1. Lecture 3 Public Goods and Government intervention
Suggested Readings: Connolly & Munro, The economics of the public sector, chapter 4

2. Market failures
Market failures occur when prices do not fully reflect either the marginal social benefits or costs
such failures provide scope for political interaction
how does this happen?
Potential sources of market failure
Public Goods

3. Public Goods Introduction
In market economies, private suppliers provide the majority of goods and services to consumers. However, certain goods are publicly provided. These include for example defense, education, and health. Why does the government instead of the market provide these goods? Which characteristics differentiate goods that are privately provided from goods that are publicly provided? How do we define public goods?
The terminology might induce the conclusion that public goods are good that are publicly provided as opposed to private goods. This conclusion is simply WRONG! The public or private nature of the good is an intrinsic characteristic of goods that is not related to the provider of the good
Hence, it may well be that the state provides a private good or that the market provides a public good.

4. Public Goods When is a good public? Definition:
A pure public good is a good that has two characteristics
NON-EXCLUDABLE
NON-DEPLETABLE (NON-RIVAL, NO-CONGESTION)
Non excludability: once the good is provided, it is not possible to prevent any individual (even individuals that eventually have not paid to access the good!) from using the good. The reason for non-excludability could be for example that is technically impossible to check who is using the good or that the cost of monitoring the use of the good is so high that “de facto” monitoring does not take place
Non-depletability (non rivalness): the fact that some people are using the good doesn’t not prevent other people from using the same good. In other words, the consumption by one person doesn’t reduce the quantity available for the consumption of other individuals
When a good has these two characteristics, i.e. is non-excludable and non-depletable, then it is a pure public good. On the other hand, if a good is excludable and depletable, then the good is a private good. Finally, you have some good that possess just one of these properties.

5. Public Goods

6. Public Goods Pure public goods: street light defense air
radio emissions

7. Public Goods
What are the implications of non-excludability and non-rivalness?
Let’s compare a pure private good (X) and a pure public good (G)
Suppose that X=1 and G=1
Suppose there are two consumers: Anne and Bill
Who consumes X?
Who consumes G?

8. Public goods versus Private Goods
Since X is excludable and rival, either Anne or Bill will consume it (it cannot be consumed by both!). Hence, the consumer that values the good the most (i.e. the consumer who is willing to pay the highest price) will consume X.
With the public good this is not the case

9. OPTIMAL PUBLIC GOOD PROVISION
To provide optimally G, we need to take into account that G is simultaneously consumed by Anne and Bill, i.e. we need to take into account that each unit of G is going to increase the utility of both agents!
Social Marginal Benefit as opposed to Private Marginal Benefit!

10. Market Failure Can the market provide efficiently public goods?
Private provision through voluntary contributions
examples: charity, private security
naively following own demand curves can lead to over or under provision

11. Marginal benefit and demand curve for public goods
Marginal Cost
Marginal cost 15
Optimal provision of Public good 10
No provision of public good 10 5 5
Individual marginal benefit
Social marginal benefit 10
7.5
7.5 10

12. Strategic contributions
contributors are not naïve – they observe and react to others’ behavior so act strategically
Suppose that the student union decides to buy a new big TV screen (let’s say to watch soccer or cricket!) and every member of the student union declares that he will really enjoy a new big screen!. To purchase the TV screen the union relies on the voluntary contributions of each member of the student union. Once the TV screen is bought, each member of the student union has access to the TV independently on the fact that he has contributed or not to the purchase of the TV.

13. Strategic contributions
The TV screen is in other words a public good for the members of the student union since it is
non-excludable (no member can be prevented from watching the TV)
non-rival (the fact that one member watches the TV does not prevent other members from watching it)
Question: assuming that you care about watching the next World Cup (or something better!) will you contribute to buy the TV screen?

14. Strategic contributions
Let’s give some numerical values
Suppose that the cost of the TV is £100. Suppose that if two people contribute they will each pay $50. On the other hand if just one person contributes while the other refuses to pay, then she will pay the entire cost of £100. If nobody contributes, the TV is not bought. Let’s assume that the benefit for each individual from watching the TV in monetary terms is £75, on the other hand if the TV is not bought their payoff is just zero.
Let’s write down the payoffs of the contribution game

15. Payoffs

16. The free-rider problem
This is an example of prisoner dilemma. The two individuals would clearly be better off contributing but they end up not contributing!
Why do we obtain this result?
This result is related to the public nature of the good. Because the good is non-excludable and non-rival, there is a strategic interdependence in the contribution decision of the two players.
Loosely speaking, consider what individual 1 is thinking when he has to decide whether or not to buy the TV
if he buys the TV, he cannot prevent individual 2 from using the TV
if individual 2 buys the TV, he can use it for free
and similarly for individual 2!
Hence, although each individuals enjoys having the TV, since each would enjoy it much more to use it for free, then they end up having no TV!
This is known as the free-rider problem

17. The free-rider problem
The essence of the free-rider problem is that the contribution by one player is an exact substitute for the contribution of the other player. Therefore, each player tries to exploit the contribution from the other in order to obtain the good for free. As each player is reasoning in the same way, the result is that none of the players will voluntary contribute!
In this example, where the quantity of the good is discrete (either the good is provided or it is not provided), if we rely on voluntary provision the good is not provided. In general, if we consider a continuos case, then the outcome will be that a sub-optimal quantity of public good is provided. It can also be shown that the free-riding problem becomes more severe as the number of players increases

18. The free-rider problem
To overcome the free rider problem, co-operation or co-ordination of society is required.
Obstacle one – enforcement is needed to implement this behavior
repeated interaction with tit-for-tat punishments
government activity or centralized decision making such as compulsory taxation or regulation

19. Welfare
We have learned that when a good is public, because of strategic interdependence, the quantity of the public good provided by voluntary contributions is not Pareto-efficient.
This is equivalent to say that if we rely on the market to provide the good, then the outcome is not efficient.
This is an example of market failure
Is there a way to solve the market failure?

20. Government Intervention
The government considers the utility of all the individuals in the society “jointly”, chooses the level of public goods that maximises the social surplus and introduces a tax to finance the public good.
Therefore, if the government knows the preferences of each individual, he can provide efficiently the public good
This is not particularly difficult if all individuals have the same preferences (for example, if you all enjoy in the same way watching the TV at the student union)

21. Government Intervention
However, individuals typically are heterogeneous in their preferences for goods
How should the government choose the quantity of public good if individuals have different tastes?
Suppose that g is the public good and c(g) is the cost of providing the public good. Let’s denote U1(g) the benefit for individual 1 from using g and U2(g) the benefit for of individual 2.

22. The Samueson Rule
The social surplus is the sum of the utilities of the two individuals, minus the cost of provision of the good. The government has to decide the optimal level of g, that is the level of g that maximises the social surplus:
Social surplus : U1(g)+U2(g)-C(g)
the optimal g is reached when the marginal benefit is equal to the marginal cost. Note that, since we are not considering one individuals, but several, then the optimal g is reached when the sum of the marginal benefit of the individuals is equal to the marginal cost (Samuelson rule)
U’1(g)+U’2(g)=C’(g)
Samuelson rule: the optimal quantity of g is such that the sum of the marginal evaluation of the goods for the two individuals is equal to the marginal cost of the good.

23. Samuelson Rule and Pareto frontier
The social surplus maximising outcomes can be represented graphically using the Pareto-frontier (remember the frontier of UPS from last lecture).
We can represent all the levels of net utilities that can be achieved choosing different levels of g.
Every point on the frontier satisfies the Samuelson rule. Therefore, the Samuelson rule does not determine a precise outcome (doesn’t pick a specific point on the frontier).

24. Utility possibility frontier (UPF)UB • A 45 • B • M UA

25. Mechanism of collective decision making
How is a point on the frontier actually chosen?
To choose a precise point we need to specify some type of collective choice rule
Ex1: the government has some welfare function (i.e. a function that gives a precise weight to each individual in the society) and he chooses a point according to this welfare function. Then depending on the weight he gives to each individual, he can choose a different point
Ex2: there is some political mechanism, like majority voting to decide

26. Local public goods and the Tiebout Mechanism
Individuals vote with their feet
If there are as many communities as there are types, then efficiency will result
Argument is related to club solutions to public goods
This mechanism relaxes assumption somewhat on excludability

27. Aggregation of preferences
If there are not as many communities as types, individuals with different preferences have to find a way to undertake decisions affecting the entire group
Group preferences and group choice

28. Questions (prepare and answer all questions before next week seminar)
Which one of the following goods is a pure public good?
Health care
Roads
Education
Radio emission
Wireless
Suppose that Anne and Bill have agreed to buy a new dishwasher for their house. Bill values the dishwasher more than Anne and he would be willing to pay up to £300 pounds for a new dishwasher, while Anne is willing to spend up to £150. They finally agree to buy a dishwasher whose cost is £250. If both of them contribute, they will share equally equally the cost of £250. If one of them refuses to contribute, the other will pay the entire cost. If none of them contributes they will not buy the dishwasher. Will Anne contribute? Does your answer change if we assume that Anne and Bill both are willing to pay up to £160 for the dishwasher? Explain whether the Nash equilibrium in both cases is Pareto-efficient and discuss whether a compulsory contribution scheme would be welfare improving.