The Continua of Excludability and Rivalry
The classic definition of a “public good” is that it is both “non-excludable” and “non-rival.” Textbooks normally treat these traits as binary, delivering this 2 x 2 typology:
Yet in the real world, both excludability and rivalry lie on a continuum. Almost nothing is 0% excludable. If you spend enough effort, you can prevent non-payers from enjoying your product. At the same time, almost every good requires some effort to exclude non-payers. Hence, nothing is 100% excludable either.
Think about software. If you add a little security, you can prevent some people who haven’t paid you from enjoying your product. But if that’s all you do, plenty of non-payers will slip through the cracks. And the more you spend on security, the more non-payers you get to exclude.
The same goes for rivalry. Virtually nothing is 0% rival. Adding consumers almost always slightly raises cost or reduces quality. Other people at a fireworks show obstruct your view. Extra customers in a near-empty theater increase the costs of cleaning, wear-and-tear on the seats, and air conditioning costs (via body heat). At the same time, almost nothing is 100% rival. If you’re running a restaurant, you almost always end up throwing away some perfectly good food. Furthermore, some goods are more than 100% rival. It’s called congestion. Doubling driving at rush hour doesn’t just double wear-and-tear on the roads; it can easily turn 60 mph roads into 20 mph roads. You can even argue that some goods are less than 0% rival. If there are only two people in your nightclub, adding more guests improves the experience for those already there.
Despite the textbook 2 x 2 matrix, econ teachers normally insinuate that excludability and rivalry are at least positively correlated. With binary traits, this basically means that the top left and bottom right boxes contain more goods than the top right and bottom left boxes. Once you accept that excludability and rivalry lie on a continuum, however, matters become far less clear. Even assigning proper excludability-rivalry coordinates is a challenge. What, for example, are the average coordinates for Route 66 in the DC area? We’ve added electronic toll collection, so clearly the road is excludable to some degree; but adding the tolls did come at great expense. And when you don’t charge tolls, the roads are highly congested for many hours per day. Knowing what I know, I’d probably assign excludability-rivalry coordinates of (.8, 1.3). But that could be way off.
Once you’ve assigned credible excludability-rivalry coordinates, you can finally test the standard insinuation that the two traits are positively correlated. Are they really? And from there, you can explore Dan Klein’s visionary hypothesis that technological progress gradually transforms public goods into private goods. Not to mention my view that the correlation between “public goods” and “goods provided by government” is awfully low.
Public goods theory is now about 70 years old. So why has economics barely progressed beyond the simplistic textbook understanding of the problem? I suspect that it’s left-wing bias. If the textbook treatment sounds pro-market, most economists are eager to run empirical tests in the hopes of discrediting the textbook result. If the textbook treatment sounds pro-government, in contrast, most economists want to just treat it as fact and move on. Public goods theory sounds pro-government.
Hence, we see hundreds of empirical papers testing whether the minimum wage “really reduces employment,” but near-zero empirical papers that test whether government “really supplies public goods.”
Update: Jonathan Meer pointed me to this useful related piece by Jeremy Horpedahl.