The implied institutional setting for neo-classical economic theory, including theoretical welfare economics, is a regime of private property, in which all and services are privately (individually) utilized or consumed. Only within the last two decades have serious attempts been made to extend the formal theoretical structure to include communal or collective ownership-consumption arrangements.2 The pure theory of public goods remains in its infancy, and the few models that have been most rigorously developed apply only to polar or extreme cases. For example, in the fundamental papers by Paul A. Samuelson, a sharp conceptual distinction is made between those and services that are purely private and those that are purely public . No general theory has been developed which covers the whole spectrum of ownership-consumption possibilities, ranging from the purely private or individualized activity on the one hand to purely public or collectivized activity on the other. One of the missing links here is a theory of clubs , a theory of co-operative membership, a theory that will include as a variable to be determined the extension of ownershipconsumption rights over differing numbers of persons. Everyday experience reveals that there exists some most preferred or membership for almost any activity in which we engage, and that this membership varies in some relation to economic factors. European hotels have more communally shared bathrooms than their American counterparts. Middle and low income communities organize swimming-bathing facilities; high income communities are observed to enjoy privately owned swimming pools. In this paper I shall develop a general theory of clubs, or consumption ownership-membership arrangements. This construction allows us to move one step forward in closing the awesome Samuelson gap between the purely private and the purely public good. For the former, the optimal sharing arrangement, the preferred club membership, is clearly one person (or one family unit), whereas the optimal sharing group
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