4. Public Goods. SO FAR… We have seen that the role of government in promoting efficiency is to intervene in the pricing mechanism of goods that create

4. Public Goods

SO FAR…

We have seen that the role of government in promoting efficiency is to intervene in the pricing mechanism of goods that create externalities.

Now we will investigate a class of goods where it is usually more efficient for the government to supply instead of the private sector.

Public Goods:=(Law and Order, defence, refuse collection, roads, education, public health,…)

Outline

1. Definition and Description2. Free-riding 3. Optimal Provision:4. Problems of Preference Revelation

Definition

A Public Good has 2 properties:

(1) If it has been provided to one consumer it is difficult/impossible to stop another from enjoying it too.

“Non-Excludable”

(2) The amount of the good I enjoy has no affect on the amount you enjoy.

“Non-rival”

Example: TV Signals

NON-RIVAL RIVAL

NON-EXCLUDABLE

TERESTRIALPure Public Good

BASIC CABLEImpure Public

Good

EXCLUDABLE SATELLITEImpure Public

Good

Pay-per-ViewPure Private Good

CONSEQUENCES

Non-excludable:Very difficult for the private sector to provide it and make a profit.(Basic Research, Information, R&D)

Non-rivalry:Do not want to exclude people as it is inefficient

(The marginal cost of them getting the good is zero and they get positive benefit.)

The Free Rider Problem

The fundamental problem of all public goods is I’d rather someone else paid for the public goods I consumed.

This is called the free-rider problem.

Prisoners’ Dilemma in Action

Imagine it costs £4 to provide a clean street outside my house.

Either I or my neighbour can pay for it.

We both value clean streets at £3.

If one of us pays £4 we are both better off.

He PaysHe

Doesn’t Pay

I Pay

I Don’t Pay






He PaysHe

Doesn’t Pay

I Pay (-1,-1) (-1,3)

I Don’t Pay

(3,-1) (0,0)






He PaysHe

Doesn’t Pay

I Pay (-1,-1) (-1,3)

I Don’t Pay

(3,-1) (0,0)

Other Examples of Free Rider Problems

In the USA people pay voluntary subscriptions for the public broadcasting service – less than 10% do so. (In the UK it is mandatory to pay the TV licence fee.)

The town of Cambridge distributed 350 bikes around the town for people to use free of charge. (You had to return the bike to a special stand after using it.) Within 4 days they had all gone.

When can private provision of public goods work

You often find shops forming groups to improve the environment they act in. e.g. Oxford Street Traders Association.

Also rich neighbourhoods sometimes pay for security patrols, (e.g. Bishops Avenue, Hampstead)

Why does this work?• People are not all the same – some people value

the public good a lot.• Altruism• People feel good if they contribute to the public

good (warm glow)

User Fees for Excludable Public Goods and for Publicly Provided Private

Goods• Some public goods are excludable – roads,

bridges etc.• Some goods (education, water) have large cost of

supplying additional individuals are often publicly provided.

Price/Fee

# of users

Demand/Users’ Value


Goods

Price/Fee

# of users

Demand/Users’ Value

How does welfare get maximized?

The best possible is to allow everyone to travel and to ‘somehow’ pay for the bridge.


Goods

Price/Fee

# of users

Demand/Users Value

Welfare = Cost of the Bridge


Goods

Price/Fee

# of users

Demand/Users Value

If you charge a fee to recoup the cost of the bridge welfare goes down.

FEE

COST OF BRIDGE


Goods

Price/Fee

# of users

Demand/Users Value

If you charge a fee to recoup the cost of the bridge welfare goes down.

FEE

COST OF BRIDGELOST

VALUE

Impure Public Goods

Anything with a positive consumption externality.

Congested goods: Roads

Club Goods: Excludable with congestion = Museum

Local Public Goods: Parks, libraries etc.

Efficient Provision of Public Goods

How much Public Goods should the Government provide?

MC of the PG

Marginal Benefit of the Public Good

Marginal Benefit

Non-Excludable

Marginal Benefit =

Marginal Benefit1 + Marginal Benefit2 + …

+ Marginal BenefitN

= Marginal Benefiti

How do we know whether we have the socially optimal quantity of public

goods?

Marginal Benefit from the public good

= MU(pg)

Marginal Cost of Providing one more unit of Public Good

= MC(pg)

How do we know whether we have the socially optimal quantity of public

goods?

Marginal Benefit from the public good

= MU(pg)

Marginal Cost of Providing one more unit of Public Good = MC(pg)

Marginal Benefit from the Private good = MUi

Marginal Cost of Providing one more unit of Private Good = MC

Right Mix if

MB(public good) = MB(private good)MC(public good) MC(private good)

Equivalently

MU(pg) = MUi

MC(pg) MC

Equivalently

MU(pg) = MUi

MC(pg) MC

Equivalently

MU(pg) = MUi

MC(pg) MC

Equivalently

MU(pg) = MC(pg)

MUi MC

Equivalently

MRS = MRT

This is called the Samuelson Condition after Paul Samuelson who first noticed it applied.

Mechanisms for Efficiently Providing the Public Good

How do you get to provide people with the right quantity of the public good if:

1. When it is provided at zero MC people will tend to overstate their desire for it.

2. When it is provided at positive MC people will tend to understate their desire for it hoping to free ride.

Mechanisms for Efficiently Providing the Public Good

How do you get to provide people the right quantity of the public good if:

1. When it is provided at zero MC people will tend to overstate their desire for it.

2. When it is provided at positive MC people will tend to understate their desire for it hoping to free ride.

We want to find “Incentive Compatible Mechanisms”i.e. provision schemes where it is in everyone’s interest to

correctly report how much they value the good.

Example 1: Vickrey Auctions

Assumptions:• One unit of a good to be sold.• People have independent and private values:

v1 ,v2 ,…,vn . (This rules out situations where your value is affected by what others know.)


Assumptions:• One unit of a good to be sold.• People have independent and private values. (v1 ,v2 ,

…,vn)

Rules: • Bids are submitted and the highest bid gets the object.• The winner pays the amount bid by the second highest

bidder.

Optimal strategy = Bid how much you value the object.(i.e. truthfully reveal your value)


Analysis:The highest bid from everyone else is B.My value is v*.

If I submit a bid b > B => I win and pay B (I get v*-B)

If I submit a bid b < B => I lose and I get zero.

Case 1: B>v*In this case winning (and bidding above B) will lose

me money bidding v* is optimal here.

Example 1: Vickrey Auctions Case 1: B > v*In this case winning (and bidding above B) will lose

me money bidding v* is optimal here.

Case 2: B < v*In this case my payoff from winning (v* - B) is

positive.This is also independent of what I bid.If I bid b=v* I will be sure I always win the auction

in this case.

WHATEVER THE OTHERS DO BIDDING v* IS BEST!(Note: this is not true if my value depends upon what

you know.)

Clark-Groves Mechanism

This is a process that will get individuals to truthfully to reveal their preferences for the public good.

Step 1 : Individuals report their value for the bridge vi

Note : they don’t have to report the truth vi ≠ vi*




Step 2 : Add up the reported values.





Step 3 : If Sum of Reports – Cost of Bridge >0 then build the bridge.





Step 3 : If Sum of Reports – Cost of Bridge >0 Build Bridge

If Sum of Reports – Cost of Bridge <0 Don’t Build




Step 3 : If Sum of Reports – Cost of Bridge >0 Build Bridge

If Sum of Reports – Cost of Bridge <0 Don’t Build

Step 4 : If the individual’s value was decisive, i.e.

Sum of Others’ Reports < Cost of Bridge < Sum of all Reports

Clark-Groves MechanismStep 1 : Individuals report their value for the bridge vi


Step 3 : If Sum of Reports – Cost of Bridge >0 Build Bridge If Sum of Reports – Cost of Bridge <0 Don’t Build

Step 4 : If the individual’s value was decisive, i.e.

Sum of Others’ Reports < Cost of Bridge < Sum of all Reports

Charge the individual = Cost of Bridge – Sum of others’ reports


Optimal to tell the truth.

Let U be the sum of the other’s reports and let v be my value.

If U>Cost:I don’t care what I say so reporting truthfully is fine.


Optimal to tell the truth.

If U+v > Cost > U:Then any report u such that U+u>Cost (or u>Cost-U)

will get me utility v – (Cost –U) >0 . (independent

of report!)

But any report u < Cost – U will get me utility =0.

To ensure I get this positive utility should then report truthfully.


Properties:(1)Optimal to tell the truth(2)Voter only pays when decisive.(3)Payments < benefits received(4)As population grows less of a problem with excess

revenue.

Documents

4. Public Goods. SO FAR… We have seen that the role of government in promoting efficiency is to intervene in the pricing mechanism of goods that create