Transcript Chapter 25

Public Goods, the Consequences
of Strategic Voting Behavior, and
the Role of Government




Chapter 21 shows that trade between individuals results in
a Pareto efficient allocation of goods
In General, competitive markets are efficient
o Goods cannot be reallocated to make one person better off without
making another worse off
o The right amount of goods will be produced
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However, under certain situations competitive markets do
not achieve efficiency
o Externalities
o Information asymmetry
o Public goods
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The nature of public goods implies that competitive markets
do not provide the socially optimal amounts
o The market fails
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Private goods
o Excludable
• Consumption is restricted to people who are willing to pay
o Rival
• Consumption - by one person decreases availability to others
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Public goods
o Nonexcludability
o Nonrival consumption
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Free-rider problem
o Members of society have an incentive to take advantage of public
good without paying
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(a)
Price
(b)
Price
Demand for public good
A
Demand for private good
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D (consumer 2)
D (consumer 1)
MC
5
x2* Quantity of
Private good
The marginal benefit received by
each person from consumption of the
private good equals the marginal cost
of providing the private good
0
x1*
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12
MC
Societal demand
(vertical sum of D1 +D2)
D1
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1
D2
q*
Quantity of
Public good
The sum of the marginal benefits received by
all people from consumption of the public
good equals the marginal cost of providing
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the public good.
0
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Pareto-optimal allocation, private goods
o Same MRS (goods)
o Same MRTS (inputs)
o MRS=MRT
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Public goods
o Once produced
o All consume – same amount
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Pareto-optimal allocation, public goods
o Private goods - allocate until
• MRS=price ratio
o
Same MRTS (inputs)
o MRS private for public goods=MRT private for public goods
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Assumption
o People – truthful
• Preferences for public goods
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Private goods market
o No intervention
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Public goods market
o Government – market aid
• Cost shares (prices)
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Maximize utility - Equilibrium
o No change in demand
• Private goods prices
• Public goods cost shares
o Private goods: Supply = Demand
• Same price, different quantity
o Public goods – same amount demanded
• Nonexcludable
• Different price, same quantity
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Private
Good
 The
(b)
(a)
Lindahl
Solution
Private
Consumption
path
A’
Person 2
δ
Cost
Share to
A’
Person 1
γ
B’
x’
A
B1
0
x*
Public Good
B2
Private good
h’
D
h
A
α
B
1-h
Cost
Share to
β Person 2
0
g’ g* g”
Person 1
Public good
At the Lindahl equilibrium, point D, both agents demand the level of the public
good provided (g units), given their assigned cost shares (h for person 1 and
1-h for person 2)
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Lindahl equilibrium
o Competitive equilibrium
o Market: private & public goods
o Pareto-optimal allocation for society
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Weakness
o Incentive – people lie
• Free rider
o Truth-telling – not Nash equilibrium
o Amount provided < Pareto-optimal amount
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0
 The Lindahl
A
Cost
Share to
Person 1
h
equilibrium is not a Nash equilibrium
Person 2
B’
C
h0*
hb B
ha
hc
O*
a b
A’
c
0
g0* ga C’ gh
Person 1
Public good
I2
Cost
Share to
Person 2
By claiming a false
demand curve, CC’,
instead of her true
demand curve, AA’,
person 1 can reach
a point 0* that is
better for her than
the Lindahl
equilibrium point
(the intersection of
AA’ and BB’).
I3
I1
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Free riding
o Real problem – to be addressed
• Optimal sharing - costs of public goods
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Allocating costs
o People – incentive
• Truth - public goods preferences
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Demand-revealing mechanism
o Creates incentive
o People – reveal public goods preferences
• Truthful manner
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Optimal plan
o Maximize difference
• Willing to pay
• Cost
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Weakness: subsidies
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A demand-revealing mechanism based on a true willingness
to pay for streetlights
Plan
Member
A
B
C
Tax
1
2
3
4
Total willingness to pay
$60
30
20
40
150
$50
70
80
20
220
$40
50
25
90
205
0
5
40
0
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N people
Vi(X) – value of X units public good
o Vi(0)=0
1.
Each person – bid (bi, Xi)
o Cost share (q-Bi)X; Bi=Σj≠ibj; X=Σ Xk/N
2.
3.
Each person – reject or agree cost share
If all agree: X, cost share (q-Bi)X
o If no agreement, X=0, payoff Vi(0)
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Subject valuations of three public goods projects in Smith’s
experiments
Subject
Project
1
2
3
4
5
6
Total
1
2
3
$5
60
-20
-$30
5
45
-$30
5
45
$25
-10
0
$25
-10
0
$0
55
-25
$-5
105
45
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Telling the truth
o Not dominant strategy
o Nash equilibrium strategy
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Auction election mechanism
o Group level – satisfactory
o Individual level – less well
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Smith’s auction election experiments
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Smith’s auction election experiments (cont’d)
The auction election
experiments usually
result in the rational
group choice, but
they do not always
induce truth-telling.
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Function of government
o Create institutions – mediate conflicts
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Government mediation
o People – private bargaining
o Prerequisites for private bargaining
o Reduce transaction costs
o Zero-sum game
o Aggregate: individuals’ preferences
o Socially desirable outcome
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Average percentage of endowment contributed to public
good due to the negative frame contributions
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Percentage free riding: the positive frame has fewer people
free riding
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Government
o Aggregate - preferences of individuals
o Decision – affect welfare
o Rational social choices
• Reflect true preferences
• Complete
• Transitive
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Voting institution
o Majority voting rule
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Voting paradox
o If all people in society
• Transitive preferences
o Preference of society as a whole
• Not transitive
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Problem for society
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A preference matrix for a three-person society
Person
Rank of Preference
1
2
3
First
Second
Third
x
y
z
z
x
y
y
z
x
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1.
Group Rationality
o Social preferences
• Complete and transitive ordering
• Set of alternatives
2.
Unrestricted Domain
o Every ordering - individual preferences
• Complete and transitive (rational)
• Allowed
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3.
Pareto Optimality
o If x preferred to y
• Then, x - referred to y in social ranking
4.
Independence
o Social ranking of x and y
• Individuals’ preferences between x and y
5.
Nondictatorship
o Not allowed: One powerful individual
• Voting mechanism - own preferences
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Arrow’s impossibility theorem
o Voting mechanism
• Determines transitive social preferences
• Satisfies five conditions
• Desirable voting mechanism
o Doesn’t exist
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Transitive social preferences – attained
o Abandon desire for democracy
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Simple majority voting rule
o Transitive social preferences
o Restrictions on preferences (condition 2)
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Single-peaked preferences
o Voting: one-dimensional issues
o Preferences - single peaked
• Uniquely best alternative preferred
• Preferences decline
• Increasing distance: best alternative
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Utility
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Single-peaked preferences
Person
2
Person
1
Person
3
Person
4
$B
0
Spending
For each person, alternatives become steadily worse as they get further and
further away, in either direction, from the preferred alternative
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Agenda manipulation
o Individual – controls committee’s agenda
• Manipulates: order - pairs of alternatives
• Influence the outcome
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Levine-Plott experiment
o Majority voting rule
• Intransitive
• Used – by leader
• To skew voting
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A preference matrix for a three-person committee
Person
Rank of Preference
1
2
3
First
Second
Third
x
y
z
z
x
y
y
z
x
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Agenda: Levine-Plott agenda manipulation experiment
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Strategic voting
o Doesn’t reflect true preferences
o Affect vote’s outcome
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Strategy: tell truth
o Not Nash equilibrium strategy
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Decision tree: player who engages in strategic voting
By lying in the first
round of voting,
person 1 can ensure
that y, his second
choice, is elected
over z, his third
choice, in the second
round of voting.
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Borda count method
o Choose: k alternatives
o Allocation of votes
• First alternative: k votes
• Second alternative: k-1 votes
o Alternative chosen - number total votes
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Strategy: lie - Nash equilibrium
Borda count method
o Can be manipulated
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Person
A preference matrix for a five-person
committee
Rank of Preference
1
2
3
4
5
First
Second
Third
Fourth
Fifth
x
c
d
y
e
y
c
e
d
x
y
c
x
e
d
c
d
x
e
y
x
y
e
d
c
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Gibbard-Satterthwaite theorem
o Single outcome
• Chosen from > two alternatives
o Only voting rule - cannot be manipulated
• Dictatorial voting rule
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Gibbard-Satterthwaite theorem
o Problem – government
o Any mechanism
• Manipulated
• Undesirable outcomes
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Solution
o Mechanisms with Nash equilibria
• Satisfactory outcomes
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The design of institutions
Because the government
does not have full
knowledge of the
environment, it cannot
construct the performance
correspondence indicating
which outcomes are
desirable for that
environment. Instead, the
government attempts to
specify a voting mechanism
such that the citizens will
choose the same outcomes
that the government would
if it had full knowledge of
the environment.
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Environment
o Complete description
• Economy
• Voting body
• Preferences - each member
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Performance correspondence
o Relationship: environment & set of desired outcomes
• Which outcomes – satisfy performance criteria
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Rent-seeking behavior
o Behavior of interest groups
• Attempt - extract rents
• From government
• From other authorities
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Regulated monopoly
o Profit – economic rent
o Lobby – against deregulation
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Price
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Rent-seeking behavior
b
pm
Rm
pc
c
e
Demand
A firm would be willing to
pay an amount equal to
the potential monopoly
profit, Rm = area pmbcpc ,
for a government franchise
permitting it to operate as
a monopolist
Marginal
Revenue
0
qm
Quantity
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
Competitive rent-seeking
o Seek monopoly franchise
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Rent-seeking
o Wasteful
o Increased cost to society
• Deadweight loss
• Lobbying costs
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