In law and economics, the Coase theorem (pronounced /ˈkoʊs/) describes the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem states that if trade in an externality is possible and there are no transaction costs, bargaining will lead to an efficient outcome regardless of the initial allocation of property. In practice, obstacles to bargaining or poorly defined property rights can prevent Coasian bargaining. This "theorem" is commonly attributed to The University of Chicago's Nobel Prize laureate Ronald Coase. However, Coase himself has stated that the theorem was based on perhaps four pages of his 1960 paper The Problem of Social Cost and that the "Coase theorem" is not about his work at all. 
This 1960 paper, along with his 1937 paper on the nature of the firm (which also emphasizes the role of transaction costs), earned Ronald Coase the 1991 Nobel Memorial Prize in Economic Sciences. In this 1960 paper, Coase argued that real-world transaction costs are rarely low enough to allow for efficient bargaining and hence the theorem is almost always inapplicable to economic reality. Since then, others have demonstrated the importance of the perfect information assumption and shown using game theory that inefficient outcomes are to be expected when this assumption is not met.
Nevertheless, the Coase theorem is considered an important basis for most modern economic analyses of government regulation, especially in the case of externalities, and it has been used by jurists and legal scholars to analyse and resolve legal disputes. George Stigler summarized the resolution of the externality problem in the absence of transaction costs in a 1966 economics textbook in terms of private and social cost, and for the first time called it a "theorem." Since the 1960s, a voluminous literature on the Coase theorem and its various interpretations, proofs, and criticism has developed and continues to grow.
- 1 The theorem
- 2 Efficiency and invariance
- 3 Equivalence version
- 4 Application in United States contract and tort law
- 5 Example of application
- 6 Criticism
- 7 Notes
- 8 References
- 9 Further reading
- 10 External links
Coase developed his theorem when considering the regulation of radio frequencies. Competing radio stations could use the same frequencies and would therefore interfere with each other's broadcasts. The problem faced by regulators was how to eliminate interference and allocate frequencies to radio stations efficiently. What Coase proposed in 1959 was that as long as property rights in these frequencies were well defined, it ultimately did not matter if adjacent radio stations interfered with each other by broadcasting in the same frequency band. Furthermore, it did not matter to whom the property rights were granted. His reasoning was that the station able to reap the higher economic gain from broadcasting would have an incentive to pay the other station not to interfere. In the absence of transaction costs, both stations would strike a mutually advantageous deal. It would not matter which station had the initial right to broadcast; eventually, the right to broadcast would end up with the party that was able to put it to the most highly valued use. Of course, the parties themselves would care who was granted the rights initially because this allocation would impact their wealth, but the end result of who broadcasts would not change because the parties would trade to the outcome that was overall most efficient. This counterintuitive insight—that the initial imposition of legal entitlement is irrelevant because the parties will eventually reach the same result—is Coase’s invariance thesis.
Coase's main point, clarified in his article 'The Problem of Social Cost,' published in 1960 and cited when he was awarded the Nobel Prize in 1991, was that transaction costs, however, could not be neglected, and therefore, the initial allocation of property rights often mattered. As a result, one normative conclusion sometimes drawn from the Coase theorem is that property rights should initially be assigned to the actors for whom avoiding the costs associated with the externality problem are the lowest. The problem in real life is that nobody knows ex ante the most valued use of a resource, and also that there exist costs involving the reallocation of resources by government. Another, more refined, normative conclusion also often discussed in law and economics is that government should create institutions that minimize transaction costs, so as to allow misallocations of resources to be corrected as cheaply as possible.
- Version 1: A clear delineation of private property rights is an essential prelude to market transactions.
- Version 2: As long as private property rights are well defined under zero transaction cost, exchange will eliminate divergence and lead to efficient use of resources or highest valued use of resources.
- Version 3: The allocation of resources is invariant to the assignment of private property rights under zero transaction cost and zero income effect.
Efficiency and invariance
Because Ronald Coase himself did not originally intend to set forth any one particular theorem, it has largely been the effort of others who have developed the loose formulation of the Coase theorem. What Coase initially provided was fuel in the form of “counterintuitive insight” that externalities necessarily involved more than a single party engaged in conflicting activities and must be treated as a reciprocal problem. His work explored the relationship between the parties and their conflicting activities and the role of assigned rights/liabilities. While the exact definition of the Coase theorem remains unsettled, there are two issues or claims within the theorem: the results will be efficient and the results in terms of resource allocation will be the same regardless of initial assignments of rights/liabilities.
Efficiency version: aside from transaction costs, the prevailing outcome will be efficient
The zero transaction cost condition is taken to mean that there are no impediments to bargaining. Since any inefficient allocation leaves unexploited contractual opportunities, the allocation cannot be a contractual equilibrium.
Invariance version: aside from transaction costs, the same efficient outcome will prevail
This version fits the legal cases cited by Coase. If it is more efficient to prevent cattle trampling a farmer's fields by fencing in the farm, rather than fencing in the cattle, the outcome of bargaining will be the fence, regardless of whether victim rights or unrestricted grazing-rights prevail. Subsequent authors have shown that this version of the theorem is not generally true, however. Changing liability placement changes wealth distribution, which in turn affects demand and prices. These wealth effects may be small, however.
In his UCLA dissertation and in subsequent work, Steven N. S. Cheung (1969) coined an equivalence version of the Coase theorem: aside from transaction costs, all institutional forms are capable of achieving the same efficient allocation. Contracts, extended markets, and corrective taxation are equally capable of internalizing an externality. To be logically correct, some restrictive assumptions are needed. First, spillover effects 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. It does not apply to pollution generally, since there are typically multiple victims. Equivalence also requires that each institution has equivalent property rights. Victim rights in contract law correspond to victim entitlements in extended markets and to the polluter pays principle in taxation.
Notwithstanding these restrictive assumptions, 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 equivalence 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.
Application in United States contract and tort law
In contract law, Coase is often used as a method to evaluate the relative power of the parties during the negotiation and acceptance of a traditional or classical bargained-for contract.
In modern tort law, application of economic analysis to assign liability for damages was popularized by Judge Learned Hand of Second Circuit Court of Appeals in his decision, United States v. Carroll Towing Co. 159 F.2d 169 (2d. Cir. 1947). Judge Hand's holding resolved simply that liability could be determined by applying the formula of B < PL, where B = the burden (economic or otherwise) of adequate protection against foreseeable damages, P = the probability of damage (or loss) occurring and L = the gravity of the resulting injury (loss). This decision flung open the doors of economic analysis in tort cases, thanks in no small part to Judge Hand's popularity among legal scholars.
In resultant scholarship using economic models of analysis, prominently including the Coase theorem, theoretical models demonstrated that, when transaction costs are minimized or nonexistent, the legal appropriation of liability diminishes in importance or disappears completely. In other words, parties will arrive at an economically efficient solution that may ignore the legal framework in place.
For example, two property owners own land on a mountainside. Property Owner #1's land is upstream from Owner #2 and there is significant, damaging runoff from Owner #1's land to Owner #2's land. Four scenarios are considered:
- If a cause of action exists (i.e. #2 could sue #1 for damages and win) and the property damage equals $100 while the cost of building a wall to stop the runoff equals $50, the wall will probably exist. Owner #1 will build the wall, or pay Owner #2 between $1 and $50 to tolerate the runoff.
- If a cause of action exists and the damage equals $50 while the cost of a wall is $100, the wall will not exist. Owner #2 may sue, win the case and the court will order Owner #1 to pay #2 $50. This is cheaper than actually building the wall. Courts rarely order persons to do or not do actions: they prefer monetary awards.
- If a cause of action does not exist, and the damage equals $100 while the cost of the wall equals $50, the wall will exist. Even though #2 cannot win the lawsuit, he or she will still pay #1 some amount between $51 and $99 to build the wall.
- If a cause of action does not exist, and the damage equals $50 while the wall will cost $100, the wall will not exist. #2 cannot win the lawsuit and the economic realities of trying to get the wall built are prohibitive.
The Coase theorem considers all four of these outcomes logical because the economic incentives will be stronger than legal incentives. Pure or traditional legal analysis will expect that the wall will exist in both scenarios where #2 has a cause of action and that the wall will never exist if #2 has no cause of action.
Example of application
The Externality of Planting Pear Trees:
The Jones family plants pear trees on their property which is adjacent to the Smith family. The Smith family gets an external benefit from the Jones family’s pear trees because they pick up whatever pears fall to the ground on their side of the property line. This is an externality because the Smith family does not pay the Jones family for utility received from gathering the fallen pears and, therefore, does not participate in the market transaction of pear production. It results in the pears being underproduced, which means too few pear trees are planted.
Let's assume the following:
Possible solutions to internalize the externality:
By applying the Coase Theorem two possible solutions arise for internalizing this externality. These solutions can occur because the positive external benefits are clearly identified and we assume that 1)transaction costs are low; 2)property rights are clearly defined.
After realizing that the Smith family gets utility from the Jones family’s pear trees, the Jones family thinks it is unfair that the Smiths get utility from picking up the pears that fall from their pear trees. The first option to eliminate the externality could be to put up a net fence that will prevent pears from falling to the ground of the Smith’s side property line, which will automatically decrease the Smith family’s marginal benefit to 0.
The second option for the Jones could be to impose a cost on the Smith family if they want to continue to get utility from their pear trees. Say, if the Jones family has a MC of $25 for each pear tree produced, it allows them to plant 3 pear trees a year (Jones’ MB = MC). However, if the cost is imposed on the Smiths, the optimal quantity of pear trees produced a year will increase to 4 (Jones’ MB + Smiths’ MB = MC). By internalizing the externality, both the Smith family and the Jones family increase their overall utility by increasing production from 3 pear trees a year to 4. It should be noted that $5 is the maximum price the Smiths are willing to pay for an additional, fourth, pear tree, which implies their marginal benefit to plant a fifth pear tree is 0.
Ronald Coase's work emphasised a problem in applying the Coase theorem: transactions are "often extremely costly, sufficiently costly at any rate to prevent many transactions that would be carried out in a world in which the pricing system worked without cost." (Coase, 1960—first paragraph of section VI.) This isn't a criticism of the theorem itself, since the theorem considers only those situations in which there are no transaction costs. Instead, it is an objection to applications of the theorem that neglect this crucial assumption.
So, a key criticism is that the theorem is almost always inapplicable in economic reality, because real-world transaction costs are rarely low enough to allow for efficient bargaining. (That was the conclusion of Coase's original paper, making him the first 'critic' of using the theorem as a practical solution.) Economist James Meade argued that even in a simple case of a beekeeper's bees pollinating a nearby farmer's crops, Coasean bargaining is inefficient. (Though bee-keepers and farmers do make contracts and have for some time.)
David Friedman has argued that the fact that an "economist as distinguished as Meade assumed an externality problem was insoluble save for government intervention suggests...the range of problems to which the Coasian solution is relevant may be greater than many would at first guess." Friedman is scathing of most critical attacks on the Coase theorem.
In many cases of externalities, the parties might be a single large factory versus a thousand landowners nearby. In such situations, say the critics, not only do transaction costs rise extraordinarily high, but bargaining is hindered by the basic incentive to free-ride and poorly defined property rights—classic public good problems.
A third critique can be found in the work of the critical legal scholar Duncan Kennedy, who argues that the initial allocation always matters in reality. This is because psychological studies indicate that asking prices often exceed offer prices. In other words, a person who already has an entitlement is likely to request more to give it up than would a person who started off without the entitlement.
Steven N. S. Cheung thinks that private property rights are institutions that arise to reduce transaction costs. The existence of private property rights implies that transaction costs are non-zero. If transaction costs are really zero, any property rights system will result in identical and efficient resource allocation, and the assumption of private property rights is not necessary. Therefore, zero transaction costs and private property rights cannot logically coexist
In 2009, in their seminal JEI article, Hahnel and Sheeran highlight several major misinterpretations and common assumption, which when accounted for substantially reduce the applicability of Coase's theorem to real world policy and economic problems. First, they recognize that the solution between a single polluter and single victim is a negotiation—not a market. As such, it is subject to the extensive work on bargaining games, negotiation, and game theory (specifically a "divide the pie" game under incomplete information). This typically yields a broad range of potential negotiated solutions, making it unlikely that the efficient outcome will be the one selected. Rather it is more likely to be determined by a host of factors including the structure of the negotiations, discount rates and other factors of relative bargaining strength (cf. Ariel Rubenstein).
If the negotiation is not a single shot game, then reputation effects may also occur, which can dramatically distort outcomes and may even lead to failed negotiation (cf. David M. Kreps, also the Chainstore paradox). Second, the information assumptions required to apply Coase's theorem correctly to yield an efficient result are complete information—in other words that both sides lack private information, that their true costs are completely known not only to themselves but to each other, and that this knowledge state is also common knowledge. When this is not the case, Coasian solutions predictably yield highly inefficient results due to perverse incentives—not "mere" transaction costs.
If the polluter has the ownership rights, it is incentivized to overstate its benefits from polluting, if the victim has the ownership rights, (s)he has the incentive to also misrepresent her/his damages. As a result, under incomplete information (probably the only state of knowledge for most real world negotiations), Coaseian yield predictably inefficient results. Third, if there are multiple victims, victims who would be required to pay have incentive to pretend that they are not harmed (freeriding) or understate their harm. If the polluter is required to pay, victims overpresent, overestimate their damage, and/or hold out.
Hahnel and Sheeran emphasize that these failures are not due to behavioral issues or irrationality (although these are also quite prevalent (Ultimatum Game, Cognitive biases), are not due to transaction costs (although these are also quite prevalent), and are not due to absorbing states and inability to pay, rather it is due to fundamental theoretical requirements of Coase's theorem (necessary conditions) that are typically grossly misunderstood, and that when not present systematically eliminate the ability of Coaseian approaches to obtain efficient outcomes—locking in inefficient ones. Hahnel and Sheeran conclude that it is highly unlikely that conditions required for an efficient Coaseian solution will exist in any real-world economic situations.
Another criticism is that the relative value determinations of the parties cannot reflect the actual values sought by the parties unless the parties start off at equal economic positions. In reality, the parties are more likely to start off at economically disparate positions. The result is that a dollar may have more relative worth to the victim than the polluter. Additionally, Coase's theorem assumes that anything of value can be characterized in economic terms. But some attributes of property simply cannot be reduced to monetary figures.
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- An overview of the theorem as well as criticism and further discussion, by David D. Friedman
- A statement and proof of a simple mathematical version of the theorem.
- A simple illustration of the Coase Theorem
- Overview and discussion of efficiency
- Libertarian criticism against Coase theorem by Hans-Hermann Hoppe
- An overview of the different insights, including discussion of wealth effects and the theorem
- Dilbert and the Coase Theorem 'The Coase theorem fails in the presence of asymmetric information.'
- Coase, Demsetz and the Unending Externality Debate
- The Coase Theorem by Seth J. Chandler, The Wolfram Demonstrations Project.