How Much of a Public Good Should Be Provided?

In some cases, provision of a public good is an “either-or” decision: London would 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 in which there are 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, where a unit is equal to 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 benefit of another unit of the public good.

Using this information plus 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 cost of producing it. Recall from Chapter 16 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 individual marginal benefits that are 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 individual marginal benefit from that additional cleaning plus Alice’s individual marginal benefit.

We all benefit when someone else does the cleaning up.
Telekhovskyi/Shutterstock

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 people can all simultaneously consume the same unit of a public good, the marginal social benefit of an additional unit of that good is the sum of the individual marginal benefits of all who enjoy the public good. And the efficient quantity of a public good is the quantity at which the marginal social benefit is equal to the marginal cost of providing it.

Figure 17-2 illustrates the efficient provision of a public good, showing three marginal benefit curves. Panel (a) shows Ted’s individual marginal benefit curve from street cleaning, MBT: 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 individual marginal benefit curve from street cleaning, MBA. Panel (c) shows the marginal social benefit curve from street cleaning, MSB: it is the vertical sum of Ted’s and Alice’s individual marginal benefit curves, MBT and MBA.

A Public Good Panel (a) shows Ted’s individual marginal benefit curve of street cleanings per month, MBT, and panel (b) shows Alice’s individual marginal benefit curve, MBA. Panel (c) shows the marginal social benefit of the public good, equal to the sum of the individual marginal benefits to all consumers (in this case, Ted and Alice). The marginal social benefit curve, MSB, is the vertical sum of the individual marginal benefit curves MBT and MBA. At a constant marginal cost of $6, there should be 5 street cleanings per month, because the marginal social benefit of going from 4 to 5 cleanings is $8 ($3 for Ted plus $5 for Alice), but the marginal social benefit of going from 5 to 6 cleanings is only $2.

FOR INQUIRING MINDS: Voting as a Public Good

It’s a sad fact that many Americans who are eligible to vote don’t bother to. As a result, their interests tend to be ignored by politicians. But what’s even sadder is that this self-defeating behavior may be completely rational.

As the economist Mancur Olson pointed out in a famous book titled The Logic of Collective Action, voting is a public good, one that suffers from severe free-rider problems.

Imagine that you are one of a million people who would stand to gain the equivalent of $100 each if some plan is passed in a statewide referendum—say, a plan to improve public schools. And suppose that the opportunity cost of the time it would take you to vote is $10. Will you be sure to go to the polls and vote for the referendum? If you are rational, the answer is no because it is very unlikely that your vote will decide the issue, either way. If the measure passes, you benefit, even if you didn’t bother to vote—the benefits are nonexcludable. If the measure doesn’t pass, your vote would not have changed the outcome. By not voting and free-riding on those who do vote you save $10.

Of course, many people do vote out of a sense of civic duty. But because political action is a public good, in general people devote too little effort to defending their own interests.

The result, Olson pointed out, is that when a large group of people share a common political interest, they are likely to exert too little effort promoting their cause and so will be ignored. Conversely, small, well-organized interest groups that act on issues narrowly targeted in their favor tend to have disproportionate power.

Is this a reason to distrust democracy? Winston Churchill said it best: “Democracy is the worst form of government, except for all the other forms that have been tried.”

To maximize society’s welfare, the government should clean the street up to the level at which the marginal social benefit of an additional cleaning is no longer greater than the marginal cost. Suppose that the marginal cost of street cleaning is $6 per cleaning. Then the city should clean its streets 5 times per month, because the marginal social benefit of going from 4 to 5 cleanings is $8, but going from 5 to 6 cleanings would yield a marginal social benefit of only $2.

Voting as a Public Good: The Global Perspective

Despite the fact that it can be an entirely rational choice not to vote, many countries consistently achieve astonishingly high turnout rates in their elections by adopting policies that encourage voting. In Belgium, Singapore, and Australia, voting is compulsory; eligible voters are penalized if they fail to do their civic duty by casting their ballots. These penalties are effective at getting out the vote. When Venezuela dropped its mandatory voting requirement, the turnout rate dropped 30%; when the Netherlands did the same, there was a 20% drop-off.

Other countries have policies that reduce the cost of voting; for example, declaring election day a work holiday (giving citizens ample time to cast their ballots), allowing voter registration on election day (eliminating the need for advance planning), and permitting voting by mail (increasing convenience).

This figure shows turnout rates in several countries, measured as the percentage of eligible voters who cast ballots, averaged over elections held between 1945 and 2013. As you can see, Australia, Singapore, and Belgium have the highest voter turnout rates. The United States has a relatively high voter turnout during presidential elections. However, turnout drops significantly in nonpresidential elections, when the United States has the lowest turnout rate among advanced countries. In general, the past four decades have seen a decline in voter turnout rates in the major democracies, most dramatically among the youngest voters.

Source: International Institute for Democracy and Electoral Assistance.

Figure 17-2 can help reinforce our understanding of why we cannot rely on individual self-interest to yield provision of an efficient quantity of public goods. Suppose that the city did one fewer street cleaning than the efficient quantity and that either Ted or Alice was asked to pay for the last cleaning. Neither one would be willing to pay for it! Ted would personally gain only the equivalent of $3 in utility from adding one more street cleaning—so he wouldn’t be willing to pay the $6 marginal cost of another cleaning. Alice would personally gain the equivalent of $5 in utility—so she wouldn’t be willing to pay either.

The point is that the marginal social benefit of one more unit of a public good is always greater than the individual marginal benefit to any one individual. That is why no individual is willing to pay for the efficient quantity of the good.

Does this description of the public-good problem, in which the marginal social benefit of an additional unit of the public good is greater than any individual’s marginal benefit, sound a bit familiar? It should: we encountered a somewhat similar situation in our discussion of positive externalities. Remember that in the case of a positive externality, the marginal social benefit accruing to all consumers of another unit of the good is greater than the price that the producer receives for that unit; as a result, the market produces too little of the good.

In the case of a public good, the individual marginal benefit of a consumer plays the same role as the price received by the producer in the case of positive externalities: both cases create insufficient incentive to provide an efficient amount of the good.

The problem of providing public goods is very similar to the problem of dealing with positive externalities; in both cases there is a market failure that calls for government intervention. One basic 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.

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 individual marginal benefit from provision of the 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 street cleaning—the potential for free-riding makes 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.