[PD - One of the major reasons the market fails is because many things that provide us with valuable services have at least some "public" good characteristics. When we think of most goods and services, we tend to think of things like shoes (i) that we can own individually (and exclude others from using them) and (ii) get consumed away as we use them (and would disappear faster if others could use them!). However, there are many types of goods and services that don't have these "private" features.]

PUBLIC GOODS

Why does the government provide certain goods and services such as a legal system, a system of national defense, schools and highways, and public health services? Why don't we simply leave the provision of these goods and services in the hands of private firms that sell their output in markets? How much national defense would we have if a private firm, Star Wars Inc., had to compete for our dollars in the marketplace in the same way as McDonald's and Coca-Cola do?

Most of the answers to these questions lie in the distinction between private and public goods.

Private Goods and Public Goods

A private good is a good or service each unit of which is consumed by only one individual. An example of a private good is a bottle of beer. There are two important features of a private good. The first feature is called rivalry. Rivalry emphasizes the idea that one person's consumption can take place only at the expense of another person's. If you increase your consumption of beer by one bottle, other things being equal, someone else has to consume one bottle less. The second feature of a private good is called excludability. Once you have bought a bottle of beer, the beer is yours to do with as you choose. You can exclude others from using it.

A pure public good is a good or service each unit of which is consumed by everyone and from which no one can be excluded. An example of a pure public good is the national defense system. There are two important features of a pure public good that parallel the two features that we identified concerning a private good. The first feature is called nonrivalry. One person's consumption of a pure public does not reduce the amount available for someone else. For example, your consumption of the security provided by a national defense system does not decrease the security of anyone else. The second feature is called nonexcludability. No one can be excluded from the additional security that every citizen enjoys from the national defense system.

Many goods lie between a pure public good and a private good. Such goods are called mixed goods. An example of a mixed good is a highway. A highway is like a pure public good until it becomes congested. One more car or truck on a highway with plenty of space on it does not reduce the consumption of highway services of anyone else. But once the highway is congested, the addition of one more user lowers the quality of the service available for everyone else - it becomes like a private good.

Pure public goods and mixed goods with a large public element - all referred to as public goods - give rise to what is called the free-rider problem.

Free Riding

A free rider is someone who consumes a good without paying for it. The free-rider problem is the tendency for the scale of provision of a public good to be too small if it is produced and sold privately. The free-rider problem arises because there is no incentive for a person to pay for a good if their payment makes no difference to the quantity of the good that the person is able to consume. Public goods are such goods. To see why, let's look at an example.

[PD - sorry about the militaristic examples; they do represent a very pure form of public good. You should think how environmental services fit into a similar role.]

Imagine that an effective, antirnissile laser weapon has been developed. One of these new weapons can attack and destroy 400 intercontinental ballistic missiles within seconds of their being launched. The larger the number of antimissile laser weapons deployed, the larger is the number of missiles destroyed. Potential enemies have 1500 missile launchers and four of the new weapons can eliminate all of them. Three can do a pretty good job and even two can severely limit the amount of damage that will he inflicted by missiles that get through the laser deense. But the new weapons system is very expensive. To build it, resources have to be diverted from peaceful space programs and from the development of other productive uses of lasers in medicine. As a result, the larger the number of weapons installed, the greater is their marginal cost [to society].

Our task is to work out the scale on which to install this new defense system to achieve allocative efficiency. We'll then examine whether private provision can achieve allocative efficiency and we'll discover that it cannot - that there is a free-rider problem.

Benefits and Costs

The benefits provided by a weapons system are based on the preferences and beliefs of the consumers of the services of that system. Its costs will be based on technology and the prices of the factors of production used to produce the system. When studying private goods, we observed that the value of a good to an individual is the maximum amount that the person is willing to pay for one more unit of the good. We worked out this value from the individual's demand curve. That is, the demand curve tells us the quantity demanded at a given price, or for a given quantity, the maximum price that is willingly paid for last unit bought. We can work out the value a person places on a public good in a similar manner. That is, the value that a person places on a public good is maximum amount willingly paid for one additional unit of the good.

To calculate the maximum amount that a person is willing to pay for one more unit of a public good, we first need to establish that person's total benefit schedule. Total benefit is the total dollar value that a person places on a given level of provision of a public good. The greater the scale of provision, the larger is the total benefit. The table in Fig 19.1 sets out an example of the total benefits to Lisa and Max of different scales of provision of the proposed antimissile lasers. Lisa and Max believe that the weapons system reduces the chance of a nuclear war occurring and, if it does occur, increases the chance of preventing nuclear warheads from reaching their targets. The more lasers there are in place, the greater is the degree of security, but up to a maximum level. Each additional laser is believed to provide less additional security than the previous one. The increase in total benefit resulting from a unit increase in the scale of provision of a public goods is called its marginal benefit. The marginal benefits to Lisa and Max are calculated in the table in Fig 19.1 As you can see, the greater the scale of provision, the smaller is the marginal benefit. By the time 4 lasers are deployed, Lisa perceives no additional benefits, and Max perceives only $10 worth. Lisa's and Max's marginal benefits are graphed as MBL and MBM, respectively, in parts (a) and (b) of the figure.

The table shows various scales of provision of an antimissile laser defense system. It also lists the total benefits accruing to Lisa, Max, and the economy (comprised of Lisa and Max) of different scales of provision. The table also calculates the marginal benefit - the change in total benefit resulting from a unit increse in the scale of provision - to Lisa, Max and the economy. The marginal benefit to the economy at each level of provision is the sum of the marginal benefits to each individual and is shown in part (c).

The marginal benefit of a public good is the maximum amount that a person is willing to pay for one more unit of the good. This maximum amount varies with the quantity of the good consumed. The greater the quantity, the smaller is the maximum amount that will be paid for one more unit.

Part (c) of the figure shows the economy's marginal benefit curve, MB (where the economy has or two people, Lisa and Max). The marginal benefit curve of a public good for an individual is similar the demand curve for a private good. But there is important difference between the economy's marginal benefit curve for a public good and the market demand curve for a private good. To obtain the market demand curve for a private good, we add up the quantities demanded by each individual at each price. In other words, we sum the individual demand curves horizontally. In contrast, to find the economy's marginal benefit curve of a public good, we sum the marginal benefits to each indiviudal at each quantity of provision. That is, we sum the individual marginal benefit curves vertically. The resulting marginal benefit for the economy comprised of just Lisa and Max is calculated in the table, and the economy's marginal benefit curve is graphed in part (c) - the curve labelled MB.

An economy with just two people would certainly not buy any antimissile lasers - their total benefits fall far short of their cost. But an economy with 250 million people might.

[PD - To determine the efficient scale of provision of anti-missile lasers we would have to plot
(i) the market demand or marginal benefit curve (calculated like for Lisa and Max but for the whole economy) together with
(ii) the market supply or marginal cost curve
As with most market analyses, the point where the two meet would be the point of (allocative) efficiency and would suggest the ideal number of lasers to be set up.

We will do this a more environmental-oriented example in the exercises.
Note that this example has not considered external environmental or social side effects that should probably be included in the costs and benefits of this proposed program.]