Public Goods Provision and Altruistic Behavior

One of the primary applications of economics to public policy is in the study of how one can efficiently provide public goods. A public good is defined as a good that is nonrival and nonexcludable. Nonrival means that one person consuming the good does not prevent others from consuming the good also and does not diminish others’ utility of consumption. Nonexcludable means that it is not possible to bar someone from consuming the good. One example of a public good is national defense. It would not be possible to provide a defense from foreign invasion only to people in the country who paid for the defense. We must either defend our borders and government functions to preserve them for all or let the invading power take over for all. This makes it a nonexcludable good. Moreover, my deriving utility from the national defense does not diminish your utility from that same national defense. The problem with providing public goods is that a free market cannot generate the revenues necessary to provide the level of the good that would make all consumers best off.

Consider the issue of flood control on the Mississippi river. Suppose each farmer in the floodplain of the Mississippi is asked to contribute to the flood control system. There are thousands of farmers in the floodplain. Suppose each one has a utility function uc, x = c + x0.5, where c is consumption denominated in dollars and x is the level of flood control provided, also denominated in dollars. Suppose further that each farmer has an endowment of wealth, w, that can be allocated to consumption or given to the floodcontrol effort. Although consumption is private, and thus dollars spent on c are consumed only by the farmer spending the dollars, flood control is public. If any farmer contributes to flood control, every farmer is able to benefit from that contribution.

If flood control were excludable, a firm could charge each farmer her willingness to pay for the level of flood control provided. The profits to this firm would be given by willingness to pay for the level of flood control multiplied by the number of farmers, minus the cost of flood control. This can be written as

where n is the number of farmers. Note, x0.5 is willingness to pay for flood control because x0.5 would be required to purchase consumer goods yielding the same utility as this x amount of flood control. Marginal revenue of this flood-control firm is given by MR = 0.5 × nx − 0.5 and marginal cost is given by MC = 1. Hence, profit would be maximized where

Thus, if we could charge the farmers for their flood protection and exclude those who did not pay, we could charge n2 and provide n24 to all who paid. Suppose there were 4,000 farmers. This would result in x = 4,000,000 in flood protection. Summing up the utility from each of the farmers, this results in total utility to all farmers from flood protection of nx0.5 = 4,000 × 2,000 = 8,000,000.

But recognize that because x is a public good it is thus nonexcludable. All farmers will benefit from flood protection whether they contribute their own money to additional flood protection or not. In this case, no one will be willing to pay for additional units of x unless their personal benefit directly from the increase in x exceeds their own cost. Note that, x =ixi, where xi indicates the contribution of farmer i to flood control. The individual farmer decides how much to contribute by setting her own marginal utility of consumption equal to her private marginal utility of flood protection. Marginal utility of consumption is given by uc = 1, and marginal utility of flood protection is given by uxi = 0.5x− 0.5, where x =ixi. Recognizing that the budget constraint requires that c = w − xi, the optimal allocation occurs where

where the farmer will choose to contribute nothing if all other farmers combined have already contributed 0.25 or more. If all farmers are identical and make identical contributions in equilibrium, the solution is for each to contribute xi = 0.25n, which if there are 4,000 farmers, is only 0.0000625. This results in exactly x = 0.25, a much lower level of flood control than if we could exclude farmers from flood protection they did not pay for. This results in total utility of all farmers from flood protection of only nx0.5 = 4,000 × 0.5 − 2,000, much less than the 8,000,000 that would result if we could exclude people from consuming flood protection they did not pay for. This is an example of the free-rider problem.

One way that governments and policy makers have tried to deal with the free-rider problem is by providing government grants for public goods. For simplicity, let us suppose that the government now taxes each individual farmer T and then contributes the total to the public good—in this case flood protection. The question is how this public funding affects the private giving by each farmer. Under the tax-and-grant plan, x =ixi + nT, because now each farmer must pay T. The condition for the optimal level of individual contribution is again solved where the marginal utility of consumption equals the marginal utility of contributing to flood control, where now equation 14.8 becomes

So long as the tax is not so much that the individual farmer does not give at all, every dollar that is given in the grant (represented by nT) results in a completely equivalent reduction in the giving of the farmers. So long as there is still private contribution in addition to the grant, x = 0.25 no matter how much is given through the tax. Thus public contributions crowd out private contributions and should only result in an efficient allocation if private contributions are crowded out entirely. This general result is called the crowding-out effect and holds for almost any public goods problem in which the individual farmer cares about the provision of the public good.

EXAMPLE 14.7 Warm Glow Giving

Several studies have tried to test for the crowding-out effect. For example, Kenneth Chan led a team of researchers who ran experiments in a laboratory simulating the public goods problem as described in the previous section. Participants were placed in small groups and were given an apportionment of tokens that could be allocated either to a private good or a public good. The private good would yield a money payoff just for them. The public good would yield a payoff for all in the group. The experiment was run several times, with some treatments involving a mandatory tax to provide a public good. Participants were given 20 tokens to allocate in each round. With no tax, people voluntarily contributed an average of 4.9 tokens to the public good. A second round taxed each participant 3 tokens and allocated it toward the public good. Notice that 3 tokens is less than the average contribution, and thus we would expect the tax to reduce voluntary contributions by exactly 3 tokens to 1.9. Instead people voluntarily gave 2.9 tokens in addition to the 3-token tax. A third round of the experiment required a 5-token tax. In this round, people voluntarily contributed 1.5 tokens. In other words, there was some degree of crowding out, but not to the extent economic theory would predict.

This result mirrors results observed in the real world. For example, increases in federal or state contributions to higher education do not lead to a dollar-for-dollar decrease in voluntary giving to higher education. Neither did the rise of public welfare programs eradicate private contributions to welfare. Why do people continue to give their private contributions to these public goods even when the government increases their contributions? One theory is that people are motivated to give by the warm glow of knowing that they have contributed. Thus, people might have a utility function described by uc, x, xi, so that they derive some utility from the provision of the public good, x, but also derive some utility from contributing to that public good. Preferences of this nature are referred to as reflecting impure altruism, because they display a selfish (or private) value of giving to the public good.

Suppose, for example that uc, x, xi = c + x + xi0.5. Under this new utility function, marginal utility of consumption is still uc = 1. But now, marginal utility of contributing

Note that raising the tax by 1 unit per person increases provision of the good by n units but decreases private giving only by n2. Increasing the government contribution to the public good reduces the amount of the personal contribution to the public good, but by less than the amount of the tax on the individual, so long as uc, x, xixi > 0. Because the decision maker derives utility directly from giving and not just from the public good itself, government contributions will not directly crowd out private giving.

Although the theory of warm-glow giving has found much support in both field and laboratory tests, it is not the only possible explanation for incomplete crowding out. For example, one alternative explanation for why people might continue to give even when government has forced some contribution through a tax is that they believe their gift will lead others to decide to give also. For example, placing money in a plate passed at a church service provides some information to others and might induce them to decide to give as well. If the individual contributor believes that a contribution will result in contributions from others, she will believe her donations matter more than just the value of a dollar. If the primary motivation to give is to induce such donations from others, the government contribution might not be fully crowded out. The experimental evidence is quite consistent with the notion that people truly behave as if they receive some private satisfaction from contributing to others, and this has become the most commonly accepted theory among public goods economists.

EXAMPLE 14.8 Disaster Recovery

Several times each year, pictures from some wasteland of a developing country grace our television and computer screens. Whether from hurricanes, earthquakes, tsunamis, or human-made causes, widespread disaster can have a devastating impact on the lives of poor people throughout the world. The call goes out to donate for the relief efforts, and international organizations send in money, food, and other supplies to help. Despite the best efforts of all, recovery is often a long and difficult path. Many continue to feel the effects of the disaster decades after the initial event.