Wednesday 30 May 2012

On the Definition of Public Goods

Frances Woolley had a nice post over at the Worthwhile Canadian Initiative yesterday about the textbook treatment of public goods. Her beef is with the use of national defence as the canonical example.

I have a more fundamental beef. Could we please please all agree to change the definition of what constitutes a pure public good. The classic definition is that a pure public good is one that is a) non-rivalrous in consumption, and b) non-excludable.

I want to remove the second of these from the definition. Non-rivalrousness relates to the nature of the good; non-excludability relates to what mechanisms would allow for it to be provided. This conflates two quite distinct ideas and so is not helpful for a number of reasons.

First, microeconomics courses typically move straight from the definition of a public good to finding the condition for the optimal level of its provision (the Samuelson condition in intermediate micro; or, in partial-equilibrium terms, stating that the sum of the willingness to pay should equal the marginal cost). This optimality condition is equally true of any good that is non-rivalrous in consumption, whether it be excludable or not, but that is not the impression you would get reading treatments that show the optimality conditions after imposing a definition of excludability.

Second, non-excludability is neither necessary nor sufficient for public provision to be the only or even the best means of provision: Just because a good is excludable, it does not necessarily follow that it can be profitably supplied by the private sector if there is variation in consumers’ willingness to pay and limited opportunities for price discrimination; and a good being non-excludable does not mean that it could not be provided privately through philanthropy, being tied to other goods, etc.

Third, the standard definition leaves a gaping hole in most (possibly all) textbook treatments of market failures. We typically move from the first welfare theorem (a competitive market outcome is Pareto efficient) to a listing of potential market failures under which the theorem may not hold—incomplete markets, lack of property rights, transactions costs, monopoly, asymmetric information, externalities, and public goods. If public goods are required to be non-excludable by definition, this list is missing a very important market failure—non rivalrous but excludable goods, which might be provided by a private market, but not at the efficient level.

Finally, by conflating properties relating to the provision of a good with properties relating to how it enters consumers preference functions, we add to the likelihood of students thinking that a public good is one that is provided by the government and a private good one provided by the public private sector. And this, I think, leads to exactly the problem that Frances raises: that arguments about national defence being a public good “confounds the abstract—defence, protective services—and real world military spending”.

O.K. So I am not going to be able to bring about a change in the world’s textbooks with this post, but any prospective Canterbury ECON 203 students who might be reading this, please take note: We will be using the non-standard definition next semester!

11 comments:

  1. Actually, Frances has been railing against that one for a while now.

    http://economics.ca/2006/papers/0901.pdf

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  2. Excellent. And then as Arlo Guthrie would point out, we only need one more and we can say we have a movement.

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  3. Trying to think of real-world non-rivalrous but excludable goods that might have failure in supply. Something like how, were SkyTV able to come closer to perfect price discrimination, total surplus would increase as more people would subscribe?

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  4. Seamus - would it make you happy to know that the man himself would agree with you? There's a little rant by Paul Samuelson here (and you really feel, reading it, as if he's just losing it, feeling incredibly frustrated with people who just don't understand):

    http://www.econ.ucsb.edu/~tedb/Courses/UCSBpf/readings/SamPayTV.pdf

    This is more or less what he says:

    "the essence of the public goods phenomena was not intrinsically tied up to the ability to "exclude" people from a common service....[even if TV signals could be scrambled] we would still be faced with a case of intrinsically increasing returns to scale and in all such cases there is an element of the public-good dilemma."

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    1. Correct me if I'm wrong here, Frances and Seamus. But wouldn't we generally expect the losses coming from nonexcludability to be larger than the losses from nonrivalrousness? Surely the latter is more like the Harberger Triangle from underprovision while the former can be the whole trapezoid.

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    2. Thanks for the Samuelson link, Frances. I am no expert on the history of thought. Who was it, then, who first insisted on wrapping non-excludability up with non-rivalrousness in the definition of public goods. BTW, I don't get the impression that Samuelson is losing it in that piece, it read to me as classic Samuleson. Compare for instnace his debates in the 70s with Kemp and Ng!

      @Eric: The losses from a non-rival good with non-excludability and *no* government provision will likely be no less than the losses from a non-rival good with excludability and *no* government provision, ceteris paribus to the existence of other mechanisms for private provision, but that fact alone does not imply a conclusion that government provision is desirable in the former case nor that it is not desirable in the latter.

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  5. Seamus - I've noticed that your blog posts are rather dry, in contrast to your classes (in tone, not necessarily material). Eric, on the other hand, maintains a similar tone between his posts and classes. (Caveats: small and slightly dated sample sizes). What do you think this says about your respective objective functions?

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  6. Why bother calling a non-rival good a public good? Why not call it .... I don't know ... how about ...... a non-rival good??? Seems simple. If you want to talk about non-rival goods why not just call them that?

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  7. Seamus - I think Eric hints at the answer to your question about the inclusion of non-excludability - without excludability there is not reason to assume under-provision thus a different type of government intervention is needed, if government intervention is needed at all. With non-rival excludable goods, e.g. medical research, over-provision can easily occur - just think about the amount of effort that goes into creating copy-cat medications.

    My guess would be that Musgrave and Musgrave made that point in their public finance text, but can't be sure. I've read the section, but it was a while ago and I don't remember it perfectly.

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  8. Paul - "Why not call it .... I don't know ... how about ...... a non-rival good???" Samuelson's original term was collective consumption good, and his definition was all about non-rivalness. Collective consumption good would have a long and distinguished history behind it.

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    1. Collective consumption good sounds good, I just don't see what a re-definition of the term public good buys us.

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