1. 4. Public Goods

2. 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,…)

3. Outline Definition and Description Free-riding Optimal Provision:
Problems of Preference Revelation

4. Definition “Non-rival” 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”

5. Example: TV Signals NON-RIVAL RIVAL NON-EXCLUDABLE TERESTRIAL
Pure Public Good
BASIC CABLE
Impure Public Good
EXCLUDABLE
SATELLITE
Pay-per-View
Pure Private Good

6. 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.)

7. 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.

8. 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
I Don’t Pay

9. 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)

10. 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)

11. 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.

12. 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)

13. 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

14. 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

15. User Fees for Excludable Public Goods and for Publicly Provided Private Goods
Welfare = Cost of the Bridge
Price/Fee
Demand/Users Value
# of users

16. 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

17. 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
LOST VALUE
FEE
# of users

18. Impure Public Goods Anything with a positive consumption externality.
Congested goods: Roads
Club Goods: Excludable with congestion = Museum
Local Public Goods: Parks, libraries etc.

19. Efficient Provision of Public Goods
How much Public Goods should the Government provide?
Marginal Benefit of the Public Good
MC of the PG

20. Marginal Benefit Non-Excludable Marginal Benefit =
Marginal Benefit1 + Marginal Benefit2 + …
+ Marginal BenefitN
= S Marginal Benefiti

21. 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)

22. 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

23. Right Mix if MB(public good) = MB(private good)
MC(public good) MC(private good)

24. Equivalently
S MU(pg) = MUi
MC(pg) MC

25. Equivalently
MU(pg) = MUi
MC(pg) MC S

26. Equivalently
MU(pg) = MUi
MC(pg) MC S

27. Equivalently
MU(pg) = MC(pg)
MUi MC S

28. S MRS = MRT Equivalently
This is called the Samuelson Condition after Paul Samuelson who first noticed it applied.

29. Mechanisms for Efficiently Providing the Public Good
How do you get to provide people with the right quantity of the public good if:
When it is provided at zero MC people will tend to overstate their desire for it.
When it is provided at positive MC people will tend to understate their desire for it hoping to free ride.

30. Mechanisms for Efficiently Providing the Public Good
How do you get to provide people the right quantity of the public good if:
When it is provided at zero MC people will tend to overstate their desire for it.
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.

31. 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.)

32. 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)

33. 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.

34. 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.)

35. 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*

36. 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.

37. 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.

38. 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

39. 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

40. 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

41. 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.

42. 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 =0.
To ensure I get this positive utility should then report truthfully.

43. Clark-Groves Mechanism
Properties:
Optimal to tell the truth
Voter only pays when decisive.
Payments < benefits received
As population grows less of a problem with excess revenue.