Neoclassical economic theory, the kind we mostly teach in graduate schools today, has difficulty dealing with publicness. The main sticking point is methodological individualism. While I believe that we need to build a more social economic theory, I also think we should remember the hard-won achievements of the branch of economics called public economic theory. They ought to have something to teach us as we try to build a more social, more psychologically aware, economics.
The ultimate attempt to study society formally from the point of view of methodological individualism is social choice theory. This theory views a society as a collection of individuals that face a collective choice. There is a set of possible, mutually exclusive decisions, out of which they must select only one decision to make. Each individual has a ranking of these possible decisions. These rankings are the preferences of the individuals and, in true Enlightenment spirit, the choice of society is assumed to be based on the individuals’ preferences alone. Kenneth Arrow burst into the scene with his famous, and field-creating, discovery around 1950 that some particular, very appealing to democratically-minded people, axioms on how such decisions must be made, are logically incompatible with each other. The basic message of this theorem seems to be that a well-functioning democracy is hard to achieve, especially when the preferences of the society’s members are wildly different from each other, no matter what the decision-making rule is, as long as it respects these basic axioms.
A good exposition is in Amartya K. Sen’s 1998 Nobel lecture. There is a nice formal summary exposition in chapter 9 of Multiagent Systems, by Yoav Shoham and Kevin Leyton-Brown, Cambridge University Press 2009. The authors make the book available online for those without easy access to its physical form. Wulf Gaertner has written an introductory book, A Primer in Social Choice Theory, Oxford University Press revised edition 2009 (here is the Google Books page). Finally, my own book, mentioned in the About page, devotes a chapter to social choice theory.
Public goods and general equilibrium
General equilibrium theory considers models of economies with many commodities (goods and services), each of which is measurable with to commonly agreed units and sold in competitive markets. Production technology is taking as given, as are the preferences of individuals and the amounts of goods that individuals are endowed with at the outset. Each individual has a budget constraint and expresses net demands and supplies based on the budget constraint in such a way as to get to the highest affordable consumption bundle on her/his preference ranking. Each firm that engages in production arranges its use of goods and services as inputs and supplies net outputs to the individuals in the marketplace, in an effort to maximize its profit. Both individuals and firms take market prices as given (the theory is silent as to how these prices are actually established). It is a basic aim of the theory to show the possibility of the simultaneous establishment of prices for all the commodities in such a way as to make all these markets clear (meaning that the amount offered for sale of each commodity at these equilibrium prices equals the amount demanded for purchase at these prices). From that follow the “welfare theorems”, which show that such equilibration of all markets leads to efficient allocations, and every efficient allocation can be derived from it. Another important aim is to study how equilibrium prices (and allocations) change when the fundamentals of the economy change.
Public goods have a place in general equilibrium theory. I find that this place is overly restrictive of the concept of publicness, but this does not excuse ignorance of what theorists have achieved in integrating public goods in general equilibrium analysis. The integration goes like this: imagine that there is a good or service that is consumed by many people at the same level without each person’s consumption reducing the amount available for the others—this is what being a public good means. Think of streetlights or national defense services. Then imagine that some organization (a government agency) provides the public goods and uses private goods to produce them. Individuals have preferences for public and private good bundles and express their demands for private goods with the influence of the public goods already embedded. However, how (and if) they express their desires for public good provision is less clear, and depends on the theory we are looking at.
Easily accessible online sources include Wikipedia and this incomplete (but good) essay. There are also numerous expositions in books, as practically every textbook in microeconomics covers the topic. The classic reference at the graduate level is Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green (chapters 15-17, mostly), Oxford 1995. My book, mentioned above, has extensive coverage of public goods in general equilibrium. A nice set of lecture notes (but fairly demanding in terms of mathematical preparation) is this set by Nicholas Yannelis.
There are not many freely accessible expositions of public goods online. A nice undergraduate course by Jeff Ely gives a grounding in the main concepts, although the slides listed are a bit terse.
The standard view of public goods in general equilibrium considers them measurable in the same sense that we can measure how much bread we buy at the supermarket. For many public goods and services, the measurability assumption is overly strong. The basic welfare theorems can be shown without this assumption, as Andreu Mas-Colell showed in 1980 in a model with a single private good and a public good without any assumption on the structure of the public good. This model does not allow one to talk about the level of provision of the public good, yet a variation of the competitive equilibrium, called valuation equilibrium, delivers efficient allocations if one makes the usual assumptions of complete and perfectly competitive markets in the private goods of the economy.
[Latest draft: 2010-07-08. This page is under construction and will keep growing and evolving for a while.]