public finance, chapter 4

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Chapter 4

Public Goods and

Political Economy

Prepared and Taught by

Lecturer: YIN SOKHENG, Master in Finance

2 Instructed by YIN SOKHENG, Master in Finance

The Concept of A Public Good

• Public good: A good that is made to be

financed by taxation and paid for by

government.

• Private good: A good that has excludability

and rivalry

• Pure public goods share two characteristics

– Nonrival – Cost of another person

consuming the good is zero

– Nonexcludable – Very expensive to

prevent others from consuming the good


Examples of Public and Private Goods

• Public Goods

– National defense

– House cleaning in an

apartment with many

roommates

– Fireworks display

– Music file sharing

– Uncongested freeway

• Private goods

– Pizza

– Health care

– Congested freeway

– Public housing

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Valuation of Public Goods

• Everyone consumes same quantity of public

good

• Marginal benefit of public good varies by

person

– In the housecleaning example, different

roommates value the clean apartment

differently.

Instructed by YIN SOKHENG, Master in Finance

...A B cQ Q Q Q

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Private Goods can Be Provided by the Public Sector

• These are called “publicly provided private

goods.”

• Public housing is rival (one family consumes

one apartment) and excludable (easy to

prevent consumption).


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The Socially Optimal Quantity of the Public Goods

• Figure 4.1 The height of each family’s MB

curve shows the maximum dollar amount

that family would pay for an additional foot

of thickness. We assume that each height,

uses the same material, and surrounds the

entire island; the only issue is how thick to

make the wall.

• We label the families H (height), M

(medium), and L (low) according to the

height of the family’s MB curve.


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Figure 4.1 • Equations:

– MBH = 450 – 15Q

– MBM = 300 – 10Q

– MBL = 150 – 5Q

– We can write MB = 900 – 30Q

If Q = 10, MBH = $300, MBM = $200, and MBL = $100.



• A 1-foot-thick wall costs $600 (MC)to build


Figure 4.1 The Socially Optimal of a Public Good

MBM

MBL

MBH

Wall thickness (feet)

$900 -

$800 -

$700 -

$600 -

$500 -

$400 -

$300 -

$200 -

$100 -

I I I I I I I

2 4 6 8 10 12 14

MC

MC>MBH，MC>MBM, MC>MBL

0 Instructed by YIN SOKHENG, Master in Finance 8

MBM

MBL

MBH

Wall thickness (feet)

$900 -

$800 -

$700 -

$600 -

$500 -

$400 -

$300 -

$200 -

$100 -

I I I I I I I

2 4 6 8 10 12 14

MC

MB > MC

MB

•Thickness <10,

MB > MC

•Thickness of

10, MB =MC

•Thickness > 10,

MB < MC

Figure 4.1 The Socially Optimal of a Public Good

Instructed by YIN SOKHENG, Master in Finance 9

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• A 1-foot-thick wall costs $600 (MC)to build

• At a thickness of 10 feet, MB =MC

• MBH = $300, MBM = $200, and MBL = $100

• MB = $600 ($300 + $200 +$100) = MC

• At a thickness of 0 feet, MB >MC

• MB = $900 ($450 + $300 +$150) > MC

• At a thickness of 12, MB <MC

• MB = $540 ($270 + $180 +$90) <MC


Figure 4.1

• The efficiency quantity of a public good is the quantity at

which the sum of the MBs of all who consume the good

equals the MC. By contrast, the efficiency quantity of a

private good is the quantity at which the MB of the

person who consumes the good equals the MC.

• Hence,

– At the efficiency, socially optimal quantity of a public good, MB =MC.

– At the efficiency, socially optimal quantity of a private good, MB =MC.

• So 10 feet is the socially optimal (efficiency) thickness of

the wall.


Figure 4.1 Conclusion


Political Economy

• Each family alone (even H) would be

unwilling to pay even a 1-foot wall if it must

pay the entire $600 per foot itself.

• Assume that the three families get along

well and are glad to cooperate. Then

families sit down and together draw Figure

4.1.

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The Cost-share • The cost-share is the price that the family

must pay per unit of the public good.

• Suppose the families agree that, since their

MBs are in the ratio of 3:2:1, they will share

the cost in the ratio of 3:2:1. In other words,

costs will be shared in the same ration as

benefits.

• With cost-shares decided, each family looks

at its own MB curve, compares the height of

its MB at each foot of thickness to its cost-

share (price) and decides how thick a wall it

would want.


A Unanimity

• To achieve unanimity, they must agree to

cost-shares that are in the same ratio as

their MBs.

• All three (families) will then support a 10-foot

wall and enjoy a net benefit when it is

constructed.

• So 10 feet was the best wall for all three

families given their cost-shares.


Majority-Rule Voting and the Median Voter

• Each family must know its cost share in order to know

how to vote; each will decide how to vote by comparing

its MB to its cost-share.

• So with these cost-shares, voters unanimously prefer

a 10-foot wall.

• With majority voting, the outcome will be what the

median voter prefers.

• The socially optimal quantity will be chosen under

majority-rule voting if the median voter prefers it;

otherwise, not. To get the median voter to prefer the

social optimum, it is necessary to assign the median

voter the cost-share that will cause that voter to prefer

the socially optimal quantity.

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D

Thin

Thick

Intermediate

L

Thin

Intermediate

Thick

Choice H M

First Thick Intermediate

Second Intermediate Thin

Third Thin Thick

Table 4.1 Majority-Rule Voting

For the moment, ignore family D, assume the three

families voting are H, M, and L.



Figure 4.2 Voter Preferences

Only voter D has two peaks.

Wall thickness Thin Intermediate Thick

Choice

1st

2nd

3rd

H

D

M, L


When There Are Many Families

The legislature will need to have the power of

taxation.

• Optimal Taxation

• Proportional tax: A tax that applies the same

tax rate to all households regardless of

income.

• Progressive tax: A tax that applies a higher

tax rate to high-income households.

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The Behavior of Government

Decisions about public goods are made by a

legislature (perhaps with the approval of as

executive) – not by citizens directly.

• The legislators are elected by the citizens to

represent them.

• Of course, this dose not automatically meant

that the legislature will do what the citizens

want.


Public Choice, Government Failure, and

Constitutions

Market failures

Governments use the pollution tax and tradable

permits to correct the externality

Governments collect revenues to provide the

public good

Government failures

Restrict the functions of government

public finance, chapter 4

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