1. Jonathan Gruber Public Finance and Public Policy
Chapter 7 Public Goods
Jonathan Gruber
Public Finance and Public Policy
Aaron S. Yelowitz - Copyright 2005 © Worth Publishers

2. Introduction
Some markets do not work very well because the good in question has public good characteristics to it.
For example, in Dhaka, Bangladesh, public trash collection is fairly inefficient, but attempts at privatization have not fared any better.
The key problem with private collection of garbage is the free rider problem–with a private, voluntary system, each resident could simply sneak his garbage into his neighbor’s garbage and avoid making payments.

3. Introduction
Eventually, everyone would figure this out, and no one would be willing to pay trash collection voluntarily.
In fact, most residents have figured out the incentive to “free ride.” Only 50 of 1,100 neighborhoods have private garbage collection, however.

4. Introduction
This lesson explores the role of government in providing goods like this, and shows that the private sector tends to underprovide them.
It also explores the notion of “crowd-out” where public provision simply substitutes for already existing private provision of a good.

5. Introduction
The role of public goods is important in economics. The subsequent lessons explore issues related to:
Cost-benefit analysis
Political economy
State and local government
Education

6. OPTIMAL PROVISION OF PUBLIC GOODS
Pure public goods have two traits:
They are non-rival in consumption: The marginal cost of another person consuming the good is zero, and does not affect your opportunity to consume the good.
They are non-excludable: There is no way to deny someone the opportunity to consume the good.
Table 1 gives some examples.

7. Defining pure and impure public goods
Ice cream is rival, because my consumption of it precludes you from consuming the same ice cream. The only way for you to consume it is to make more ice cream.
Ice cream is also excludable, because I can simply not share my ice cream with you.
If a good is both rival and excludable, it is a private good.
This table shows examples of pure public goods, impure public goods, and private goods.
It is excludable, since the cable company can simply refuse to hook up the system.
Some goods are “impure” public goods because they are non-rival, but they are (to some extent) excludable.
Cable TV is non-rival, because my consumption of it in no way diminishes your consumption.
Table 1
Yet it is non-excludable because it is clearly very difficult to prohibit pedestrians from using the sidewalk.
For example, a crowded sidewalk is rival because your enjoyment is reduced as more pedestrians also use the same sidewalk.
Other goods are “impure” public goods because they are rival, but not excludable.
It is also non-excludable, because once an area is protected, everyone “consumes” that protection.
National defense is a classic example. It is non-rival because my consumption of national defense protection does not diminish your consumption of it.
Finally, pure public goods are both non-rival and non-excludable.
Defining pure and impure public goods
Is the good rival in consumption?
Yes No
Is the good
excludable?
Ice cream
Cable tv
Crowded city sidewalk
National defense

8. OPTIMAL PROVISION OF PUBLIC GOODS
It is helpful to think of public goods as goods with a large, positive externality.

9. Optimal Provision of Private Goods
Consider a private good, like ice cream.
Figure 1 shows the market for ice cream cones, assuming that the alternative use of the money is buying cookies at $1 each.
This makes cookies the numeraire good.

10. At a price of $3, neither person demands much ice cream.
Adding up Ben’s and Jerry’s individual demands at each price gives society’s demand.
At a price of $3, neither person demands much ice cream.
Ben has an individual, downward-sloping demand curve for ice cream.
Price of ice cream
Adding up Ben’s and Jerry’s individual demands give society’s demand at $3.
S=SMC
Jerry also has an individual, downward-sloping demand curve for ice cream.
At a price of $2, both people demand more ice cream.
Leading to a competitive equilibrium at $2. Ben & Jerry consume different quantities.
Adding up Ben’s and Jerry’s individual demands give society’s demand at $2. $3
There is a market supply curve associated with producing ice cream. $2
DJERRY
DBEN
SMB =DBEN+JERRY
QJERRY
QBEN
QTOTAL
Quantity of ice cream
Figure 1
Demand for a private good

11. Optimal Provision of Private Goods
In this figure, as price adjusted, each person changed his quantity consumed.
For a private good, consumers demand different quantities at the same market price.

12. Optimal Provision of Private Goods
We can also represent this relationship mathematically. Ben has preferences over cookies (C) and ice cream (IC):
As does Jerry:

13. Optimal Provision of Private Goods
Utility maximization requires that each of their indifference curves is tangent to the budget constraint. For Ben, we have:
For Jerry we have:

14. Optimal Provision of Private Goods
Recall that in equilibrium, the price of ice cream is $2, and the price of cookies is $1 (because it is the numeraire good).
In equilibrium each person must be indifferent between trading two cookies to get one ice cream.

15. Optimal Provision of Private Goods
On the supply side, ice cream cones are produced until the marginal cost equals the marginal benefit, which equals the price in a competitive market.
Recall that PC=$1, meaning:

16. Optimal Provision of Private Goods
The private market equilibrium in this case is socially efficient.
The MRS for any quantity of ice cream equals the SMB of that quantity–the marginal value to society equals the marginal value to any individual in the perfectly competitive market.

17. Optimal Provision of Public Goods
Now consider the tradeoff between a public good, like missiles, and a private good like cookies.
Figure 2 shows the market for missiles, assuming that the alternative use of the money is buying cookies at $1 each.

18. There is a market supply curve associated with producing missiles
Price of missiles
Adding up Ben’s and Jerry’s willingness to pay gives society’s demand for 1 missile.
Adding up Ben’s and Jerry’s willingness to pay for each quantity gives society’s demand.
As does Jerry. $6
There is a market supply curve associated with producing missiles
Leading to a competitive equilibrium at 5 missiles. Ben & Jerry consume the same Q.
Adding up Ben’s and Jerry’s willingness to pay gives society’s demand for the 5th missile.
Ben has a downward sloping demand curve for missiles.
While Jerry’s willingness to pay for the first missile is $4.
Ben’s willingness to pay for the first missile is $2.
S=SMC $4
DJERRY
While Jerry’s willingness to pay for the fifth missile is $2.
Ben’s willingness to pay for the fifth missile is $1. $3 $2 $2
SMB=DBEN+JERRY
DBEN $1 1 5
Quantity of missiles
Figure 2
Demand for a public good

19. Optimal Provision of Public Goods
Unlike the case of private goods, where aggregate demand is found by summing the individual demands horizontally, with public goods, aggregate demand is found by summing vertically.
That is, holding quantity fixed, what is each person’s willingness to pay?

20. Optimal Provision of Public Goods
We can also represent this relationship mathematically. Ben has preferences over cookies (C) and missiles (M):
As does Jerry:

21. Optimal Provision of Public Goods
To Ben, the marginal missile is worth:
For Jerry, the marginal missile is worth:

22. Optimal Provision of Public Goods
The social marginal benefit (SMB) of the next missile is the sum of Ben and Jerry’s marginal rates of substitution:
Where “i” represents each person in society.

23. Optimal Provision of Public Goods
The social marginal cost (SMC) is the same as earlier: the marginal cost of producing a missile:
Efficiency therefore requires:

24. Optimal Provision of Public Goods
That is, social efficiency is maximized when the marginal costs are set equal to the sum of the marginal rates of substitution (rather than each individual’s MRS).
This is because the good is non-rival. Since a unit can be consumed by all consumers, society would like the producer to take into account all consumers’ preferences.

25. PRIVATE PROVISION OF PUBLIC GOODS: Private-sector Underprovision
In general, the private sector underprovides public goods because of the free rider problem.
Consider two people, Ben and Jerry, and two consumption goods, ice cream and fireworks.
Set the prices of each good at $1, but fireworks are a public good. Assume that Ben and Jerry have identical preferences.

26. Private-sector Underprovision
Ben and Jerry benefit equally from a firework that is provided by either of them.
What matters is the total amount of fireworks.
Each person chooses combinations of ice cream and fireworks in which his own MRS equals the ratio of price.

27. Private-sector Underprovision
For both Ben and Jerry, they set:
Whereas optimal provision requires:

28. Private-sector Underprovision
With identical preferences:
Recall that marginal utilities diminish with increasing consumption of a good.
In this example, optimal provision would require that fireworks are consumed until their utility equals half the marginal utility of ice cream.
Thus, each individually buys too much ice cream privately.

29. The Free Rider Problem in Practice
Application
There are some interesting examples of the free-rider problem in practice.
Only 7.5% of public radio listeners in New York contribute to the stations–that is, there is a lot of free-riding. In the United Kingdom, the BBC charges an annual licensing fee for all television owners.
Many users of file sharing services never contribute uploaded files; they only download files. Some of these services, like Kazaa, give download priority to those who contribute.

30. When Is Private Provision Likely to Overcome the Free Rider Problem?
While the free-rider problem clearly exists, there are also examples where the private market is able to overcome this problem to some extent.
But the private market may still fall short of the socially optimal amount.

31. Can Private Providers Overcome the Free Rider Problem?
Examples of private provision of a public good:
Privately financed fireworks displays.
Privately owned British lighthouses until 1842.

32. Business Improvement Districts
Application
A final example concerns business improvement districts (BID).
The quality of city streets is a public good.
During the 1980s, New York City’s Times Square had high crime and many social problems. The city had given up on cleaning up Times Square.
In 1992, local businessmen started a BID–a legal entity to provide security and sanitation, with fees collected from local businesses.
New York law makes participation of businesses compulsory if BID organizers can get 60% of local businesses to join, allowing the organizers to overcome the free-rider problem.
The BID was a clear success in New York City.

33. Business Improvement Districts
Application
On the other hand, Massachusetts law allows businesses to “opt-out” of a BID within 30 days of the BID approval by the local government.
This deters formation of BIDs in the first place, because there are fixed costs of doing so.
As a consequence, only 2 BIDs have been formed in Massachusetts.

34. When Is Private Provision Likely to Overcome the Free Rider Problem?
Under what circumstances are private market forces likely to solve the free rider problem?
Intense preferences.
Altruism.
Utility from one’s own contribution to the public good.

35. Some individuals care more than others
When some individuals have especially high demand for a public good, private provision may emerge (but not necessarily provide efficiently).
The key intuition is that the decision to provide a public good is a function of the enjoyment that the individual gets from the total amount of the public good, net of cost.
If a person gets a lot of enjoyment, or has a lot of money, he will choose to purchase more of the public good even though it benefits others.

36. Some individuals care more than others
Olson and Zeckhauser (1966) studied the financing of NATO, which was a voluntary organization at the time.
Although countries had an incentive to free-ride on the contributions of others, the largest nations (such as the United States) did contribute.
Higher incomes or stronger tastes can mitigate the free rider problem to some extent, but are unlikely to solve it completely. Thus, underprovision is still likely to occur.

37. Altruism
Another reason is that there is evidence that many individuals are altruistic, caring about the outcomes of others as well as themselves.

38. Altruism
Laboratory experiments are becoming more popular in the economics profession.
Some experiments examine the incentive for college students to contribute to a pool of money, where the dominant, self-interested strategy should be to not contribute.
The experiments suggest that between 30% and 70% of participants contribute to the public good.
As the experiment is repeated in multiple rounds, contributions fall, but rarely reach zero contributions.

39. Private Provision of Public Goods: When is private provision likely to overcome the free rider problem ?
Of course, these experiments may be of limited applicability to the real world:
Individuals may behave differently in a contrived laboratory setting.
The stakes are often small, so the cost of being altruistic is low.
College undergraduates may not be representative of the population more generally.

40. Private Provision of Public Goods: When is private provision likely to overcome the free rider problem?
On the other hand, some real-world evidence is consistent with altruism in private support of public goods.
Brunner (1998) found that the number of public radio listeners who contribute decreases only modestly as the total number of listeners increases.

41. Warm glow
A final reason is that that individuals may provide for a public good is due to warm glow.
The warm glow model is a model of public good provision in which individuals care about both the total amount of the public good and their particular contributions as well.
For example, they may get some psychological benefit from knowing they helped a worthy cause.
In this case, the public good becomes more like a private good, though it does not fully solve the underprovision problems.

42. PUBLIC PROVISION OF PUBLIC GOODS
In principle, the government could solve the optimal public goods provision problem and then either provide the good directly or mandate individuals to provide the amount.
In practice, three problems emerge:
Crowd-out.
Measuring costs and benefits.
Determining the public’s preferences.

43. Private Responses to Public Provision: The Problem of Crowd-Out
In some cases, the private market may already be providing a socially inefficient level of the private good.
In this case, public provision may crowd-out some of the private provision–as the government provides more of the public good, the private sector provides less.

44. Private Responses to Public Provision: The Problem of Crowd-Out
For example, in the fireworks example with Ben and Jerry, if one assumes:
Ben and Jerry care only about the total number of fireworks provided.
Government provision will be financed by charging equal amounts to each of them.
And the government provides no more fireworks than were being provided privately beforehand.
Then each dollar of public provision will crowd out private provision one-for-one.

45. Private Responses to Public Provision: The Problem of Crowd-Out
The full crowd-out in the fireworks example is rare, though partial crowd-out is much more common and can occur when:
People who don’t contribute to the public good are taxed to finance its provision.
Or when individuals derive utility from their individual contributions as well as the total amount of the public good provided.

46. Private Responses to Public Provision: The Problem of Crowd-Out
If noncontributors are forced to help pay for the good (but it is still below the social optimum), then the contributors’ effective income levels are higher than before.
As a result of this income effect, contributors buy more if the public good is a normal good, offsetting the crowd-out to some extent.

47. Private Responses to Public Provision: The Problem of Crowd-Out
Alternatively, as discussed previously, there may not be full crowd-out if an individual cares about his own contributions (the warm glow model).
In this case, an increase in government contributions will not fully crowd out giving.

48. Public Provision of Public Goods: Measuring the costs and benefits of public goods
Another problem for government provision is measuring costs and benefits of the public good. This entails the field of cost-benefit analysis, discussed in the next lesson.
For example, improving a highway involves valuations of commuting time saved as well reduced traffic fatalities.

49. How Can We Measure Preferences for the Public Good?
Finally, our model of optimal public good provision assumes the government knows each person’s preferences over public and private goods.
In practice, this runs into problems with preference revelation, preference knowledge, and preference aggregation.
These issues are addressed in the field of political economy.

50. Recap of Public Goods Optimal provision of public goods
Private provision
Public provision