# 21 Public Goods

## Exploring the Policy Question

1. Does the societal benefit from the advent of new drugs outweigh the cost to society from the creation of monopolies?
2. What other way could society promote the development of new medicines?

## Learning Objectives

### 21.1 What Is a Public Good?

Learning Objective 21.1: Describe the two key features of a public good.

### 21.2 The Free-Rider Problem

Learning Objective 21.2: Explain how public goods lead to overuse.

### 21.3 Problems with the Public Provision of Public Goods

Learning Objective 21.3: Describe the problem of under-provision of public goods.

### 21.4 Policy Example Policing Fish Extraction within 10 Nautical Miles of the US Shoreline

Learning Objective 21.4: Explain how the application of property rights can help solve the free-rider problem in fisheries.

## 21.1 What Is a Public Good?

Learning Objective 21.1: Describe the two key features of a public good.

Public goods are goods that have some degree of non-rivalry and non-excludability. Rival goods are goods that are diminished with use. An example of a rival good is a sandwich. When someone consumes a sandwich, that sandwich is gone, and no one else can consume it. Non-rival goods are goods that do not diminish with individual consumption; for example, no amount of consumption of the music from a radio station leaves any less music for anyone else with a radio to listen to. Clean air, national defense, and lighthouses are other classic examples of non-rival goods. Exclusive goods are goods for which consumption can be controlled or prevented. The sandwich behind the deli counter in a market is an exclusive good; consumption can only happen if the deli workers allow it. Non-exclusive goods are things like the roads and parks in a city; anyone can drive on the roads or enjoy the park. Fisheries are another example of non-excludability.

Private goods are, like the sandwich, goods that are both rival and exclusive. What this textbook has been discussing all along are private goods. But what happens when the goods have some non-rivalry and/or some non-excludability? Public goods like these are subject to market failures. For example, suppose someone tried to charge a price for a radio transmission. The result would be that no one would pay that price because they can get the radio signal for free, and there is no way to stop those that didn’t pay from receiving the signal. This is known as the free-rider problem—when non-payers consume a good that has a positive marginal cost.

We can classify goods based on the presence of rivalry and excludability, as is shown in table 21.1.1 below. We divide goods into four categories:

1. Private Goods
2. Goods that have both rivalry and exclusion (and are the type of goods we have studied up to this point)
3. Public Goods
4. Goods that are both non-excludable and non-rival
5. Club Goods
6. Goods that are excludable but non-rival; and
7. Common Property/Common-Pool Resources
8. Goods that are rival but non-excludable.

Table 21.1.1 Goods based on the presence of rivalry and excludability

Table 21.1.1 Goods based on the presence of rivalry and excludability
Rival or Non-Rival? Excludable Goods Non-Excludable Goods
Rival Private Goods: sandwich, gasoline, computer Common property resources: fishery, roads, parks
Non-Rival Club goods: satellite radio, cable TV, sporting even Public goods: clean air, national defense, lighthouse

We also distinguish between pure public goods, goods that are completely non-rival and non-excludable like radio transmissions, and impure public goods, which have at least some of both non-rivalry and non-excludability. City roads are an example of an impure public good; they are non-excludable but not perfectly non-rival—each car takes up a little of the road space, leaving just a tiny bit less for others.

## 21.2 The Free-Rider Problem

Learning Objective 21.2: Explain how public goods lead to overuse.

Public goods are both non-rival and non-exclusive. For example, national defense is a public good. All residents of a country enjoy the protection of military defense of the territory; no one is excluded or excludable. And no matter how much one individual consumes of national defense, there is just as much national defense of the other residents of the country, so it is non-rival.

Market failures in the provision of public goods arise for a very simple reason: since non-payers cannot be prevented from consuming the good, the incentives to pay for the good are diminished. We call this problem the free-rider problem. It is easy to understand this when we think about individual incentives. Utility for the consumption of a public good is increased the less the consumer pays for it.

We can illustrate this with a simple example of two neighbors with adjacent properties considering erecting a fence between their properties to provide privacy. Neighbor 1 is a private person and someone who values privacy very highly. Neighbor 2 is someone who values privacy but much less than neighbor 1. Figure 21.2.1 shows the demand curves for the two neighbors of the length of the privacy fence in meters. $D^1$ is Neighbor 1’s demand curve, and $D^2$ is Neighbor 2’s demand curve. These demand curves represent the value to each neighbor of a meter of fence. By adding these two values together, we get the true social benefit of the fence, and we can show this in the figure as the vertical sum of the two demand curves, which is labeled $D^{SB}$, where $SB$ stands for social benefit. For example, to erect a ten-meter fence, Neighbor 1 is willing to pay $30 a meter, and Neighbor 2 is willing to pay$20 a meter. The social willingness to pay for the shared fence is the sum of the two individual’s willingness to pay, or $50. Notice immediately that the social marginal benefit of the good is not the same as the private marginal benefits for either neighbor. Contrast this with a private good, where consumption benefits only the buyer, and therefore, the social marginal benefit is the same as the private marginal benefit. Recall that when determining the total demand or the social marginal benefit curve for the market for a private good, we sum the individual demand curves horizontally because the benefit to a consumer only comes from when they consume their own private units of the good. The difference here is the lack of rivalry: the same unit of a public good benefits all consumers in the market. So we have to add up all the individual benefits for each unit of the public good or sum the demand curves vertically. Fences are costly, however, and we will assume that the cost per meter of erecting a fence is$50. This is the marginal cost of fencing and is the social marginal cost, since that is the total cost to the two neighbors of erecting a meter of fence.

The socially optimal amount of fencing for the two neighbors is the point at which the social marginal benefit of the fence, given by the demand curve $D^{SB}$, intersects with the marginal cost of the fence. In figure 21.2.1, this intersection occurs at ten meters.

To understand what will actually occur, notice that the individually optimal amount of fencing for Neighbor 1 is six meters. In other words, if the neighbor was going to build a fence individually, six meters is the amount that neighbor would build. Neighbor 2 would not build any fence individually, as the marginal cost of building is higher than the marginal benefit, even for the first meter of fence. Since Neighbor 2 does not want to collaborate on the fence, Neighbor 1 will build it alone and will build six meters of fence, and Neighbor 2 will enjoy the benefit of the fence without contributing to it. We see in this example how the private provision of public goods is subject to under-provision: Neighbor 2 free rides off Neighbor 1’s fence, and thus only six meters of fencing is constructed, while ten meters is socially optimal.

To ensure public goods are provided, governments usually step in and provide the good themselves or subsidize or mandate its provision. An example is local fire departments. Fire protection is a classic public good; all those in the fire district benefit from the service, and the protection of one household leaves no less for the other households in the district. Left to the market, we can be confident that a suboptimal amount of fire protection would be provided, thus it becomes part of the accepted role of the government to levy a tax on homeowners and provide fire protection themselves.

## 21.3 Problems with the Public Provision of Public Goods

Learning Objective 21.3: Describe the problem of under-provision of public goods.

In order to value public goods, you must look beyond the market valuation. Because of the presence of free ridership, the market will undervalue public goods. Alternatively, governments can rely on surveys, but these types of surveys are often poor because it is very hard to judge the value of a public good to an individual. An individual might be able to answer how much they would be willing to pay for a proposed new park in their neighborhood, but how much is the police protection they enjoy worth? Without knowing what life would be like in the absence of a police force, that is a very difficult question to answer. Other things for which individuals lack enough information to value correctly could include clean air and drinking water, national defense, and public education.

Another way to both value and potentially provide public goods is through a popular vote. This seems to be a reasonable solution on the surface, but upon examination, it is clear that the ability of such a system to provide public good rests pivotally on the median voter.

Consider the following example: suppose a town on a river is considering building a bridge over the river. To keep the analysis simple, let’s assume a simplified world where there are five residents of the town, and the bridge costs exactly $1,000 to construct. The bridge is worth different amounts to each resident depending on factors such as income, how close they live to the bridge, how often they anticipate using the bridge, and so on. Table 21.3.1 lists each resident and their maximum willingness to pay for a bridge, which is a measure of the monetary value to them of the bridge. Table 21.3.1 Resident’s willingness to pay for a new bridge Resident ID Willingness-to-pay price ($)
Resident A $500 Resident B$350
Resident C $175 Resident D$150
Resident E $125 Total Value to Society$1,300

Note that the total value to the society of the new bridge is $1,300, which is more than the cost of$1,000, and so from a social welfare perspective, the bridge should be built—the community will see a net benefit from doing so. Suppose the town proposes a tax of $200 on each resident, which would net exactly the$1,000 needed to build the bridge. When put to a vote, this proposal will fail because Residents C, D, and E will all vote no: the $200 they are being asked to pay is greater than their individual benefit. Note that the pivotal voter in this is Resident C. If Resident C’s willingness to pay were$200 or more, they would vote yes. Resident C is the median voter, halfway from the top and bottom, and the construction of the bridge will rest crucially on their valuation relative to the individual cost.

It is also worth noting that other means of provision in this case are also problematic. Voluntary contributions would fall prey to the free-rider problem, as C, D, and E all know that their contributions are not needed provided the others contribute fully and will therefore withhold. A toll would have to raise the $1,000 cost and thus would be the equivalent of the$200 tax. In this case, the “voting” would happen by use: only A and B would pay \$200 to use it, and the toll revenues would fall far short of the cost of the bridge.

If these willingnesses-to-pay were closely related to income, then charging a tax as a percentage of income might work, but if they have more to do with proximity, work-travel patterns, and so on, this approach would fail as well. So how do public goods get provided in most cases? Out of general funds from the government. By packaging together a whole host of public goods, including roads, parks, schools, libraries, public safety, and the like, governments can average out individual differences related to preferences and create broad support for the funding of these activities.

## 21.4 Policy exampleShould the Government Regulate the Extraction of Fish from the Ocean in waters within ten nautical miles of the us shoreline?

Learning Objective 21.4: Explain how the application of property rights can help solve the free-rider problem in fisheries.

When fishing boats set out on the ocean and decide how many fish to catch, like any economic actor, they make a marginal benefit, marginal cost calculation. They will continue to fish as long as their private marginal benefit, the value of the next fish caught, equals the private marginal cost, the expense of catching the last fish. As a common-pool resource, however, there is a social cost to the boat’s catch that is not part of their calculation: the fact that the more fish they catch, the fewer fish there are for others to catch. In addition, fisheries need a healthy population of mature fish to remain uncaught so that those fish can reproduce and provide fish to catch next season.

In this situation, the private marginal cost and the social marginal cost differ due to the cost of depleting the fishery from one fishing boat’s catch. Without regulation, each individual boat will catch more than the socially optimal amount, leading to deadweight loss.

With the application of property rights—typically a quota system that assigns the right of an individual fishing boat to catch only a limited amount of fish—the socially optimal amount of fish extraction is established.

## Review: Topics and Related Learning Outcomes

### 21.1 What Is a Public Good?

Learning Objective 21.1: Describe the two key features of a public good.

### 21.2 The Free-Rider Problem

Learning Objective 21.2: Explain how public goods lead to overuse.

### 21.3 Problems with the Public Provision of Public Goods

Learning Objective 21.3: Describe the problem of under-provision of public goods.

### 21.4 Policy ExamplePolicing Fish Extraction within 10 Nautical Miles of the US Shoreline

Learning Objective 21.4: Explain how the application of property rights can help solve the free-rider problem in fisheries.

## Learn: Key Topics

### Terms

Public goods

Public goods are goods that have some degree of non-rivalry and non-excludability. We also distinguish between pure public goods, goods that are completely non-rival and non-excludable like radio transmissions, and impure public goods that have at least some of both non-rivalry and non-excludability. City roads are an example of an impure public good, they are non-excludable but they are not perfectly non-rival, each car takes up a little of the road space leaving just a tiny bit less for others.

Rival goods

Rival goods are goods that are diminished with use. An example of a rival good is a sandwich, when someone consumes a sandwich that sandwich is gone and no one else can consume it. Non-rival goods are goods that do not diminish with individual consumption, for example no amount of consumption of the music from a radio station leaves any less music for anyone else with a radio to listen to. Clean air, national defense and lighthouses are other classic examples of non-rival goods.

Exclusive goods

Exclusive goods are good for which consumption can be controlled or prevented. The sandwich behind the deli counter in a market is an exclusive good, consumption can only happen if the deli workers allow it. Non-exclusive goods are things like the roads and parks in a city where anyone can drive on the roads or enjoy the park. Fisheries are another example of non-excludability.

Private goods

Private goods are goods that are both rival and exclusive.