voting for public goods (fisher, ch. 3) © allen c. goodman 2009
Post on 22-Dec-2015
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Bread and Schools
• Suppose that we live in a suburb.
• Suppose there are 10 residents. Each one earns $60,000.
• They can spend it on bread, or schools.
60
60
Bread
Sch
ools
PrefersBread
PrefersSchools
Bread and Schools
• They have to pick a tax level that each one of them will pay.
• If they decide on $4,000, each will pay $4,000.
60
60
Bread
Sch
ools
PrefersBread
PrefersSchools
Bread and Schools
• Let’s add a few more “identical” people.
60
60
Bread
Sch
ools
• We have five possible levels of “schools”
s1
s2
s3
s4
s5
s1 > s2 > s3 > s4 > s5
Bread and Schools
• Alternatively, individuals 1-5 are willing to give up different amounts of bread to get school resources.
60
60
Bread
Sch
ools
• We have five different levels of taxes.
s1
s2
s3
s4
s5
t1 > t2 > t3 > t4 > t5
How do we decide?
• Consider a politician. She has to win an election, and she has to get enough votes by promising the right amount of school resources
60
60
Bread
Sch
ools
• Suppose she promises s5. Person 5 is happy (he didn’t want much). But everyone else wanted more. So politician loses election 4-1.
s1
s2
s3
s4
s5
1
2
3
4
5
RolePlaying
2 Candidates
How do we decide?
60
60
Bread
Sch
ools
• Suppose she promises s4. Persons 1, 2, and 3 are happier because they’re getting closer to what they want. But she’ll still lose 3-2.
s1
s2
s3
s4
s5
1
2
3
4
5• Suppose she now promises
s3. She’ll win the election because Persons 1 and 2 are happier yet, and Person 3 is happiest, he’s getting exactly what he wants.
If you don’t believe me ...
60
60
Bread
Sch
ools
• Suppose another politician promises s2. Person 3 won’t be happy anymore because you’re providing MORE school resources than he wants … so he’ll vote against it.
• KEY POINT !!! The median voter is decisive. Eq’m school will be at s3. Each voter will pay 60 - b3 in taxes and get s3.
s1
s2
s3
s4
s5
1
2
3
4
5
b3
Median Voter and Optimum
• We’ve seen that we will agree on some particular amount, by majority vote.
• Is this amount economically optimal, based on the rule that we developed in the previous lecture?
• Why or why not!
Single Peaked Preferences
• Suppose you had 3 people with indicated preferences.
• Suppose they’re not single-peaked, i.e.
• If they are single peaked, there is a clearly defined “winner” and the individual gets less satisfaction if he/she moves away from it.
First Second ThirdPerson Choice Choice Choice
A 4000 6000 8000
B 6000 8000 4000
C 8000 4000 6000
Level 1 4000Level 2 6000Level 3 8000
Less U Even less U
Even less ULess U
What about this?
$ spent
Another Way to Look at It
UA
4 6 8
UB
4 6 8
UC
4 6 8
Singlepeak
Singlepeak
? ?
Spending Spending Spending
So?• $4,000 beats $6,000• $6,000 beats $8,000, BUT• $8,000 beats $4,000!
Choices aren’t transitive
Choices aren’t transitive
Why does this happen?
• Person C does not have single-peaked preferences, but is rather an extremist! … alternatively he/she HATES mediocrity.
• C becomes less and less happy until spending gets very low.
• C is unhappy with moderate positions.
How much should we worry?• If we believe in
standard demand theory, we shouldn’t worry too much about the single-peaked problem
• Why?
Price in $
Quantity
Q*
• At Q*, we have optimal amount of Q.
• As we go further away in either direction, happiness ↓.
Demand theory is broadly consistent with Single-Peaked preferences
Demand theory is broadly consistent with Single-Peaked preferences
Median Voter Theorem
• If voters’ preferences are single-peaked,
• if the choice to be made by voting is represented along a single continuum,
• if all alternatives are voted on, and
• if voters act on their true preferences,
• THEN the choice selected by majority vote is the median of the desired outcomes.
What does median voter model say?
• If you have some number of jurisdictions, one can argue that the levels of schools, fire protection, police protection are broadly consistent with consumer preferences.
• Is it perfect?– No, not all citizens vote.– If there are a lot of issues, the same citizen is
not likely to be the median voter on every issue.
Median and Optimum
• Median may be close to optimum as determined by theoretical criteria.
• BUT, it may be either greater than or less than the optimum.
• By the very nature of the equilibrium, some substantial number might want more … and some other substantial number might want less.
C1
Other Models
• Some (generally conservative) economists propose a model in which government officials wish to:– Maximize the amount of
government spending.
– Remain in office.
• How does this work?
Expenditure
Ev
Price ($)
Ev is preferred bymedian voter
If referendum is rejected, Expenditures revert to Er.
Er
Loss of ConsumerSurplus of C1.
C1
C1
Other Models
• Instead, government officials, in trying to maximize expenditures, pick as much as EM. Why?
• How does this work?
Expenditure
Ev
Price ($)
Ev is preferred bymedian voter
If referendum is rejected, Expenditures revert to Er.
Er
Loss of ConsumerSurplus of C1.
C1 C1
EM
Comments
• Median voter model seems to explain multiple suburbs.
• Does the monopoly model explain central cities?– How does one explain the Detroit Schools?
– How does one explain the Detroit City Council?
• These are NOT unique to Detroit.
• Many large cities have these problems.
• Are they unique to large cities?
Comments
• Median voter model seems to address consumer preferences, BUT a large group of people are dissatisfied.
• Monopoly models may appeal to some voters, BUT they don’t explain how a government that continually does not satisfy median voter stays in power.
• Michigan’s Headlee Amendment makes it very difficult to raise taxes. Suggests that at least a lot of Michigan voters are concerned about governmental powers.
NEXT!Chapter 4
NEXT!Chapter 4
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