post colonization than have the control nations.
 The treatment nations continue to suffer from the
long-run detrimental effects of inefficient
government.
Recap of Political Economy
 Unanimous consent on public goods levels
 Mechanisms for aggregating individual preferences
 Representative democracy
 Public choice theory: The foundations of
government failure
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