Transcript Public Goods - PERSONAL WEB PAGE DISCLAIMER

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.
2.
3.
4.
Definition and Description
Free-riding
Optimal Provision:
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
TERESTRIAL
Pure Public Good
BASIC CABLE
Impure Public Good
EXCLUDABLE
SATELLITE
Impure Public Good
Pay-per-View
Pure 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 Pays
I Pay
I Don’t
Pay
He
Doesn’t
Pay
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 Pays
He
Doesn’t
Pay
I Pay
(-1,-1)
(-1,3)
I Don’t
Pay
(3,-1)
(0,0)
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 Pays
He
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
Demand/Users’ Value
# of users
User Fees for Excludable Public Goods and
for Publicly Provided Private Goods
How does welfare get maximized?
The best possible is to allow everyone to travel and to ‘somehow’ pay for the
bridge.
Price/Fee
Demand/Users’ Value
# of users
User Fees for Excludable Public Goods and
for Publicly Provided Private Goods
Welfare =
Price/Fee
Cost of the Bridge
Demand/Users Value
# of users
User Fees for Excludable Public Goods and
for Publicly Provided Private Goods
If you charge a fee to recoup the cost of the bridge welfare goes down.
Price/Fee
Demand/Users Value
COST
OF
BRIDGE
FEE
# of users
User Fees for Excludable Public Goods and
for Publicly Provided Private Goods
If you charge a fee to recoup the cost of the bridge welfare goes down.
Price/Fee
LOST
VALUE
Demand/Users Value
COST
OF
BRIDGE
FEE
# of users
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?
Marginal Benefit of the Public Good
MC of the PG
Marginal Benefit
Non-Excludable
Marginal Benefit =
Marginal Benefit1 + Marginal Benefit2 + …
+ Marginal BenefitN
= S Marginal Benefiti
How do we know whether we have the
socially optimal quantity of public goods?
Marginal Benefit from the public good
= S 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
= S 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)
MC(public good)
=
MB(private good)
MC(private good)
Equivalently
S MU(pg)
MC(pg)
=
MUi
MC
Equivalently
S
MU(pg)
MC(pg)
=
MUi
MC
Equivalently
S
MU(pg)
MC(pg)
=
MUi
MC
Equivalently
S
MU(pg)
MUi
=
MC(pg)
MC
Equivalently
S 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.)
Example 1: Vickrey Auctions
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)
Example 1: Vickrey Auctions
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*
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
Step 2 : Add up the reported values.
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
Step 2 : Add up the reported values.
Step 3 : If Sum of Reports – Cost of Bridge >0 then build the
bridge.
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
Step 2 : Add up the reported values.
Step 3 : If Sum of Reports – Cost of Bridge >0 Build Bridge
If Sum of Reports – Cost of Bridge <0 Don’t Build
Clark-Groves Mechanism
Step 1 : Individuals report their value for the bridge vi
Step 2 : Add up the reported values.
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 Mechanism
Step 1 : Individuals report their value for the bridge vi
Step 2 : Add up the reported values.
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
Clark-Groves Mechanism
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.
Clark-Groves Mechanism
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
To ensure I get this positive utility should then report
truthfully.
=0.
Clark-Groves Mechanism
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.