Chapter 27

Suppose a social entrepreneur needs to raise money for a public good. He has to allocate his fund raising package to activities that persuade people of the importance of the public good and to activities that make people feel good about giving. As the population gets large, which of these do you think he will increasingly emphasize?

ANS: As the population gets large, the free rider problem becomes larger -- which means that just convincing someone that the public good is important won't raise much money. But making someone feel good about giving is all about generating private benefits from giving -- and that is unaffected by how many individuals there are.Thus, one would expect the fund raising to increasingly focus on making people feel good about giving rather than persuading them of the importance of the public good.

In our study of monopoly, we found that monopolists can increase profit by segmenting the market and price discriminating (under third degree price discrimination). Now suppose a firm is producing an excludable local public good. Can you justify a form of such market segmentation and price discrimination as efficient?

ANS: If a firm (like a movie theater) produces a local public good and can exclude non-payers, and if the firm furthermore knows how to segment consumer types into high and low demand types, then a form of third degree price discrimination can mimic Lindahl price discrimination. High demanders are charged a higher (Lindahl) price while low demanders are charged a low price.

If private giving to public goods involves externalities, what is a Pigouvian solution to the public goods problem?

ANS: Pigou suggests subsidies to internalize positive externalities. Public goods generate positive externalities, and private giving to public goods generates positive externalities. Thus, Pigou would suggest subsidizing private giving such that the per-dollar subsidy is equal to the sum of the marginal benefits of everyone other than the person who is giving.

What problem are mechanism designers attempting to overcome when they "design mechanisms" to provide public goods?

ANS: The essential problem is that, while we know how to implement the efficient level of public goods if we know people's demands, we know we can't just ask them for their demands so long as we link what they have to pay to how much they demand the public good. Mechanism design attempts to devise a "message game" in which individuals send just enough information for us to be able to implement the public good and fund it -- with truth telling emerging as the dominant strategy. (It turns out not all of that is possible, but different mechanisms "get close" in different ways.)

We say that individuals get a "warm glow" from giving to a public good if they not only get utility from the public good but also from giving itself. Explain the following: "While warm glow lessens the free rider problem, it cannot eliminate it."

ANS: The private benefits one gets from giving keep us giving even when the number of individuals increases and the free rider problem gets large. However, the free rider problem is still there -- to the extent to which we value the public good, we give too little relative to the efficient level. Only if the only utility we get is from the warm glow does the free rider problem disappear -- but that's because the public goods problem has then disappeared.

In a game where individuals are asked to contribute to a public good, best response functions slope down because each individual believes the other will not give very much.

ANS: F Best response functions slope down because each individual will only give until the private marginal benefit of an additional dollar of the public good is equal to a dollar -- and as the other individual gives more, this implies less giving leads to the last dollar satisfying this condition.

Suppose some people like national defense and others are offended by it -- i.e. some people derive positive marginal benefit and others derive negative marginal benefit. Efficiency then demands that national defense is produced until the sum of the positive marginal benefits is equal to the (absolute value) of the negative marginal benefits.

ANS: F Efficiency would still demand that the sum of all marginal benefits is equal to that marginal cost.

Consider a game where individuals are asked to contribute to a public good. Then consider the best response function for individual i, with individual i's contribution measured on the vertical axis and "the average contribution by everyone else" on the horizontal. Then as the number of individuals increases, i's best response function shifts in.

ANS: F It rotates inward, with the vertical intercept remaining constant.

Tiebout local public good provision is more easily implemented than a Lindahl equilibrium -- because people know each other's tastes locally and can more easily come up with the right way to divide the cost for public goods.

ANS: F The Tiebout public good equilibrium does not rely on people knowing each other's tastes --- rather it depends on people sorting into communities based on each others' tastes.

If a public good is financed through Lindahl prices, those whose total willingness to pay for the public good is high will end up paying a higher Lindahl price than those whose total willingness to pay for the public good is low.

ANS: F The statement is true if "total" is replaced by "marginal".

If everyone has identical preferences over public goods, Lindahl prices for providing the efficient level of the public good will be the same for everyone.

ANS: F Unless tastes are quasilinear in the public good, people with different incomes will be charge different Lindahl prices.

Our free-rider model of voluntary giving suggests that, when the government subsidizes private giving to charity, it's contribution will simply "crowd out" the private contributions so long as no one is at a corner solution.

ANS: F When the government subsidizes private giving, it lowers the price of giving -- which is different than when the government contributes directly (when crowd out can happen.)

When the government contributes to a public good, private contributions will fall.

ANS: T Government contributions crowd out private contributions.

Public goods arise because of externalities.

ANS: T Non-rivalry means that one person's consumption can be another person's consumption too -- i.e. one person's consumption gives rise to a positive externality for another.

The optimal subsidy for private giving to a public good increases as the number of people benefiting from the public good increases.

ANS: T The optimal subsidy is equal to the sum of the marginal benefits of a dollar of giving for everyone other than the "giver" -- which increases as the number of "others" increases.

If the formation of Lindahl prices to support an efficient level of public goods is derived from individuals' reporting their marginal willingness to pay, people will under-report their true willingness to pay.

ANS: T Under Lindahl prices, everyone is charged their marginal willingness to pay -- but the overall level of the public good is determined by the sum of all MWTPs. Thus, by underreporting your MWTP, you can lower your Lindahl price without affecting the public good level much. The more individuals there are, the less the public good level will change -- and so the incentive to lie increases as the number of people increases.

If giving to public goods is subsidized through deductions under a progressive income tax, the government subsidizes public goods consumed by higher income individuals at greater rates than public goods consumed by lower income individuals.

ANS: T Under a progressive income tax, higher income individuals face a greater marginal tax rate -- and their deductions therefore receive a higher subsidy.

Any efficient allocation of public goods will be such that the sum of the marginal benefits is equal to the marginal cost -- but the level of the public good may differ depending on how income is distributed in the population.

ANS: T Unless tastes are quasilinear in the public good, redistribution of income gives rise to income effects that will cause the demands (and MWTP) for public goods to shift.