Jim Roumasset, Professor of Economics, University of Hawaii:

The Grand Equivalence Version of the Coase TheoremAs Tim Haab pointed out in January, 2006, there are multiple versions of the Coase Theorem. In what follows, I suggest a version that retrospectively fits Coase's agenda.

First, let's dispense with the oft-repeated versions and distinguish the Coase theorem from the corollary to the Coase theorem. The weak (efficiency) version of the theorem -- that unrestricted bargaining will end in a Pareto optimal outcome is tautological. The natural construct to use is the core of an economy. So the proposed theorem is that the core of an economy is Pareto optimal. But the core is already a subset of Pareto optimal points.

As Tim and others have noted, the strong (efficient and invariant to changes in liability) version of the theorem is incorrect because of income effects. This cannot be fixed by assuming no income effects, because your theorem will be tautological again -- anything that violates the invariance result is assumed away. You can restrict the utility functions in such a way as to rule out income effects, say by assuming quasi-linear utility, but then you are back to saying that the core -- which now contains only one point -- is Pareto optimal.

Additional confusion may result from the alleged corollary to the Coase Theorem: use property rules to enforce property rights when transactions costs are low, while liability rules should dominate when transactions costs are high (Micelli). This is more of a rule of thumb than a corollary, but let's return to the world of zero transaction costs.

An alternative view of the Coase theorem was part of the UCLA oral tradition, when Armen Alchian, Harold Demsetz, and Ben Klein were working and teaching together. According to Demsetz, Klein's version of the Coase theorem is that absent transaction costs, alternative institutions such as markets and contracts are equivalent. In order to elucidate this equivalence version, we first need to introduce competition.

When Coase famously presented the ideas behind, "The Problem of Social Cost" at a 1959 Chicago seminar, and pursuant dinner at the home of Aaron Director, he revealed that he had in mind situations of

a prioricompetitive bargaining (again, according to Demsetz). If bargaining is costless, then the farmer can be viewed as selecting among several ranchers to bargain with; likewise the rancher. It was Steven Cheung who explored this idea further. In his Theory of Share Tenancy, Cheung argued that if tenants are competing with other tenants to get favorable contractual terms regarding share and labor/hectare and landlords are similarly bargaining with other landlords, the outcome of competitive bargaining will be identical to the labor-market equilibrium. Similarly if beekeepers and orchard owners bargain over contractual terms for locating hives in particular orchards, the outcome will be identical to a (costless) market for pollination services.Cheung's insights inspire the grand equivalence version of the Coase theorem: transaction costs aside, if property rights are commensurate and competition prevails, then any bilateral externality will be equivalently internalized by markets, contracts, and Pigouvian taxes. The Pigouvian tax solution is equivalent to a competitive market in pollution rights where polluters must buy rights from victims. And the core of a competitive contracting economy shrinks to the same market solution -- ergo all three institutions are equivalent.

Note that for the full equivalence to hold however, spillovers must be bilateral. This applies to the cases that Coase investigated. Cattle trample a farmer's fields; a building blocks sunlight to a neighbor's swimming pool; a confectioner disturbs a dentist's patients etc. In each case the source of the externality is matched with a particular victim.

Notwithstanding this limitation, the equivalence version helps to underscore the Pigouvian fallacies that motivated Coase. Pigouvian taxation is revealed as not the only way to internalize an externality. Market and contractual institutions should also be considered, as well as corrective subsidies.

The theorem also is a springboard for Coase's primary achievement -- providing the pillars for the New Institutional Economics. First, the Coasean maximum-value solution becomes a benchmark by which institutions can be compared. And the institutional equivalence result establishes the motive for comparative institutional analysis and suggests the means by which institutions can be compared (according to their respective abilities to economize on transaction costs).

The equivalency result also underlies Coase's (1937) proposition that the boundaries of the firm are chosen to minimize transaction costs. Aside from the "marketing costs" of using outside suppliers and the agency costs of central direction inside the firm, whether to put Fisher Body inside or outside of General Motors would have been a matter of indifference.

Jim Roumasset, University of Hawaii

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