Anarchy, the Market, and the State

Abstract

The characteristics of private and public goods, and the conditions defining the Pareto optimal allocation of each are as opposite as are anarchy and dictatorship. Pareto optimality with private goods requires the horizontal summation of demand schedules, the equation of each individual's marginal rate of substitution to the price ratio. Pareto optimality with public goods requires vertical summation of demand schedules, the equation of the summation of marginal rates of substitution to the price ratio. Increasing the number of buyers and sellers improves the allocation of private goods, as does increasing their mobility. The orderly anarchy of the market achieves a Pareto optimal allocation of resources for pure private goods, if there is either a large number of buyers and sellers, or perfect mobility into and out of all markets.' In contrast, Pareto optimality in the anarchic provision of a pure public good can be assumed with certainty only in the trivial case of a community of one. Once Crusoe is joined by Friday, public goods provision becomes a prisoners' dilemma with non-Pareto outcomes likely. With small numbers, Pareto optimality may still emerge in an anarchic prisoners' dilemma game, if the same players repeat the game indefinitely, through the familiar logic of the prisoners' dilemma supergame [12, ch. 2; 1]. Thus, small numbers and immobility favor the anarchic achievement of Pareto optimality for public goods provision, just as large numbers and high mobility favor the anarchic achievement of Pareto optimality in private goods markets. This dichotomous view of the potential for a Pareto optimal allocation of resources under anarchy has the obvious twin implication, that the case for government intervention is strongest when the numbers of buyers and sellers of private goods are small and mobility absent, and for public goods when numbers are large and mobility high. Although this dichotomous depiction of the allocation problem is highly simplified, it does provide some insight into where we can (should) expect to find governments intervening, where we can (should) not. Now consider the further implication. The characteristics of a community in terms of the number of members and their mobility are usually the same with respect to both private goods allocation and public goods allocation. A medieval village consisted of a small number of families, most of whose members never traveled more than a few kilometers from the village throughout their lives. This same small group of people would confront each other in the many public good-prisoners' dilemma situations a community faces, as they would in whatever market transactions that took place. One expects from the discussion above that the provision of public goods in a medieval village, e.g., law and order, and the resolution of other prisoners'