Quasi-public goods and the spectrum

The same gym in two different boxes

At six o'clock in the morning, a members-only gym is almost empty. Rafael uses a treadmill, and every other treadmill is still free. His use takes nothing from anyone. At six o'clock in the evening, the same gym is full. Rafael takes the last treadmill, and Mei waits twenty minutes for it.

The last lecture sorted goods into four boxes with two yes-or-no questions. It also promised that the boxes are not as tidy as they look. Here is the problem. Is the gym rival? In the morning the answer is no. In the evening the answer is yes. Nothing about the gym has changed except the number of people inside it.

So the two questions do not always have a yes-or-no answer. Rivalry can grow as a good gets crowded. Excludability can grow when someone builds a gate, writes a password or passes a law. Most real goods sit somewhere between the boxes, and many of them move. This lecture is about those in-between goods, and about why their position matters so much for policy.

Rivalry comes in degrees

Think about a road. When traffic is light, one more car slows nobody down. The road is non-rival. As more cars join, the road fills. Each new car now makes every other car a little slower. At some point the road is clearly rival: your use of it takes something real from everyone else, which is their time.

A good like this is called congestible. It is non-rival up to a point, and then it becomes more and more rival as it gets crowded. Roads, parks, beaches, museums, swimming pools and mobile phone networks all behave this way.

The important word is "each". When a road is crowded, one extra car adds only a tiny delay to each other car. But there are thousands of other cars. A tiny delay multiplied by thousands is a large cost. And the driver who causes it does not pay it. That is exactly the shape of a negative externality, which you met earlier in this topic.

Traffic planners describe how trip time rises with traffic using a formula developed by the US Bureau of Public Roads. The explorer below uses that formula for an invented road: a trip takes 10 minutes when the road is empty, and the road is designed for 2 000 cars an hour. Move the traffic and watch two things: your own trip time, and the total delay your car adds to everyone else.

What did you see? Up to about 1 000 cars an hour, one more car adds almost nothing to anyone, less than half a minute in total. The road behaves like a non-rival good. Beyond the design figure, the extra delay grows very fast. At 2 500 cars an hour, one more car adds about 15 minutes of delay, spread across all the other drivers. At $15 an hour, that is about $3.66 of other people's time. The driver feels none of it.

That is it. That is the whole idea of a congestible good. The same road is non-rival at night and rival at rush hour, and the change is gradual, not a jump from one box to another.

Excludability depends on cost, technology and law

The last lecture defined excludability as being able to keep non-payers out "at a reasonable cost". That phrase is the key to the second half of the story. Whether exclusion is reasonable depends on three things.

Cost. A long open beach is hard to fence. A small beach with one path to it can be fenced cheaply, with a gate and a ticket booth. The beach did not change. The cost of exclusion did.

Technology. For decades, a television signal sent over the air could be received by anyone with an aerial. It was non-excludable. Then signals could be scrambled, so that only paying homes could unscramble them. Later, video moved to the internet, where a password decides who watches. The same film moved from the public-good corner to the club-good corner, because technology made exclusion cheap.

Law. Technology can also work the other way. Cameras that read number plates made it possible to charge every car that enters a city centre, without stopping any of them. A road that was non-excludable in practice can become excludable once the law allows a charge and cameras collect it.

Put rivalry and excludability together, and the four boxes become a map. A good can sit anywhere on it. It can also move.

Many textbooks draw a simpler version: a single line from "pure public good" at one end to "pure private good" at the other, with quasi-public goods in between. Defence and flood barriers sit near the public end. Street lighting and open parks come next. Toll roads, museums with entry fees and swimming pools come after them. Food, clothing and haircuts sit at the private end. The line is a useful summary. The map shows why each good sits where it does.

One road, four economic goods

The last case shows why a congestion charge is two policies at once. It creates excludability, because only drivers who pay may enter. And it works as a Pigouvian tax: it makes each driver pay something towards the delay that the driver causes to others. Ideally, the charge would equal that delay, valued in money. In the explorer, that is about $1.50 at 2 000 cars an hour and about $3.66 at 2 500.

A real case: London's congestion charge

Stockholm's experience shows the other half of the story, which is public opinion. The city ran a seven-month trial charge from January to July 2006. Traffic across the charging cordon fell by about 22%. Queuing time fell by roughly a third in the morning peak and about half in the evening peak. Residents voted in a referendum in September 2006, and the charge was brought back permanently in August 2007. A study of the trial concluded that the faster journeys were large enough for ordinary people to notice, and that this changed many minds.

Education: a private good with a public side

Is education a public good? Many people say yes, because educated people benefit everyone. Ask the two questions instead.

A place in a classroom is rival: when the class is full, another pupil cannot join it. A teacher's attention is rival too. And a school can charge fees and refuse pupils who do not pay, so education is excludable. By the two questions, a school place is close to a private good.

But education also has large benefits for people other than the student. A society with more educated people tends to have more ideas, better public debate and more people able to do skilled work. These are positive externalities, which you met earlier in this topic. They mean that a free market would produce too little education. They do not change the two properties. A good can be rival, excludable and still create benefits for others. Test this kind of argument below.

This difference matters for policy. If education were a public good, the argument would be about free riding, and only compulsory payment through taxes could supply it. Because it is mostly a private good with positive externalities, the argument is about the externality. So the tools can be subsidies, grants or free school places, alongside private schools. Different reasons lead to different tools.

Where a good sits decides the policy

Here is the main reason the map matters. Each region of it points to a different kind of policy.

Technology keeps moving goods across this table. Each time exclusion becomes cheap, a good that once needed taxes can be sold instead. This shrinks the public-goods problem, because firms can now collect payment. But it raises a question of fairness. A good that everyone once received, such as a free television broadcast, may now reach only those who can pay. Economics can describe that trade-off. It cannot decide it on its own.

Three classic mistakes