Pub Econ Lecture 09 Political Economy

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:


type 2:


type 3:

20% vote for east

central wins



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



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

Pub Econ Lecture 09 Political Economy

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