¹ It is necessary for efficiency that the lake be run as a firm, and not simply divided up as private property among the fisherfolk. For in the latter case, if there are decreasing returns to scale in labor, there will be externalities in production: what happens on one section of the lake affects productivity of other sections. The firm internalizes these externalities.

² The ‘Coase theorem’, for instance, states that regardless of the distribution of (private) property rights in a heretofore commonly-owned asset, the allocation of the asset's productive uses will be the same after privatization if there are no income effects on demand. The criticisms one can raise against this statement are not my concern here.

³ The proofs of all theorems quoted are available, unless otherwise indicated, in Roemer, John, “Public Ownership Resolutions of the Tragedy of the Commons,” Department of Economics, University of California, Davis. Working Paper No. 295 (1987).Google Scholar

⁴ Locke, John, Two Treatises on Government, ed. P., Laslett (Cambridge: Cambridge University Press, 1976)Google Scholar, section 27.

⁵ Nozick, Robert, Anarchy, State, and Utopia (New York: Basic Books, 1974)Google Scholar, chapter 7, section 1.

⁶ Note that Nozick's proviso is weaker than Locke's because in the case of decreasing returns it is impossible to leave enough and as good in common for others. Thus, the substitution of a welfare criterion for a physical one is not innocuous. For an elaboration of this point, see Cohen, G. A., “Self-Ownership, World Ownership, and Equality. Part II,” Social Philosophy and Policy, vol. 3, issue 2 (1986).CrossRefGoogle Scholar

⁷ This theorem is due to Weitzman, M., “Free Access vs. Private Property as Alternative Systems for Managing Common Property,” Journal of Economic Theory, vol. 8 (1974), pp. 225–34CrossRefGoogle Scholar.

⁸ This result holds because the appropriators have no scarce talent, which they might otherwise use to increase, let us say, the productivity of the lake. Many of Nozick's examples refer to situations where the appropriators do have skills lacking in the rest of the population.

⁹ Roemer, John E. and Silvestre, Joaquim, “Public Ownership: Three Proposals for Resource Allocation,” Department of Economics, University of California, Davis, Working Paper No. 307 (December 1987).Google Scholar

¹⁰ The proof is available in Roemer and Silvestre, ibid., Theorem 8.

¹¹ Theorem 9 in Roemer and Silvestre, ibid.

¹² The general theory of implementation of allocation mechanisms in Nash equilibrium is developed in Maskin, E., “The Theory of Implementation in Nash Equilibrium: A Survey,” eds. Leo, Hurwicz, David, Schmeidler, and Hugo, Sonnenschein, Social Goals and Social Organization (New York: Cambridge University Press, 1985).Google Scholar

¹³ There are other theories of implementation than Maskin's. Recently, a theory of implementation in sub-game perfect Nash equilibria by games in extensive form has been developed; see Moore, John and Repullo, Rafael, “Implementation by Stage Mechanisms,” European Economic Review (1987).Google Scholar For reasons beyond the scope of my discussion, I do not view this kind of implementation appropriate for solving the problem here.

¹⁴ Joshua Cohen has questioned whether such an interventionist state might, nevertheless, not still be considered minimal by Nozick's definition, for the purpose of the interference is to learn the endowments of the population, not to tax their wealth. If privacy is a right which a minimal state must not transgress, then surely the state required to implement a mechanism that Pareto-dominates common ownership is not minimal.

¹⁵ This is so because, in a small economy, some agents (by definition of ‘small’) do not optimally behave by taking announced prices as given. An agent who has some market power will, strategically, set prices at what the market will bear; that he can significantly alter the supply of some good by withdrawing from the market enables him to manipulate prices. Because of this, the Walrasian equilibrium cannot be implemented by strategic players in a small economy playing a non-cooperative game, where dominant strategy equilibria are the rule.

¹⁶ An anonymous allocation rule is one that distributes commodities according to the traits people have, but not according to their names or other extraneous identifying information. The class of allocation rules that are anonymous, Pareto-efficient, and implementable in dominant strategy equilibrium is characterized in a series of recent papers by Makowski, Louis and Ostroy, Joseph: “Vickrey-Clarke-Groves Mechanisms and Perfect Competition,” Journal of Economic Theory (1988)Google Scholar; “Dominant Strategy Mechanisms in Nonatomic Transferable Utility Economies: Characterization and Existence,” Department of Economics, University of California, Los Angeles, Working Paper No. 421 (1986); and “Efficient Dominant Strategy Mechanisms in Large Economies,” Department of Economics, University of California, Davis (1987). There are no dominant-strategy-implementable, anonymous, Pareto-optimal allocation mechanisms on the class of economies with a finite number of agents.

¹⁷ The proof, available in Roemer, (ibid.) is based upon Makowski and Ostroy (1986 and 1987, ibid.).

¹⁸ This result is not so strong as it may appear, due to the assumptions of the model. It is assumed that (a) no one has any special technological knowledge -fis common knowledge, and (b) there is no prior private ownership of the technology (or the lake). Suppose, instead, it is assumed that there are two fisherman, A and B, each of whom knows a technology for fishing, f_A and f_B respectively, where f_A is slightly better than f_B. The rest of the fishermen know nothing about fishing. Then it will, in general, be possible to decentralize, using dominant strategies, an anonymous allocation mechanism in which A receives profits equal to the difference in total product from using f_A and f_B, and every other fisherman receives the marginal product of his labor plus a per capita share of the remaining profits. Only if some agents uniquely possess valuable knowledge will they receive special profits. (If, in particular, A and B each know the same technology, then neither of them will be able to appropriate any profits above their per capita share under a dominant-strategy-implementable, efficient mechanism.)

¹⁹ The model of fisherfolk with different endowments of labor is a limited one for evaluating the claimed virtues of private property. The Austrian school advocates private ownership as the unique institution that elicits scarce talents and entrepreneurship from members of society. To study this claim requires a model in which there are several kinds of labor and many (potential) commodities. The concept of Proportional Equilibrium extends to such economies; see Roemer and Silvestre, ibid. The implementation theory of public ownership for such economies is a project for future work.