A public good is the exact opposite of a private good: it is both nonexcludable and nonrival in consumption. A public sewage system is an example of a public good: you can’t keep a river clean without making it clean for everyone who lives near its banks, and my protection from sewage contamination does not prevent my neighbor from being protected as well.

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Here are some other examples of public goods:

Because these goods are nonexcludable, they suffer from the free-rider problem, so private firms would produce inefficiently low quantities of them. And because they are nonrival in consumption, it would be inefficient to charge people for consuming them. As a result, society must find nonmarket methods for providing these goods.

Public goods are provided in a variety of ways. The government doesn’t always get involved—in many cases a non-governmental solution has been found for the free-rider problem. But these solutions are usually imperfect in some way.

Some public goods are supplied through voluntary contributions. For example, private donations help support public radio and a considerable amount of scientific research. But private donations are insufficient to finance large programs of great importance, such as the Centers for Disease Control and Prevention and national defense.

Some public goods are supplied by self-interested individuals or firms because those who produce them are able to make money in an indirect way. The classic example is broadcast television, which in the United States is supported entirely by advertising. The downside of such indirect funding is that it skews the nature and quantity of the public goods that are supplied, while imposing additional costs on consumers. TV stations show the programs that yield the most advertising revenue (that is, programs best suited for selling antacids, hair-loss remedies, antihistamines, and the like to the segment of the population that buys them), which are not necessarily the programs people most want to see. And viewers must endure many commercials.

Some potentially public goods are deliberately made excludable and therefore subject to charge, like pay-per-view movies. In the United Kingdom, where most television programming is paid for by a yearly license fee assessed on every television owner (£145.50, or about $244.50 in 2014), television viewing is made artificially excludable by the use of “television detection vans”: vans that roam neighborhoods in an attempt to detect televisions in non-licensed households and fine them. However, as noted earlier, when suppliers charge a price greater than zero for a nonrival good, consumers will consume an inefficiently low quantity of that good.

In small communities, a high level of social encouragement or pressure can be brought to bear on people to contribute money or time to provide the efficient level of a public good. Volunteer fire departments, which depend both on the volunteered services of the firefighters themselves and on contributions from local residents, are a good example. But as communities grow larger and more anonymous, social pressure is increasingly difficult to apply, compelling larger towns and cities to tax residents and depend on salaried firefighters for fire protection services.

As this last example suggests, when other solutions fail, it is up to the government to provide public goods. Indeed, the most important public goods—national defense, the legal system, disease control, fire protection in large cities, and so on—are provided by the government and paid for by taxes. Economic theory tells us that the provision of public goods is one of the crucial roles of government.

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In some cases, the provision of a public good is an “either–or” decision: a city can either have a sewage system—or not. But in most cases, governments must decide not only whether to provide a public good but also how much of that public good to provide. For example, street cleaning is a public good—but how often should the streets be cleaned? Once a month? Twice a month? Every other day?

Imagine a city with only two residents, Ted and Alice. Assume that the public good in question is street cleaning and that Ted and Alice truthfully tell the government how much they value a unit of the public good, one unit being one street cleaning per month. Specifically, each of them tells the government his or her willingness to pay for another unit of the public good supplied—an amount that corresponds to that individual’s marginal private benefit from another unit of the public good.

Using this information along with information on the cost of providing the good, the government can use marginal analysis to find the efficient level of providing the public good: the level at which the marginal social benefit of the public good is equal to the marginal social cost of producing it. Recall that the marginal social benefit of a good is the benefit that accrues to society as a whole from the consumption of one additional unit of the good.

But what is the marginal social benefit of another unit of a public good—a unit that generates utility for all consumers, not just one consumer, because it is nonexcludable and nonrival in consumption? This question leads us to an important principle: In the special case of a public good, the marginal social benefit of a unit of the good is equal to the sum of the marginal private benefits enjoyed by all consumers of that unit. Or to consider it from a slightly different angle, if a consumer could be compelled to pay for a unit before consuming it (the good is made excludable), then the marginal social benefit of a unit is equal to the sum of each consumer’s willingness to pay for that unit. Using this principle, the marginal social benefit of an additional street cleaning per month is equal to Ted’s marginal private benefit from that additional cleaning plus Alice’s marginal private benefit.

Why? Because a public good is nonrival in consumption—Ted’s benefit from a cleaner street does not diminish Alice’s benefit from that same clean street, and vice versa. Because Ted and Alice can simultaneously “consume” the same unit of street cleaning, the marginal social benefit is the sum of their marginal private benefits. And the efficient quantity of a public good is the quantity at which the marginal social benefit is equal to the marginal social cost of providing it.

Figure 76.2 illustrates the efficient provision of a public good, showing three marginal benefit curves. Panel (a) shows Ted’s marginal private benefit curve from street cleaning, MPB_T: he would be willing to pay $25 for the city to clean its streets once a month, an additional $18 to have it done a second time, and so on. Panel (b) shows Alice’s marginal private benefit curve from street cleaning, MPB_A. Panel (c) shows the marginal social benefit curve from street cleaning, MSB: it is the vertical sum of Ted’s and Alice’s marginal private benefit curves, MPB_T and MPB_A.

To maximize society’s welfare, the government should increase the quantity of street cleanings until the marginal social benefit of an additional cleaning would fall below the marginal social cost. Suppose that the marginal social cost is $6 per cleaning. Then the city should clean its streets 5 times per month, because the marginal social benefit of each of the first 5 cleanings is more than $6, but going from 5 to 6 cleanings would yield a marginal social benefit of only $2, which is less than the marginal social cost.

One fundamental rationale for the existence of government is that it provides a way for citizens to tax themselves in order to provide public goods—particularly a vital public good like national defense.

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Of course, if society really consisted of only two individuals, they would probably manage to strike a deal to provide the good. But imagine a city with a million residents, each of whose marginal private benefit from a good is only a tiny fraction of the marginal social benefit. It would be impossible for people to reach a voluntary agreement to pay for the efficient level of a good like street cleaning—the potential for free-riding would make it too difficult to make and enforce an agreement among so many people. But they could and would vote to tax themselves to pay for a citywide sanitation department.

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