PUBLI C GOODS 1 Hillman 2009: Chapter 3 Public goods Public goods - - PowerPoint PPT Presentation

Hillman 2009: Chapter 3 Public goods 1

Public Finance and Public Policy: Responsibilities and Lim itations of Governm ent, Arye L. Hillm an Cam bridge University Press, 2 0 0 9 Second edition Presentation notes, chapter 3

PUBLI C GOODS

Hillman 2009: Chapter 3 Public goods 2

Public goods are “collective” Public goods are not “public” because supply is necessarily by the public sector or a government Public finance for public goods does not require or imply public supply (or supply by the government)

Hillman 2009: Chapter 3 Public goods 3

3 .1 TYPES OF PUBLI C GOODS

• A. Properties of public goods

For a private good

1 n j j

X x



 

For public goods

1 2 3 n

G=g =g =g =........=g .

Personal valuations of public goods in general differ

Hillman 2009: Chapter 3 Public goods 4

The transition from private to collective benefit For one person alone, all goods are in effect private goods because no one else is present to benefit. When others are present, benefits are collective, and questions arise about the quantity of public goods to be supplied and paying for public goods. (1) How much of the different public goods should be supplied? (2) How should the public goods be financed? These are normative questions about efficient supply of public goods.

Hillman 2009: Chapter 3 Public goods 5

Pure and congestible public goods

A pure public good A congestible public good

n2 n1 Number

• f users

O

Individual benefit Number

• f users

O

Individual benefit Constant benefit

Hillman 2009: Chapter 3 Public goods 6

Congestible public goods Examples: Gyms, movie theaters, concerts, sports events, transportation, private schools, private hospitals, and toll roads, tunnels, and bridges Duplication and exclusion allow markets for private supply of congestible public goods If markets can supply the congestible public goods, government supply is not necessary Taxes can have two distinct purposes: (1) to reduce congestion when public goods are congestible (2) to provide revenue to finance public supply of public goods

Hillman 2009: Chapter 3 Public goods 7

We now focus on pure public goods All pure public goods are natural monopolies Who is the monopoly supplier – a private supplier or the government?

Public good: Number of users n Private good: Quantity Q O Public good AC=F/n Private good AC=F/Q Average cost

Hillman 2009: Chapter 3 Public goods 8

Public inputs Conclusions about public goods in general apply to public inputs Collective harm A public “good” can do harm. Example: Damage to the environment collectively harms everybody Public goods and altruism The intent of altruistic behavior is to help others without personal benefit for oneself When people pay for public goods, they benefit – and others also benefit

Hillman 2009: Chapter 3 Public goods 9

Exclusion Where exclusion is possible, excluding people from benefitting from a pure public good is Pareto inefficient The total benefit to n people from a public good is

1

.

n n j j

W B C



 



With (n+1) beneficiaries

1 1 1

.

n n j j

W B C

  

 



1

0.

n

W B    

Allowing an additional person to benefit from an available public good is Pareto-improving

Hillman 2009: Chapter 3 Public goods 10

Efficient use of a public good

use

MC 

. Efficient use requires:

use use

MB MC 

Therefore efficient use requires no exclusion use

P 

. Example: a bridge Efficient use requires that access to pure public goods be free (there should be no exclusion)

Hillman 2009: Chapter 3 Public goods 11

• B. Voluntary personal paym ents for public goods

The basic question is: How far can a society go in supplying public goods without a government that has the authority to tax?

Market demand for private goods

Market supply Market demand PE MB1 Price

O

q1*

x1

MB2 Price

O

q2*

x2

Price

O

QE Q = q1 + q2

Hillman 2009: Chapter 3 Public goods 12

Demand for public goods A market for public goods

F

Value P* = P1* +P2*

 MB

P1* P2* MB2 MB1 O G* Quantity or standard

E

Value PE = P1

E +P2 E

 MB

P1

E

P2

E

MB2 MB1 O GE Quantity or standard Supply of the public good

Hillman 2009: Chapter 3 Public goods 13

At the point E,

i i

MB MC 



. This is the requirement for efficient supply of the public good, derived by choosing the quantity or quality supplied to maximize total net benefit from the public good

i i

W B C  



If people were prepared to voluntarily pay for public goods according to their personal MB, W would be maximized and so supply of public goods would be efficient

Hillman 2009: Chapter 3 Public goods 14

Asymmetric information and undersupply of public goods  There is asymmetric information because a person’s MB from a public good is personal subjective information  Others do not know if someone is being truthful in declaring person MB  People know the rule for contributing to the public good is Pi=MBi  An individual can understate personal MB to reduce the personal price paid in contributing to financing public goods

The personal gain from understating benefit Inefficient supply due to misrepresented benefits

Supply Quantity GE G0 O

∑ Untrue MB ∑ True MB

Valuation Personal price P2 P1 True personal MB Untrue personal MB O G* Quantity

Hillman 2009: Chapter 3 Public goods 15

Inefficient undersupply of voluntarily financed public goods occurs because of incentives to understate personal benefit so as to reduce personal payment We also call such behavior free riding – because of the intent to have access to public goods without personally paying according to true benefit

Hillman 2009: Chapter 3 Public goods 16

The efficient ideal Lindahl consensus We can represent a market in public goods in another way that differs from the usual supply and demand representation A market can be based on the recognition that payments for a public good by one person reciprocally provides free supply to the

• ther

Hillman 2009: Chapter 3 Public goods 17

Person 1’s demand for a public good depends on the share s1 that he or she pays There is consensus that the efficient quantity GE should be supplied when cost shares are sE

1 and sE 2.

The personal price is the share of the total price

i i

s P P 

smax1 smax2

Cost shares O2 O1 GE Quantity MB1 MB2 sE

2

sE

1

s1

smax1 1

O Quantity MB1 (Demand

• f person 1)

Share of the price paid by person 1

Hillman 2009: Chapter 3 Public goods 18

In the Lindahl equilibrium,

1 2

MB MB  ( ) 1, 2.

E i i i E

P s P MB G i   

1 2 1 2

( ) ( )

E E

P P s s P MB    

With P = MC , (sE

1 + sE 2) =1, we have the efficiency condition for

public-good supply

i i

MB MC 



The Lindahl voluntary-payment consensus results in efficient voluntary payments for public-good supply

Hillman 2009: Chapter 3 Public goods 19

The Lindahl financing solution does not resolve the incentive for free riding

Lindahl cost sharing is not sustainable because costs shares can be manipulated by misrepresenting personal benefit

Strategic behavior: Person 1 does not want to understate benefit too much because person 2 responds to increased cost shares by supplying less

O2 s2 smax1(true) E E’ smax2 s1 O1 Go G* True MB1 Understated MB1 Quantity of public good Cost shares True MB2 Reduced cost share for person 1, increased cost share for person 2

Hillman 2009: Chapter 3 Public goods 20

The prisoners’ dilem m a and public goods Voluntary supply of a public good can be represented as a prisoners’ dilemma Person 2 contributes Person 2 does not contribute Person 1 contributes Person 1 does not contribute 3,3 4,1 1,4 2,2 The outcome for voluntary payments for public goods is the inefficient Nash equilibrium

Hillman 2009: Chapter 3 Public goods 21

The difference between Nash behavior of the prisoners’ dilemma and the Lindahl mechanism Nash behavior in the prisoners’ dilemma:  Decisions are independent (the decision is made given the decision of the other person or is a reaction to the other person’s decision)  The response to greater supply of the other person is to supply less Lindahl mechanism:  Decisions are interdependent (each person views the willingness to pay of the other as a subsidy for own payment)  The response to greater supply of the other person is to supply more

Hillman 2009: Chapter 3 Public goods 22

Experim ental evidence on the public-good gam e

• Two people are each given 10
• They can keep the money or contribute all the money to

providing a public good

• The contribution of 10 provides public good benefits of 7 to

everyone (including the person contributing) The result is the prisoners’ dilemma Person 2 contributes Person 2 does not contribute Person 1 contributes Person 1 does not contribute 14, 14 17, 7 7,17 10, 10 Why do people often cooperate in single and finitely repeated interactions?

Hillman 2009: Chapter 3 Public goods 23

The public good game with divided money Each individual has a budget constraint 10

1, 2.

i i

x g i   

When the game is against one other person

1 2

G g g  

. Example of a formula that determines personal total benefits Bi

1 2

3 2 3 2( ) 1, 2.

i i i

B x G x g g i      

Person 2 contributes Person 2 does not contribute Person 1 contributes Person 1 does not contribute 40, 40 50, 20 20,50 30, 30

Hillman 2009: Chapter 3 Public goods 24

Total benefit from a personal contribution of one dollar = 4 Max B=B1+B2: all money for the public good The dominant strategy is not to contribute to the public good Cooperation often occurs except in the final round People appear to anticipate punishment, should they cease to cooperate – except the last time

Hillman 2009: Chapter 3 Public goods 25

Trust and norms of conduct People often begin by trusting others to reciprocate People are willing to punish others who did not cooperate, even if in the act of punishment they themselves incur a loss Economics students and cooperation Economics students tend to cooperate less Economics students may better understand the logical consequence of common knowledge

Hillman 2009: Chapter 3 Public goods 26

Cooperation as expressive Expressive behavior by economics students People confirm their identity The sums of money are small How significant is the experimental evidence on public goods for public finance and public policy? Even if people cooperate in experiments, governments could not rely on voluntary payments to finance public goods If contributions were voluntary, there would be no tax evasion.

Hillman 2009: Chapter 3 Public goods 27

Sequential voluntary-financing public-good games When valuations of public goods differ, do high-valuation or low- valuation beneficiaries contribute first? What behavior do we expect when a discrete public good requires a minimal level of contributions before providing benefits?

Hillman 2009: Chapter 3 Public goods 28

• C. W eakest-link and volunteer-type public goods

For a public good described by the prisoners’ dilemma:

1 n i i

G g





For weakest-link public goods:

 

1 2, 3 1 2 3

min , , ,..., ....

n n

G g g g g G G G G      

The lowest standard determines the overall standard

• A wall that protects homes against sea water on a circular

island

• Safety in a neighborhood
• The quality of a road
• The effectiveness of defense
• The time taken for a group to complete a hike

Hillman 2009: Chapter 3 Public goods 29

Strategic behavior for weakest-link public goods

Person 2 contributes Person 2 does not contribute Person 1 contributes Person 1 does not contribute 24, 24 (0.3).(0.3)= 0.09 10,4 (0.7).(0.3)= 0.21 4, 10 (0.3).(0.7)= 0.21 10, 10 (0.7).(0.7)= 0.49

Derivation of the mixed-strategy equilibrium Utility (not contribute) = 10 Utility (contribute) = P.24 + (1 – P).4 Equate and solve: P = 0.3

Hillman 2009: Chapter 3 Public goods 30

Sequential decisions for weakest-link public goods solve the coordination problem

Cheap talk

• A declaration of intent on which it is costless to renege
• In coordination games such as supply of weakest-link

public goods, “cheap talk” provides valuable communication

• It is in the self-interest of people who declare that they will

contribute to the public good to actually do so

YES NO Person 2 decides Person 1 decides Person 2 decides 10,10 24, 24 4, 10 YES NO YES NO 4, 10

Hillman 2009: Chapter 3 Public goods 31

A role for government?

• Free riding is impossible: unless everyone pays, the public

good is not provided

• Paying for a weakest-link public good is therefore like

paying for a private good

• Every person needs to pay and wants to pay – provided

everyone else pays

• Taxation and public spending are not necessary because

everyone has an interest in participating to provide the efficient outcome

Hillman 2009: Chapter 3 Public goods 32

Volunteer-type public goods

 

1 2, 3 1 2 3

max , , ,..., ....

n n

G g g g g G G G G      

• Help to move a disabled car
• Remove a rock from a road
• A broken bottle on a path
• A story from the Netherlands: a boy who placed his finger

in a hole in a dyke

• Passengers lining up to board a plane may notice that a

person is acting suspiciously

Hillman 2009: Chapter 3 Public goods 33

Who provides the public good? The game of chicken

Person 2 contributes Person 2 does not contribute Person 1 contributes Person 1 does not contribute 10,10 (0.8).(0.8)= 0.64 12,10 (0.2).(0.8)= 0.16 10,12 (0.8).(0.2)= 0.16 2,2 (0.2).(0.2)= 0.04

There is no dominant strategy The two Nash equilibria are efficient For the mixed strategy, P= 0.8

Hillman 2009: Chapter 3 Public goods 34

Sequential decisions for volunteer type public goods

The first person to decide imposes the cost of supply on the second person Larger populations and sequential decisions: each person can choose to rely on the next person, if there is a next person

YES NO Person 2 decides Person 1 decides Person 2 decides 2, 2 10,10 10, 12 YES NO YES NO 12, 10

Hillman 2009: Chapter 3 Public goods 35

Social norms and volunteer public goods

• Personal contributions can be based on convention, as

within a household

• Within broader society, can we rely on similar conventions?
• Social norms influence personal behavior, through our

expectations about how we feel we should act in different situations

• A society in which the social norm is to take personal

responsibility has more volunteer-type public goods The role for government? Since decisions are personal and voluntary, there is no role for government – except perhaps through education Example: Personal freedom as a voluntarily privately supplied public good

Hillman 2009: Chapter 3 Public goods 36

• D. National security

Special characteristic of national security as a public good The effectiveness of defense spending depends spending of potential adversaries Spending on defense as a prisoners’ dilemma

Country 2 does not spend on military preparedness Country 2 spends on military preparedness Country 1 does not spend on military preparedness Country 1 spends on military preparedness 3, 3 4, 1 1, 4 2, 2

Hillman 2009: Chapter 3 Public goods 37

International treaties and free-riding problems between allies Free riding within a country Peace as a public good: A strong country acting ethically provides a pure public good, in sustaining peace in an otherwise anarchic world. Democracies and conflict  In autocracies, the ruler personally enjoys the benefits of conquest and imposes the costs on the people  In democracies, the benefits of conquest are not personal but the costs are personal, so voters oppose initiation of war.

Hillman 2009: Chapter 3 Public goods 38

Defense against terror and asymmetric warfare What is asymmetric warfare? What are the costs of terror for the population of intended victims? Income and terror: Is economic derivation the reason for terror? Definition: A supreme-value objective is an objective that is sought without the possibility of compromise. Is deterrence effective in the face of supreme-value terror? Are there other solutions for defense against terror?

Hillman 2009: Chapter 3 Public goods 39

Penalties on family assets Terrorists’ decision Victims’ decision Commit terrorist acts No terror Family assets are appropriated No penalty on terrorists’ families 2, 3 1, 4 3, 1 4, 2  Neither the victims of terror nor the terrorists want the terrorists’ families to be penalized  The victims have no dominant strategy The dominant strategy of the terrorists is to commit acts of terror

Hillman 2009: Chapter 3 Public goods 40

Sequential decisions

• The terrorists decide first
• (3, 1) and (1, 4) are not possible equilibria
• Terrorists are better off at (2, 3) than at (4, 2)
• Deterrence has been ineffective

Alternative preferences: Intending terrorists prefer (no terror, no penalty) to (terror and penalty on the family) and deterrence is effective By choosing first, the terror organization determines the outcome

2 1 4, 2 4,3 2, 3 2,2 NO YES Terrorist decides Victim decides Victim decides 1, 4 YES NO YES NO 3, 1 Alternative terrorist preference

Hillman 2009: Chapter 3 Public goods 41

Repeated “games” between terrorists and victims: If the penalty is not imposed, there is no credible deterrent when intending terrorists prefer the (no terror, no penalty) solution Moral dilemmas for intended victims when the identity of the terrorists is not known with certainty  Profiling  Unintended collective punishment Social and political divisions because of the moral dilemmas

Hillman 2009: Chapter 3 Public goods 42

3 .2 I NFORMATI ON AND PUBLI C GOODS

The public-good information problem Weakest-link public goods

• A coordination problem
• No one wants to free ride

Volunteer-type public goods

• Social norms and personal values determine behavior
• Free riding is efficient

Public goods of the prisoner’s dilemma

• There is a role for government because of free riding
• When people seek to free ride, government has the

advantage of being able to legally coerce payment through taxation

Hillman 2009: Chapter 3 Public goods 43

• A. Can governm ents solve the inform ation problem ?

Can governments solve the public-good information problem and overcome the free-riding incentives that prevent efficient supply of prisoners’- dilemma type public goods? Another form of the same question: Can government replicate the efficient Lindahl consensus when MB’s are private information of individuals? The problem is more complex than was illustrated in the public- good prisoners’ dilemma

Hillman 2009: Chapter 3 Public goods 44

Choosing the efficient quantity to supply Can government determine GE? The government replicates the efficient Lindahl solution through taxes if

, 1,...,

i i

T MB i n  

i i

MB MC 



∑MB is required information for the government

Quantity GE O P = MC = AC ∑MB Price and valuation of the public good

Hillman 2009: Chapter 3 Public goods 45

Governments wishing to levy taxes to finance public goods confront the same asymmetric information problem that impedes efficient voluntary payments for public goods We shall consider three solutions to the public-good information problem:

• 1. A mechanism designed to elicit truthful responses
• 2. User prices
• 3. Locational choice

Hillman 2009: Chapter 3 Public goods 46

• B. The Clarke tax and truthful self-reporting

People could be asked their MB with assurance that reported personal MB will not be used to determine personal payments for financing the public good The incentive is then to overstate benefit Illusion: “governments” and not taxpayers are paying Can incentives be provided for people to report their benefits from public goods voluntarily and truthfully?

Hillman 2009: Chapter 3 Public goods 47

The Clarke tax Person 1 Person 2 Person 3 100 70

• 80

Tax=10 Tax=0 Tax=0 W = B – C > 0 The government does not know the personal benefits and costs There is asymmetric information: only the three people know their own personal benefits or losses

Hillman 2009: Chapter 3 Public goods 48

Rules for the Clarke tax

• People pay a tax for being decisive
• The amount of the tax payment is equal to the net loss imposed
• n all other people as a consequence of being decisive
• The tax revenue is not used to finance the project nor to

benefits the persons involved in other ways

Hillman 2009: Chapter 3 Public goods 49

 The impossibility of gain from misrepresentation: Nothing that people say about their own valuations of benefits or costs affects the value of the Clarke tax that a person pays  The Clarke tax results in Nash equilibrium: The dominant strategy is to reveal truthfully personal benefit or loss from the public good and to pay the Clarke tax  Why cannot the revenue benefit the people involved?

Hillman 2009: Chapter 3 Public goods 50

A case where no one is decisive Person 1 Person 2 Person 3 Person 4 20 20 20

• 30

Tax=0 Tax=0 Tax=0 Tax=0 The tax is zero for everybody because no one’s participation in the evaluation of benefit and cost is decisive in changing the

• utcome

Hillman 2009: Chapter 3 Public goods 51

The Clarke tax with two projects Person 1 Person 2 Person 3 Project A 70 80 20 Project B 30 50 80 Clarke tax Tax=30 Tax=20 Tax=0

Hillman 2009: Chapter 3 Public goods 52

No government ever appears to have used the Clarke tax as a means of solving the public-good asymmetric-information problem Why is the Clarke tax not used?  Complexity?  Unfairness: the taxes do not finance the public good  Political reasons: the uncertainty of not knowing beforehand how the Clarke mechanism will determine tax obligations for different people

Hillman 2009: Chapter 3 Public goods 53

• C. User prices

Apply the benefit principle and exclude people who do not pay to create a market for use Definition: The benefit principle (a normative proposition) People who benefit should pay People who do not benefit should not have to pay Efficient Lindahl prices do not exclude people from benefits of public goods (we saw that exclusion for pure public goods is inefficient) User prices differ from efficient Lindahl prices.

Hillman 2009: Chapter 3 Public goods 54

If a person i voluntarily pays a user price, we know that

use i i

MB P 

 People reveal their personal benefit by paying user prices  The efficient user price is zero, so user prices inefficiently exclude from pure public goods  User prices provide revenue to pay for public goods

Hillman 2009: Chapter 3 Public goods 55

Indirect user prices

• A tax on gasoline is a tax on use of roads
• A tax on automobiles is a tax on the option to use a road
• The user prices can be avoided by not using or owning an

automobile. Subsidies and partial user prices

• School fees (user prices) may cover only part of the cost of

education

• User prices for health care may be subsidized

Two-part user prices User prices can be in two parts for fixed and variable costs Example: School administrators and teachers

Hillman 2009: Chapter 3 Public goods 56

User prices and fixed costs Pure public goods have fixed costs that are independent A total fixed cost of use F per period of time can be imputed from the value of the initial investment plus interest payments and deprecation over time With n users, the average cost of use per period of time is

. F AC n 

Hillman 2009: Chapter 3 Public goods 57

Are self-financing user prices feasible? Definition: Puse=AC is a self-financing user price AC is a rectangular hyperbola

The self-financing user- price is equal to average cost Demand for use of a public facility

O User valuation v Demand for use Number of users n AC=F/n P1

use

P2

use

O n1

n2

Number

• f users

Self–financing user price

Hillman 2009: Chapter 3 Public goods 58

 People are excluded by the user price  Without user prices, there may be no bridge or no college, because of the free-rider problem due to asymmetric information.  The self-financing user price finances availability of public goods by requiring payment for benefit

Hillman 2009: Chapter 3 Public goods 59

In case A a population smaller in size than n1 cannot self-finance the public good through user prices In case B self-financing user-prices do not exist – although with free access, W = (B - C) > 0 Case A Case B Self-financing user prices may not exist for projects that satisfy the cost-benefit criterion W = (B - C) > 0

AC=F/n J H Demand for use O Number

• f users

n R A E Valuation and cost P2

use

O P1

use

1 2 n2 n n1 Demand for use AC Number

• f users

Valuation and cost

Hillman 2009: Chapter 3 Public goods 60

Private supply Example: A bus service

Private supply by a monopoly

• The private profit-maximizing supplier excludes (n - nM)

potential users

• For efficient use, all n potential users should be given access

at a zero price: there is then no revenue, so a subsidy from government is required

n2 O PM n nM Demand for use AC Valuation and cost MR MC=0 Maximized profits

• f an unregulated

private supplier Number of users P2

use

Per-unit subsidy required for private supply with no exclusion

Hillman 2009: Chapter 3 Public goods 61

Subsidies from government budget to private suppliers are undesirable because of principal-agent problems Governments can ask for competitive bids from private suppliers: then there are problems of incomplete contracts With government ownership:

• Subsidies are avoided
• There is a bureaucratic principal-agent problem, because of

incentives for budget maximization of the officials in the administering government bureaucracy

Hillman 2009: Chapter 3 Public goods 62

A basic question: Are user prices desirable means of resolving the public-good asymmetric-information problem?

Hillman 2009: Chapter 3 Public goods 63

Social justice The normative principle of ability-to-pay. The ability of pay principle of taxation is that people should pay for public goods according to their means and without regard for personal benefit.

• Under the ability to pay principle, people with higher

incomes pay higher taxes

• Under the benefit principle on which user prices are based,

people pay the same user prices independently of income.

Hillman 2009: Chapter 3 Public goods 64

Efficiency

• We consider user prices because of the objective of

efficiency, not social justice

• We ideally want efficient Lindahl prices but Lindahl prices

are not feasible: hence we turn to user prices

• The case for user prices is that, in voluntarily paying,

people reveal MB from public goods

• Ability-to-pay taxes: people finance public goods that they

do not use and so the link between personal benefit and personal payment is broken

• User prices directly link voluntary personal spending to

personal benefit The inefficiency of exclusion

• Self-financing user prices inefficiently exclude

Hillman 2009: Chapter 3 Public goods 65

Accountability

• User prices provide accountability
• When payment is made through user prices, people are

more attentive to whether appropriate benefits have been received. User prices as an alternative to government supply

• Government schools in some countries and locations fail to

provide quality education

• When governments provide free-access tax-financed health

care, user prices paid for private health care may be the

• nly escape from inadequacies of government supply

Hillman 2009: Chapter 3 Public goods 66

Prisons and police

• Prisons can be financed through user prices paid by

inmates

• The user prices are involuntary
• Should taxpayers and citizens, as victims of crime, be
• bliged to pay for prisons
• Competitive bidding for private supply of prisons

Police protection

• It is unjust or unethical to compel victims of crime to pay

when government has been ineffective in enforcing the rule of law

• User prices for calling on the police would also assist

criminals by deterring reporting of crime.

Hillman 2009: Chapter 3 Public goods 67

Diversity in application of user prices

• In some countries user prices are applied extensively to

solve the public-good asymmetric-information problem

• In other countries, user prices are uncommon
• In low-income societies, voluntary user prices are paid to

substitute for absent or inadequate government supply

Hillman 2009: Chapter 3 Public goods 68

• D. The Tiebout locational choice m echanism

Locational choice is an application of the benefit principle of taxation Does choice of location among government jurisdictions achieve efficiency, as a substitute for a competitive market in public goods? Does locational choice replicate the efficient Lindahl voluntary-payment solution for public goods?

Hillman 2009: Chapter 3 Public goods 69

 The efficient Lindahl solution requires everyone in the one jurisdiction to finance pure public goods.  If people choose to finance public goods in different locations, there is inefficient duplication of supply (because a pure public good is a natural monopoly).  Still, locational choice is the efficient second-best solution, given the asymmetric information problem that prevents the efficient solution.

Hillman 2009: Chapter 3 Public goods 70

Tiebout and Samuelson on spontaneous and imposed order The Tiebout locational mechanism (1956) is named after Charles Tiebout (1924–68) Tiebout replied to Paul Samuelson (1954, 1955). Samuel on proposed:

• ∑MB=MC for efficient public good supply could not be

achieved through voluntary payment for public goods because people would not pay according to their true MB.

• Imposed order was therefore required for public goods

through supply decisions of centralized government agencies and financing through taxes Tiebout replied:

• Spontaneous order could be provide by a locational market
• Individuals make personal decisions about public goods in

response to taxes (or prices) that they wish to pay

• Although taxes paid to governments are compulsory, the

ability to choose governments to whom to pay taxes makes payment of taxes voluntary

Hillman 2009: Chapter 3 Public goods 71

Limitations of the Tiebout mechanism Employment opportunities: Is location for employment distinct from public-good choice? The scope of choice

• Does the scope of choice replicate a competitive market for

local public goods?

• Public goods come in bundles: large numbers of alternative

jurisdictions may be required to offer the sought-after combinations of quality and quantity.

Hillman 2009: Chapter 3 Public goods 72

Norms and conventions as public goods

• How to dress
• How people entertain themselves, including being drunk in

public places

• Locational choice allows people to choose a community in

which they feel comfortable

Hillman 2009: Chapter 3 Public goods 73

The Tiebout mechanism when people seek different types of public goods The outcome is efficient supply of public goods within a jurisdiction

Hillman 2009: Chapter 3 Public goods 74

Different quantities or qualities of the same public good The Tiebout locational mechanism is more complex when people want different quantities or qualities of the same public good

Separation of low- and high-benefit people by choice of jurisdiction

• Low-benefit person wants GL
• The high-benefit person wants GH
• Neither may be offered in this jurisdiction but people can

move

O GH GL R MBL S J Valuation and cost Quantity MBH T Tax per unit of the public good V Z Loss of the low-benefit person from locating in the high-benefit jurisdiction Loss of the high-benefit person from locating in the low-benefit F

Hillman 2009: Chapter 3 Public goods 75

Locational choice among government jurisdictions solves the public-good preference revelation problem Natural monopoly and cost sharing We have not taken account of the attribute of natural monopoly

• f public goods

The Lindahl voluntary-pricing consensus solution: Costs of supply per person are minimized by providing the public good in a single jurisdiction Efficient cost-sharing requires a single jurisdiction Separation into different jurisdictions for revealing information about preferences contradicts efficient cost sharing

Hillman 2009: Chapter 3 Public goods 76

The second-best

• The first-best Lindahl solution is not feasible
• The Tiebout locational-choice solution is a second-best
• utcome when the first-best Lindahl solution is not available.
• The second-best is the only feasible outcome: both revelation
• f preferences and cost minimization per person are not

simultaneously possible

Hillman 2009: Chapter 3 Public goods 77

Demonstrating the cost-sharing efficiency of a single jurisdiction In a jurisdiction, the government does not know personal Lindahl prices The government sets a common per-unit self-financing tax T

. P T n 

This is the minimum possible price or tax No Lindahl consensus: at the minimum tax or per unit price T, there is disagreement on the quantity or quality of the public good that low and high-benefit people want to have supplied

Hillman 2009: Chapter 3 Public goods 78

Cost sharing in separate jurisdictions: We divide the population of n people

L H

n n n  

. nL have MBL nH have MBH In separate jurisdictions, individuals’ personal per-unit payments are higher than in a combined jurisdiction:

,

L H L H

P P T T n n  

Hillman 2009: Chapter 3 Public goods 79

There are costs and benefits of separate jurisdictions  The cost of separation into in different jurisdiction is the need to pay the higher unit-taxes.  The benefit of separation is choice of public spending on public goods according to own preferences. There is a trade-off

Hillman 2009: Chapter 3 Public goods 80

The decision whether to form a separate jurisdiction

nL=nH T : the per-unit tax in one jurisdiction 2T: the per-unit tax doubles in 2 jurisdictions Who controls the collective decision? The group in control of the choice of public-good supply has an incentive to attempt to block exit of others

MBL

J Y S R E O GH1 GL1 Valuation and cost Quantity

MBH

2T Tax per unit of the public good with two tax jurisdictions V D T Tax per unit of the public good with a single tax jurisdiction H Z GH GL F

Hillman 2009: Chapter 3 Public goods 81

Tiebout and Lindahl

L1 H 1 E

G G G  

The Lindahl consensus solution in a single jurisdiction is Pareto- improving compared to separate jurisdictions. Figure 3.17: The efficient Lindahl consensus and the outcome of separation People are trapped by incentives of asymmetric information in separate Tiebout jurisdictions

O TH P = MC MBL GE GL1 Taxes and cost Quantity or quality of the public good ∑ MBL + ∑ MBH MBH ∑ MBL ∑ MBH GH1 TL

Hillman 2009: Chapter 3 Public goods 82

Prices and politics in the Tiebout locational market

• The Tiebout locational mechanism is a substitute for a

market

• Payments should be like the prices paid in any market
• Price is a per-unit cost per person
• In practice, taxes are levied on the value of property or

housing, or on income, or a sales tax might be levied The Tiebout benefit principle of markets is compromised by politics

• The benefit principle of payment required for the Tiebout

mechanism can be politically unpopular, because the people who benefit are required to pay

• The benefit principle does not allow cross-subsidization

through political decisions

Hillman 2009: Chapter 3 Public goods 83

A natural experiment

• The government of Prime Minister Margaret Thatcher in the

United Kingdom introduced the benefit principle to local public finance in 1988

• In 1991 the property tax was restored
• Widespread non-compliance with the tax per beneficiary of

public services The benefit principle:

• Introduced tax obligations for people who lived in public

housing

• and for people who lived in houses where there were more

than average numbers of occupants

• Taxes increased for occupants of less expensive houses.

The policy experiment ended with successful popular (and political) resistance to the benefit principle for payment for local public goods.

Hillman 2009: Chapter 3 Public goods 84

Income and locational rents

• The Tiebout locational mechanism views people as differing
• nly in preferences for public goods: income and wealth

determine the public goods that people can afford

• Zoning implements separation by income and wealth:

housing in a jurisdiction may be expensive because zoning regulations permit only expensive houses

• Exclusion through zoning regulations: high-income people

exclude low-income people, who would live in low-valued housing and pay low property and income taxes but nonetheless would benefit from the jurisdiction’s public goods

Hillman 2009: Chapter 3 Public goods 85

Housing prices include locational rents If not for the excess demand expressed in the locational rent, housing prices for identical houses would be the same in two jurisdictions Taxes would be higher in a richer area but the higher taxes would be precisely matched by the higher spending on local public goods A jurisdiction is “exclusive” when lower-income people, who would be prepared to pay higher taxes in order to receive higher-standard public goods, are excluded from a jurisdiction by locational rents that have increased housing prices. In all markets, demand depends on preferences, prices, and incomes or wealth

Hillman 2009: Chapter 3 Public goods 86

Cost-sharing for public goods as a cooperation gam e There is no asymmetric information if personal benefits and costs are revealed

• Wealth and possessions indicate benefits from public

spending on law enforcement

• The number of children is an indicator of benefits from

public spending on schools

• Owning a car is an indicator of benefit from a road

People cannot seek to free ride by being deceptive when personal benefits and costs are known The problem is agreement on sharing of costs A cooperative game Apply the Nash bargaining solution

Hillman 2009: Chapter 3 Public goods 87

Example: cars and trucks C1 = payment by the car owner C2 = payment by the truck owner

A bargaining outcome for cost sharing

At point 2: separate roads, no agreement on cost sharing The cost of the road sufficient for the car owner = 40 The cost of the road required by the truck owner = 100 DB: efficient outcomes of one road and sharing of the cost 100

80 C1 = Cost of the car owner C2 = Cost of the truck owner O 100 100 45o 40 60 20 45o 1 2 A B D

Hillman 2009: Chapter 3 Public goods 88

Incentives

• The owner of the car will share if C1 < 40
• The truck owner will share if C1 > 0

Bargaining: Feasible bargaining outcomes (0 > C1 > 40) are AB No agreement: separate roads at the disagreement (or threat) point 2 Pareto efficiency: outcomes along AB are superior to the point 2 Equal bargaining power: equal gains from cooperation are at point 1 The gains from cooperation: 20 each = 40 C1 = 20 = (40 -20) C2 = 80 = (100 -20) The outcome is the Nash bargaining solution for cooperative games

Hillman 2009: Chapter 3 Public goods 89

3 .3 COST– BENEFI T ANALYSI S

Cost-benefit analysis is a last resort for obtaining information

• The Clarke tax would, if used, provide information about

personal benefits and costs

• User prices provide information about MB of use: although

costs of constructing a bridge are financed over time through toll charges, cost-benefit analysis is required when the bridge is built

• The locational choice mechanism: cost-benefit analysis is

required to evaluate the costs and benefits of public spending in a jurisdiction

Hillman 2009: Chapter 3 Public goods 90

• A. Costs and benefits w ithout m arket valuations

The objectives of cost-benefit analysis are (1) to determine if W = B – C > 0 (2) to determine efficient supply of a public good GE

Examples: Markets do not exist that allow biodiversity to be valued A dam may disturb the habitat of a rare toad

Quantity of the public good

∑MB

MC=P GE O Max W = ∑B – C Cost and valuation

• f the public good

Hillman 2009: Chapter 3 Public goods 91

Often the objective is to determine whether W > 0 Sensitivity analysis is used to test how the estimates of cost and benefit affect calculations Examples:

• Saving the rhino
• The value of human life

Hillman 2009: Chapter 3 Public goods 92

• B. Valuation over tim e
• The need to choose a discount rate
• The case for a zero discount rate

A high discount rate increases the likelihood that a project that harms the environment will pass the test of cost-benefit analysis

Hillman 2009: Chapter 3 Public goods 93

A project with a one-time cost and a one-time benefit

1

0. (1 ) B W C i    



If ∑B1 = 105 and C0 = 100, the project is justified if i < 5% Choosing i > 5 percent ensures rejection of the project

Hillman 2009: Chapter 3 Public goods 94

A project with benefits for multiple years

1 1 2 2 2

( ) 0. (1 ) (1 ) (1 )

N N N

B C B C B C W B C i i i             

  



When i > 0, we can define a discount factor

1 1. 1 i    

     

2 1 1 2 2

W B C B C B C         

  



where  discounts the future. In the special case where benefits and costs are the same in each year and extend indefinitely into the future:

.

i i

B C W i   

Hillman 2009: Chapter 3 Public goods 95

What should the discount rate be?

• Do returns in private capital markets reflect the time

preference of people in society?

• If the environment is a gift of nature that is not the

possession of any generation, we should choose zero discounting

• The distinction between social and private risk
• Decisions made today affect yet unborn populations, who

may not find acceptable the discount rate that was chosen in the past

• We may wish that past generations had been more

attentive to effects on the environment and had used zero

• r low discount rates

Hillman 2009: Chapter 3 Public goods 96

• C. The discount rate and choice betw een public projects

The discount rate determines choice between alternative public investments Example: choice between public investment in a subway system and highway expansion

Hillman 2009: Chapter 3 Public goods 97

Subw ay Highw ay Cost C 1,400 once 400 every 10 years Benefit each year Bi 60 per year 50 per year A time horizon of 50 years Undiscounted total benefit ∑Bi 3,000 2,500 Undiscounted net benefit ∑(Bi-C) Gain from choosing the subway 1,600 1,100 500 A time horizon of 100 years Undiscounted total benefit ∑Bi 6,000 5,000 Undiscounted net benefit ∑(Bi-C) Gain from choosing the subway 4,600 3,600 1,000 Discounted at i = 5% Total benefit ∑Bi 1,200 405 every 10 years Total net benefit ∑(Bi-C)

• 200

+5 every 10 years

Hillman 2009: Chapter 3 Public goods 98

• D. I ncom e distribution and cost-benefit analysis

Changes in incomes because of public spending

• A bridge might provide greater benefits for high-income

persons than for low-income persons because high-income persons have high value of time

• Low-income people might have low incomes because they

are cut off from high-income employment opportunities by the absence of a bridge: cost-benefit analysis should then take into account the future increase in the incomes of the low-income people

Hillman 2009: Chapter 3 Public goods 99

Social justice The objective of the cost-benefit criterion is efficiency. When the cost-benefit criterion takes account of aspects of fairness or social justice, we need to weigh efficiency and social justice We shall use a social welfare function to introduce such weights when we study social justice.

Hillman 2009: Chapter 3 Public goods 100

Cost-benefit analysis and political decisions

• A political representative may succeed in obtaining public

spending that benefits his or her constituency

• If the public investment is not justified by cost-benefit

analysis, the intended beneficiaries of the project are better off, if they are given the public money directly

• Politicians may be unable to give away money, although

they can provide publicly financed public-good projects

Hillman 2009: Chapter 3 Public goods 101

Public goods and rent seeking Seeking finance for public goods can be a rent-seeking activity The rent sought may be a publicly financed highway or bridge Rent seeking results in political distraction from cost-benefit analysis guided by efficiency objectives