Introduction

Equilibrium concepts for public goods discussed in the literature rely upon ‘individualised prices’, i.e. upon unlimited price discrimination between consumers. Such is the case, notably, for Lindahl equilibria, pseudo-equilibria and subscription equilibria; see, for example, Malinvaud (1972). In practice, however, price discrimination is either nonexistent or limited to a few broad categories of consumers. There are many good reasons for this practice, in particular: the lack of incentives for correct revelation of the preferences to which ‘individualised prices’ are related; the costs of administering and policing tariffs, of collecting and processing the necessary information, etc.; and the political and ethical constraints imposed on public services or licensed private monopolies, on grounds of equal treatment for instance.

Concepts of equilibrium with price rigidities and quantity constraints recently introduced for private goods (see, for example, Bénassy (1975), Drèze (1975) or the survey article by Grandmont (1977)) are susceptible of application to public goods. This idea underlies some work of de Carvalho (1979) on tâtonnement processes for public goods of the type defined by Malinvaud (1971) and Drèze and de la Vallée Poussin (1971). de Carvalho introduces (chapter 5) the additional constraint that individual contributions towards financing the public goods must be kept equal over predetermined groups of consumers. The properties of the constrained processes are analysed, with the help of an appropriate concept of secondbest Pareto optimality.