pub econ lecture 09 political economy
TRANSCRIPT
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8/3/2019 Pub Econ Lecture 09 Political Economy
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Public Finance
Dr. Katie Sauer
Political Economy
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Best-Case Scenario: In deciding which public goods
projects to undertake, the government appropriately
measures and aggregates the preferences of the
citizens.
Lindahl Pricing
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Suppose there is a public good, fireworks, with constant
marginal cost of $1.
- the quantity provided will be equally consumedby all
Ava and Jack are the two citizens.
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1. government announces a set of tax prices for the good
- share of cost that each individual must pay
- equal or unequal amounts
2. individuals announce how much of the good they want
at each tax price
3. government constructs a marginal willingness to pay
schedule for each individual
- tax price and quantity of good
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4. add up individual WTP at each quantity to construct
the demand curve
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5. compare demand to marginal cost to determine level of
provision
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6. finance the provision by charging each individual their
willingness to pay for that quantity of the good
Charge Ava:
$0.25
Charge Jack:
$0.75
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A Problem with Majority Voting
For ballots that use majority voting rules, the ballot often
has to be narrowed to 2 choices.
- clear winner
Often times, there are more choices than just 2 to start
with.
- need to narrow the choices
Sometimes the choices are arbitrarily determined,
sometimes an initial election is held and then the top vote
getters are subject to a run off.
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Example:
Suppose a city is deciding where to locate a new parkand there are 3 possible options: south, central, east.
Also suppose there are 3 types of voters (type 1, 2, and
3) who have different preference about the location ofthe park.
They each prefer to have the park located nearby to
where they live.
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Suppose the ballot pits south versus central. Which would win?
type 1:
35% vote for south
type 2:
45% vote for central
type 3:
20% vote for south
south wins
Type 1 Type 2 Type 3
percent of the voters 35% 45% 20%
south central east
central east south
east south central
Voter Type
Preference ranking
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Suppose the ballot pits location central versus east. Which would
win?
type 1:
35% vote for central
type 2:
45% vote for central
type 3:
20% vote for east
central wins
Type 1 Type 2 Type 3
percent of the voters 35% 45% 20%
south central east
central east south
east south central
Voter Type
Preference ranking
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Suppose the ballot pits location south versus east. Which would
win?
type 1:
35% vote for south
type 2:45% vote for east
type 3:
20% vote for east
east wins
Type 1 Type 2 Type 3
percent of the voters 35% 45% 20%
south central east
central east south
east south central
Voter Type
Preference ranking
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When the choice is south versus central, south wins.
When the choice is central versus east, central wins.
The transitive property would tell us that when the voteis south versus east, south should win.
But in reality, when the choice is south versus east, east
wins!
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Potential Solutions
Plurality Voting: The choice with the most votes wins.
- may or may not have a majority of the votes
From our example:
central would win with 45% of vote
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Borda Rule: Let voters rank each possible outcome.
- Assign points to each rank.- The outcome with the most total points wins.
Ex. Imagine that Tennessee is having an election on the
location of its capital. The population of Tennessee is
concentrated around its four major cities, which are
spread throughout the state. Suppose that everyone
wants to live as near the capital as possible.
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42% of voters
(close to
Memphis)
26% of voters
(close to
Nashville)
15% of voters
(close to
Chattanooga)
17% of voters
(close to
Knoxville)
MemphisNashville
Chattanooga
Knoxville
NashvilleChattanooga
Knoxville
Memphis
ChattanoogaKnoxville
Nashville
Memphis
KnoxvilleChattanooga
Nashville
Memphis
For each type of voter, assign 4 points to the highestranked choice, 3 points to the next highest choice, and
so on.
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42% of voters
(close to
Memphis)
26% of voters
(close to
Nashville)
15% of voters
(close to
Chattanooga)
17% of voters
(close to
Knoxville)
4Memphis3Nashville
2Chattanooga
1Knoxville
4Nashville3Chattanooga
2Knoxville
1Memphis
4Chattanooga3Knoxville
2Nashville
1Memphis
4Knoxville3Chattanooga
2Nashville
1Memphis
Memphis:
42x4 + 26x1 + 15x1 + 17x1 = 226
Nashville:
42x3 + 26x4 + 15x2 + 17x2 = 294
Chattanooga:42x2 + 26x3 + 15x4 + 17x3 = 273
Knoxville:
4
2x1 + 26
x2 + 15
x3 + 17x4
= 207
Nashville wins
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Arrows Impossibility Theorem
There is no voting rule that converts individual
preferences into a consistent aggregate decision without
eithera) restricting preferences
b) imposing a dictatorship
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Consistent Preferences Exhibit:
1. Dominance
- if one choice is preferred by all, then the
aggregation mechanism must be such that
this choice is the one made by society
2. Transitivity
- if A is preferred to B and B is preferred
to C, then A must be preferred to C
3. Independence of Irrelevant Alternatives
- if A is preferred to B, then the introduction
of choice C will not change the ranking
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Restricting Preferences to be single-peaked:
- utility falls as choices move away in any
direction from the peak
- majority voting will yield consistent outcomes
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Single-Peaked preferences over school funding and
property taxes:
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Multi-Peaked preferences over school funding and
property taxes:
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Median Voter Theory
If we assume single-peaked preferences, we can make
an even stronger assertion about majority voting:
majority voting will yield the outcomepreferred by the median voter
Convenient! Government only needs to know
preferences of the median voter.
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Often, not socially efficient because the intensity of
preferences is not included.
Suppose your hometown is considering a statue of you
to honor all of your great contributions to society.
1,001 voters (single-peaked preferences)
$40,040 is cost of statue- financed with $40 tax per person
500 voters know of your contributions and are
willing to pay $100 each
501 voters know nothing of your contributions
and are willing to pay $0 each
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501 WTP $0 500 WTP $100
median
voter
The statue will not get built.
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Is this outcome efficient?
Social marginal benefit:
500 x $100 = $50,000
Social marginal cost:1,040 x $40 = $40,040
SMB > SMC so the outcome is inefficient
- The intensity of WTP was not accounted for
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Median Voter Theory in a Representative Democracy
Assume: single-peaked preferences
Ex:Barack and John are running for office and are
trying to maximize their votes.
- defense spending
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Other Assumptions:
- single-dimensional voting (single issue)
- only two candidates
- no ideology or influence- care only about maximizing votes
- no selective voting (all people vote)
- no money
- full information