1. Department of Economics
PUBLIC GOODS
E. Nketiah-Amponsah
Department of Economics
Room W.18

2. Learning Objectives After this discussion, you should be able to;
Explain what a public good is and its characteristics
Explain the difference between pure public goods and pure private goods
Derive the demand curve for a pure pubic good and explain how it differs from the demand curve for a pure private good
Determine the conditions for efficient allocation of a pure public good
Explain why market provision of the good is likely to be inefficient
Analyse the free rider problem

3. Introduction
What are public goods? What is the rationale for its provision?
Can’t the private sector efficiently provide these goods (public goods?
Are they necessarily provided by the public sector?
Examples of such public goods are (public) roads, national defense, policing (protection), street lights and state weather forecast
Also flood control, fire protection, pollution abatement could all be regarded as examples of public goods.

4. Classification of Goods
Goods and services can be divided into four main categories:
Pure private goods
Pure public good
Quasi-Public goods
-The price-excludable public goods
-Congestible public goods
Open-access goods
Rival but nonexclusive
Fish in the ocean are rival in the sense that once caught they are not available for others to catch
Nonexclusive in the sense that it would be costly or impossible for a private firm to prevent access to these goods

5. Private Goods Private goods have two important attributes:
They are rival in consumption – the amount consumed by one person is unavailable for others to consume.
They are exclusive – suppliers can easily exclude those who don’t pay
Private goods are not necessarily provided exclusively by the private sector. -- Medical services and housing-- merit goods -- who decides on merit goods? Are these goods just a case of trying to repeal the laws of economics ?
Public provision of a good does not necessarily mean that it is also produced by the public sector.--street sweeping, refuse collection/sanitation are publicly provided services in Ghana but increasing provided by private firms such as ZoomLion Gh Ltd, Honest Waste etc

6. Quasi-Public goods
Congestible public goods are those for which crowding or congestion reduces the benefits to the existing consumers when more consumers are accommodated. The marginal cost of accommodating an additional consumer is not zero after the point of congestion is reached.
For example, an additional user of a congested road decreases the benefits to existing users by slowing down traffic and increasing the risk of accident.

7. Quasi-Public goods
Price-excludable public goods are those with benefits that can be priced. Private clubs are an example of price-excludable public goods. Membership rights, which are sold in the market, are sometimes negotiable and can be sold by their holders to others. The dues ration the facilities of the club to avoid the effects of congestion.
Club Goods: Excludable with congestion: Museum, Golf club, Tennis Club, Football Club etc
Other Quasi Public Goods: Parks, libraries e tc.
Other price-excludable public goods include such public facilities as schools and hospitals. These goods can be priced, but that provision results in positive externalities. These goods are sometimes referred to as mixed goods because they are partly public goods and partly private goods. Education is a key example.

8. Public Goods- Sampled Definitions
“Public goods (social or collective goods) are goods that are nonrival in consumption and/or their benefits are nonexcludable”.
Public goods have characteristics that make it difficult for the private sector to produce them profitably (market failure).
“Public goods are goods that can be jointly consumed by a number of consumers without reducing any one consumer’s ability to enjoy that consumption
“Public goods are goods or services that can be consumed by several individuals simultaneously without diminishing the value of consumption to any one of the individuals.
“Goods with benefits that cannot be withheld from those who do not pay and are shared by a large groups of consumers are public goods”
Caveat ??? : A number of things that are not conventionally thought of as commodities have public goods characteristics. MIT economist Lester Thurow considers income distribution as a public good. Why?? What about honesty?

9. Features/Characteristics of Public goods
Public goods are better described by their two prominent features or characteristics
Nonrival in consumption
One person’s consumption does not diminish the amount available to others
Once produced, public goods are available to all in equal amount
Marginal cost of providing the good to additional consumers is zero
Non-rivalness arises from the indivisibility of public goods
Nonexcludable
Once a public good is produced, suppliers cannot easily deny it to those who fail to pay  it is nonexclusive
Because they are nonrival and nonexclusive, for-profit firms cannot profitably sell public goods. Why???
In most cases, it is also infeasible to price units of public goods.
Nonexclusion implies that it is too costly to develop a means of excluding those who refused to pay from enjoying the benefits of a given quantity a public goods.
On efficiency consideration, it is inefficient to exclude additional consumers since the MC of admitting them is zero (o)

10. Other Minor Features of PGs
Indivisibility
Non-rejectable

11. Issues Arising from the Definition(s) of PGs
Given that people can enjoy the benefits of public goods whether they pay for them or not, they are usually unwilling to pay for them. This is referred to as the free-rider problem
A free rider is a person who seeks to enjoy the benefits of a public good without contributing anything to the cost of financing the amount made available.
Provision of goods/services financed by a voluntary fee paid by neighborhood residents (examples private trash collection, drinking water) faces the classic free rider problem.
-Goods that suffer from this free rider problem are known in economics as public goods.
The larger the group, the more severe is the free-rider problem, and hence the more likely it is that a public good could not be financed by voluntary contributions. With a larger group, the less likely a pure public good will be supplied through a strictly voluntary arrangement even if marginal social benefits exceed marginal social cost.
-Public goods provide an economic justification for government intervention in the market

12. Issues Arising from the Definition(s) of PGs
The drop-in-the-bucket problem is another problem intrinsic to public goods: The good or service is usually so costly that its provision generally does not depend on whether or not any single person pays.
-Public goods are usually made available politically through the ballot box as people vote to decide how much to supply rather than through the marketplace, where those who care to pay the price can buy as much as they like for their own exclusive use

13. Consequences/Implications
Non-excludable:
Very difficult for the private sector to provide it and make a profit (very difficult to prevent non-contributors from consuming it).
When an investment has a personal cost but a common benefit, individuals will underinvest (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.)

14. 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

15. Rival vs Non-Rival

16. Optimal Provision of Public Goods-Partial Equilib. Analysis
The analysis of demand for a pure public good is different from the demand for a pure private good.
The market demand curve for a pure private good involves the summation of the quantities demanded by all consumers at each possible price per unit of the good (horizontal summation).
For any given price, a point on the market demand curve for a pure private good is found by simply adding the quantity that each individual would purchase at that price.
The individual demand curves therefore are added laterally over the horizontal axis to obtain the market demand curve

17. Optimal Provision of Public Goods-Partial Equilib. Analysis
For a pure public good, all consumers must consume the same quantity of the good. Purchasers of a pure public good would not be able to adjust their consumption of that good.
A pure public good cannot be priced because of its nonexclusion property. Under such circumstances, how can a demand curve for a pure public good be derived?

18. Optimal Provision of Public Goods
With private goods, consumers decide what quantity to buy; market demand is the sum of those quantities at each price.

19. Optimal Provision of Public Goods
With public goods, there is only one level of output, and consumers are willing to pay different amounts for each level.
The market demand for a public good is the vertical sum of the amounts that individual households are willing to pay for each potential level of output.

20. Optimal Production of a Public Good
Optimal production of a public good means producing as long as society’s total willingness to pay per unit D(A+B) is equal to the marginal cost of producing the good.

21. Case Study: Market for Public Goods
Da and Dm are the demand curves reflecting the marginal benefits that Edna and Maina, respectively, enjoy at each rate of output
How many boreholes should the government provide?
Suppose the marginal cost of spraying is a constant GH¢15000 per decade, the efficient level of output is 2 boreholes decade, where the marginal benefit to the neighborhood equals the marginal cost D
5000 2 e
Marginal
cost
10000
15000 Da
Ghana Cedis per borehole Dm D
Number of boreholes constructed

22. Should the Government Produce the public goods it provides?
To answer this question, we need to make certain assumptions:
Publicly and privately provided goods are inputs into the production of some output that people desire.
What ultimately matters to people is the level of output and not the particular inputs used to produce it.
What then are the criteria that should be used to select the amount of each input?
Relative wage and material costs: If the public and private sectors pay differing amount for labour and other inputs, the less expensive sector is preferred on efficiency grounds, all things being equal.
Administrative Costs: Under public provision, any fixed administrative cost can be spread over a large group of people.

23. Should the Government Produce the public goods it provides?
Diversity of taste: individuals/society have diverse tastes. Individuals will either prefer public or private provision. The choice of society should reflect their preferences. For example, people who keep jewels in their homes may value property protection more than those who do not.
Distributional Issues: Society’s notion of fairness may require that some commodities be made available to everyone (this idea is sometimes referred to as commodity egalitarianism)

24. Public Provision of Public Goods
How Can We Measure Preferences for the Public Good?
Preference revelation: individuals may not be willing to tell the government their true valuation because the government might charge them more for the good if they say that they value it highly.
Preference knowledge: even if individuals are willing to be honest about their valuation of a public good, they may not know what their valuation is, since they have little experience pricing public goods such as highways or national defense.
Preference aggregation: how can the government effectively put together the preferences of millions of citizens in order to decide on the value of a public project?
These difficult problems are addressed by the field of political economy, the study of how governments go about making public policy decisions, such as the appropriate level of public goods.

25. Optimal Provision of Public Goods
Efficient approach would be to impose a tax on each resident equal to marginal valuation
Once people realize their taxes are based on how much the government thinks they value the good, people tend to understate their true valuation
Taxpayers are reluctant to offer this information, creating what is called the free-rider problem
Even if the government had accurate information about marginal valuations, some households earn much more than others  a greater ability to pay taxes
Taxing people according to their marginal valuations may be efficient, but it may not be considered fair or equitable

26. Optimal Provision of Public Goods-G. E. A
General Equilibrium analysis relaxes the ceteris paribus assumption and extend the problem to a situation in which there are many public and private goods. Both the consumption and production sides of the economy are captured.
To derive pareto-efficient provision of private and public goods, the following assumptions are required
There are 2 commodities available for final consumption of a private good X and a public good G.
There are 2 consumers, A and B.
A given production possibilities set
The taste of the two consumers are given
The problem is to solve for the system for a set of efficient relative prices and outputs for the two goods X and G.

27. Optimal Provision of Public Goods-G. E. A
The basic condition for the optimum supply of a public good is that:
The sum of the marginal rates of substitution between the public good (and some private good) must equal the marginal rate of transformation (∑MRS = MRT)
The intuitive interpretation of these conditions for full optimum is that the benefit of an extra unit of a public good is the benefit that person 1 gets, plus the benefit that person 2 gets and so on…
In contrast, an extra unit of a private good is either given to person 1 or given to person 2.
The solution may be illustrated diagrammatically for the case where there are two individuals and two goods X (private) and G (public)

28. Optimal Provision of Public Goods-G. E. A
Therefore, the optimal provision of a PG must be such that
This condition is referred to as the Samuelsonian condition for public goods
Note that for a private good say X and Y, the optimal condition is given as;

29. Optimality Condition in Terms of Efficiency Pricing
Thus

30. Optimality Condition in Terms of Efficiency Pricing
The Samuelsonian condition is the aggregation of the prices paid by all individuals for the provision of public goods which is equal to the Marginal Rate of transformation. Therefore, pareto efficient supply of public good requires a set of individualized prices, the sum of which equals the MC of the Public Good.

31. Example
Consider three neighbours Ernest, Kingsley and Wiafe who plan to provide street lights in their local community. Their inverse demand functions are given by;
Pe = 100 – Q
Pk = Q
Pw = 120 – 3Q
Where Pe, Pk and Pw are the demand functions of Ernest, Kingsley and Wiafe respectively, whilst Q is the quantity of street lights provided. Also, the marginal cost is given by MC=2Q+80
First suppose that Ernest, Kingsley and Wiafe can prevent each other from enjoying the street light that each of them produces. What is the efficient number of street lights provided by each in this case?
Now assume that it is impossible to exclude neighbours from benefiting from the street light project, what is the efficient number of street lights that will be provided in this case?

32. Home work??? (b). For a public good Pe + Pk +Pw = MC
Solution
Home work???
(b). For a public good
Pe + Pk +Pw = MC
(100-Q) + (100-2Q) + (120- 3Q) = 2Q+80
320 – 6Q = 2Q + 80
8Q = 240
Q* = 35units

33. Pareto efficiency and public good: the Left Over Curve
For a detailed description of the Leftover Curve, see PDF attachment accompanying the slides

34. Pareto efficiency and public good: the Left Over Curve
From the above diagram;
MRT – MRSi = MRSj
MRT = MRSi + MRSj

35. Conclusion
A major function of governments at all levels is the provision of public goods. In some cases, the private sector can provide public goods, but in general it will not achieve the optimal level of provision.
When there are problems with private market provision of public goods, government intervention can potentially increase efficiency.
Whether that potential will be achieved is a function of both the ability of the government to appropriately measure the costs and benefits of public projects and the ability of the government to carry out the socially efficient decision.
An efficient provision of a public good involves satisfying the Samuelsonian condition.

36. Exercises Take home assignment 2
Carefully discuss the problem of free-ridership in the context of resource allocation in a least developed country such as Ghana. Suggest three innovative ways of dealing with the problem of free- ridership.
Hint: Richard L. Stroup (2000). Free Riders and Collective Action Revisited. The Independent Review, v.IV, n.4, pp. 485– 500
Due Date: ?????