Revealed Preference for Public Goods

Abstract

The most serious problem for the modern theory of optimal public expenditure is that although it has to be based on some social welfare function, individual preferences for public goods, which constitute the elements of any individualistic social welfare function, are hard to assess. It is argued that since every individual can freely participate in the consumption of a public good, there is an incentive for him to either underreport or overreport his preferences depending on how the reported preferences are used in the financing process of the public good.I This argument will be correct if an individual's preferences for public goods can be expressed only directly. In many cases, however, the consumption of a public good has some technical or objective relationship with the consumption of some private goods. Thus, the benefit an individual derives from free highways depends on how much he spends on a car and gasoline. Even the benefit an individual derives from the judicial system depends on how much he spends to hire the services of lawyers. Also, an individual can enjoy the same security police provide by hiring private guards and installing locks, and so on. In these cases, if we know the technical relationships between the consumption of private goods and the consumption of public goods, then from the market data relating the amounts of private goods bought to prices and the data on the existing amounts of public goods, we might be able to infer (i) the amounts of final goods consumed (say the number of trips from one point to another, the degree of justice, the security from robbery, etc.), and (ii) their opportunity costs which the individual was willing to pay. But if we succeed in this inference, then all that remains to be done in order to find the individual's utility function will be to integrate back the relationship between the amounts of final goods consumed and their opportunity costs. A trivial example can be provided by assuming that each public good is perfectly substitutable with a private good. Let yi be the quantity of the ith public good and xi be the quantity of a private good which is a perfect substitute for the ith public good. Then the benefit derived from the ith public good and its perfect substitute can be measured by xi+yi. Suppose we have ascertained an individual consumer's demand functions for private good when all the yi are zero. We know from the revealed preference theory that if these demand functions satisfy a certain condition (namely the symmetry of the Slutsky matrix), then there exists a utility function unique up to a monotone transformation: