Unit 10 Market successes and failures: The societal effects of private decisions

10.6 Public goods, non-rivalry, and excludability: A model of radio broadcasting

Some of our examples of decisions that have external benefits can also be described as public goods. These are cases where, if one individual incurs a cost to provide the good, many others can benefit too. If one farmer contributes to the cost of an irrigation scheme, or one country takes measures to reduce carbon emissions, all farmers or all countries benefit. The irrigation scheme is a public good for the community where it is located. Reductions in atmospheric CO2 are a global public good.

free rider, free riding, free ride
Someone who benefits from the contributions of others to some cooperative project without contributing themselves is said to be free riding, or to be a free rider.

The distinction between public goods and positive externalities is not always clear-cut, and both terms are sometimes used loosely. But for example, we wouldn’t describe a beautiful private garden as a public good, because the owner (who incurs the costs of maintaining it) benefits much more than individual passers-by. We generally reserve the term public good for cases where, for each individual, the private costs of producing it would be high and the private benefits low, so that no individual has an incentive to provide the good. If they did, everyone else would simply free-ride on their generosity.

This is exactly the situation in the irrigation game in Unit 4—which is why we called it a public good game. Unless communities can find ways of resolving such social dilemmas collectively, public goods are unlikely to be provided efficiently in the market system. In some cases, they will not be provided at all—unless by a government.

public good
A good that, if available to anyone, can be made available to everyone at no additional cost. This characteristic is called non-rivalry. Some economists define public goods more strictly as goods that are both non-rival and non-excludable (non-excludable means that it is impossible to prevent anyone from consuming them).
non-rival, non-rivalry
A good is non-rival if, when it is made availaible to one person, it can be made available to everyone else at no additional cost. Non-rivalry is the primary characteristic of a public good.

The primary characteristic of a public good is that if it is available to one person, it can be available to everyone at no additional cost, because its use by one person does not reduce its availability to others. Expert weather forecasting is an example (if I can tune in and find out if it’s likely to rain today, so can you). National defence is a public good for a whole country, and is a primary responsibility of governments (if one person is protected from foreign invasion, everyone else is too). This characteristic is called non-rivalry, because potential users are not in competition (rivalry) with each other for the good.

Knowledge is also a public good. You can use your knowledge of a recipe for baking a cake or the rules of multiplication without affecting the ability of others to use the same knowledge. And the environment provides many public goods. Enjoying a view of the setting sun does not deprive anyone else of their enjoyment.

In all of these cases, once the good is available to anyone, the marginal cost of making it available to additional people is zero.

A model of public good provision

The earliest broadcasting stations included PCGG in the Netherlands, which began in 1919; KDKA in Pittsburgh, US (1920); the BBC in London (1922); and Radio Ceylon, Sri Lanka (1923).

Radio broadcasting to a wide audience began in the 1920s and spread quickly around the world. During the first few decades, most broadcasting companies were government-owned, although commercial stations also existed, particularly in the United States; governments still play a significant role in the broadcasting sector in many countries.

Radio broadcasting satisfies the definition of a public good. Once a radio programme has been produced and broadcast to one person who has a radio, all other radio owners can listen at no additional cost. When another listener switches on, it makes absolutely no difference to the costs of the programme provider, or to the quality of the programme. The programme is a public good, irrespective of whether it is supplied by the public sector or the private sector.

Figure 10.7 shows the demand curve for a radio programme called Min’s Music. Remember that a demand curve represents the willingness to pay (WTP) of potential buyers, lined up in order—in this case, their willingness to pay to listen to the programme. For example, the 4,000th listener would be willing to pay $9. This is a measure of how much this particular listener values the programme: it represents the listener’s private benefit, or equivalently their gain in utility (measured in monetary terms) from listening to it. The demand curve also shows people who would prefer not to listen; they would only listen if paid to do so (those to the right of the 10,000th listener).

For the broadcaster, let the total cost of making and broadcasting the programme be C. The cost doesn’t depend on the size of the audience. However many people are listening, the cost doesn’t increase if someone else turns on their radio—so the marginal cost of supplying the programme to another listener is zero. (Be careful here: the model is for a particular programme of fixed type, length, and quality, and these are the costs of supplying it. We are not considering the marginal cost of another minute of broadcasting, for example.)

In this diagram, the horizontal axis shows the number of listeners N, and ranges between 0 and 14000. The vertical axis shows the price P in dollars, and ranges between minus 8 and 16. Coordinates are (number of listeners, price). A downward-sloping, straight line passes through points (4000, 9) and (10000, 0) and is labelled Demand (WTP). A horizontal line passes through point (0, 0) and is labelled marginal broadcasting cost.

Figure 10.7 Demand and marginal cost for Min’s Music.

The figure indicates that the Pareto-efficient allocation would be for 10,000 people to listen to the programme. If there were only 8,000 listeners, for example, there would be another 2,000 who would value the experience and would be better off if they listened, too. And including them would have no effect on the broadcaster or anyone else. Conversely, if there were 12,000 listeners, 2,000 people’s lives would be improved if their radios were turned off.

The shaded area represents the sum of the private benefits of the 10,000 people who would like to listen to the programme—that is, the social benefit of the programme. Given the numbers we have chosen for purposes of illustration, it is equal to $75,000.

How could the Pareto-efficient allocation be achieved? If the price of listening was P = 0, then 10,000 people would choose to listen, and the social benefit would be $75,000. (It would also be the consumer surplus.) But in that case, the producer of the programme would receive no revenue, and overall it would incur a loss equal to C, the cost of making and broadcasting the programme. No private provider would be willing to do this.

Nevertheless, there is a net social benefit of producing and supplying it for free, provided that the production and broadcasting cost is not too high. There are no external costs, so:

\[\begin{align*} \text{private and social cost of making}\\ \text{and broadcasting } \textit{Min's Music} &= C \\ \text{social benefit} &=\$75,000 \\ \text{net social benefit} &=\$75,000-C \end{align*}\]

For example if C = $40,000, the net social benefit is $35,000, so it would be socially beneficial for the programme to be made.

What can be done? One solution is for the government to provide the broadcasting service, thereby controlling the production of radio programmes, financing them out of general taxation, and broadcasting them for free. In the early years of broadcasting, this was the dominant model in most countries. The US followed an alternative path: commercial radio stations were financed by advertising. Firms would pay to sponsor programmes, or for short adverts to be aired periodically, because broadcasting enabled them to reach a large audience.


excludable, excludability
A good is excludable if (at zero or low cost) a potential user may be denied access to the good. See also: non-rival.

In the early days of radio broadcasting, providers were unable to prevent people from listening. With technological development in radio and television broadcasting, a wider range of solutions became possible. Technology has allowed broadcasters to set a price for their programmes, and restrict access to those who pay. Broadcast programmes are now an excludable public good: the provider can choose whom to supply and whom to exclude.

Does this solve the problem? The answer is no.

deadweight loss
A measure of the total loss of surplus (that is, potential gains from trade) relative to the maximum available in the market.

Figure 10.8 shows what happens if the broadcaster sets a price of $6 for listening to Min’s Music. The number of listeners falls from 10,000 at Pareto-efficient point E, to 6,000. Since fewer people listen, at a higher price, the total benefit to listeners falls a lot. The social benefit of the programme is now the sum of the listeners’ benefits and the broadcaster’s revenue. But it is smaller than before—the higher price leads to a deadweight loss.

In this diagram, the horizontal axis shows the number of listeners N, and ranges between 0 and 14000. The vertical axis shows the price P in dollars, and ranges between minus 8 and 16. Coordinates are (number of listeners, price). A downward-sloping, straight line passes through points (4000, 9) and E (10000, 0) and is labelled Demand (WTP). A horizontal line passes through point (0, 0) and is labelled marginal broadcasting cost. Another horizontal line passes through point (0, 6) and is labelled P=6. A vertical line passes through point (6000, 6). The area between points (6000, 6), (0, 6) and (0, 15) is the benefit to listeners. The area between points (6000, 6), (6000, 0), (0, 0) and (0, 6) is the revenue. The area between points E, (6000, 0), and (6000, 6) is the deadweight loss.
Price Number of listeners Revenue Benefit to listeners Social benefit If C = 40,000 If C = 30,000
Net social benefit Profit Net social benefit Profit
0 10,000 0 75,000 75,000 35,000 −40,000 45,000 −30,000
6 6,000 36,000 27,000 27,000 23,000 −4,000 33,000 6,000
7.5 5,000 37,500 18,750 18,750 16,250 −2,500 26,250 7,500
10.5 3,000 31,500 6,750 6,750 −1,750
−8,500 8,250 1,500

Figure 10.8 Private provision of Min’s Music when it is excludable.

The table shows what happens to the social benefits of the programme as its price rises. As the audience is restricted, the social benefit falls, and the benefit to listeners falls faster. The right-hand columns show the net social benefit and the provider’s profit, which depend on the cost of making the programme, C. If C = 40,000, the provider cannot cover its costs at any of these prices. If C = 30,000, raising the price does enable the provider to make a profit: it does best at a price of $7.50. In this case, a private provider would be willing to supply the programme. But the reduction in benefits for listeners would be high.

This example illustrates two important things about excludable public goods:

  • Excludability may make it possible for the good to be supplied in the market system, but does not always do so (it depends on costs and demand in each case).
  • If the public good is provided privately with a positive price, there are deadweight losses and reductions in the benefits to consumers.

Whether an excludable good is provided in the market system depends also on the extent of competition between providers. In our example of Min’s Music, we didn’t consider the possibility that another provider might enter the market and take away some of the audience—and hence reduce demand for the programme. In particular, if Min’s Music was being broadcast regularly at a profit, a competitor might attract some of the audience with another programme with similar characteristics, making it impossible for Min’s Music to survive.

Exercise 10.8 Providing podcasts

Podcast providers face similar issues to those of radio broadcasters. Consider the following methods of raising the required money to finance an educational podcast:

  1. public provision (financed by general taxation)
  2. advertising (sponsors pay to be mentioned in the podcast)
  3. subscription (the podcast is available only to paid subscribers)
  4. ‘freemium’ model (an abridged version of the podcast is available for free, with the full version and additional features available only to paid subscribers).

Discuss the advantages and disadvantages of each method, including its effect on market surplus. Which would you recommend, and why?