Coase theorem
In law and economics
Law and economics
The economic analysis of law is an analysis of law applying methods of economics. Economic concepts are used to explain the effects of laws, to assess which legal rules are economically efficient, and to predict which legal rules will be promulgated.-Relationship to other disciplines and...

, the Coase theorem , attributed to Ronald Coase
Ronald Coase
Ronald Harry Coase is a British-born, American-based economist and the Clifton R. Musser Professor Emeritus of Economics at the University of Chicago Law School. After studying with the University of London External Programme in 1927–29, Coase entered the London School of Economics, where he took...

, describes the economic efficiency
Efficiency (economics)
In economics, the term economic efficiency refers to the use of resources so as to maximize the production of goods and services. An economic system is said to be more efficient than another if it can provide more goods and services for society without using more resources...

 of an economic allocation
Allocation may refer to:* Computers** Delayed allocation** Block allocation map** FAT** IP address allocation** Memory allocation** C++ allocators** No-write allocation ** Register allocation* Economics** Economic system** Asset 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 rights. In practice, obstacles to bargaining or poorly defined property rights can prevent Coasian bargaining.

This theorem, along with his 1937 paper on the nature of the firm
The Nature of the Firm
The Nature of the Firm 4 Economica 386–405, is an influential article by Ronald Coase. It offered an economic explanation of why individuals choose to form partnerships, companies and other business entities rather than trading bilaterally through contracts on a market.-Summary:Given that...

 (which also emphasizes the role of transaction costs), earned Coase the 1991 Nobel Prize in Economics. The Coase theorem is an important basis for most modern economic analyses of government regulation
Regulation is administrative legislation that constitutes or constrains rights and allocates responsibilities. It can be distinguished from primary legislation on the one hand and judge-made law on the other...

, especially in the case of externalities
In economics, an externality is a cost or benefit, not transmitted through prices, incurred by a party who did not agree to the action causing the cost or benefit...

. George Stigler
George Stigler
George Joseph Stigler was a U.S. economist. He won the Nobel Memorial Prize in Economic Sciences in 1982, and was a key leader of the Chicago School of Economics, along with his close friend Milton Friedman....

 summarized the resolution of the externality problem in the absence of transaction costs in a 1966 economics textbook
A textbook or coursebook is a manual of instruction in any branch of study. Textbooks are produced according to the demands of educational institutions...

 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.

The theorem

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 others' 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 station
Radio station
Radio broadcasting is a one-way wireless transmission over radio waves intended to reach a wide audience. Stations can be linked in radio networks to broadcast a common radio format, either in broadcast syndication or simulcast or both...

s 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
In economics and sociology, an incentive is any factor that enables or motivates a particular course of action, or counts as a reason for preferring one choice to the alternatives. It is an expectation that encourages people to behave in a certain way...

 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
The Problem of Social Cost
The Problem of Social Cost by Ronald Coase is an article dealing with economic problem of externalities. It draws from a number of English legal cases and statutes to illustrate Coase's belief that legal rules are only justified by reference to a cost benefit analysis, and that nuisances that are...

', published in 1960 and cited when he was awarded the Nobel Prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

 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 gaining the most utility from them. 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
Law and economics
The economic analysis of law is an analysis of law applying methods of economics. Economic concepts are used to explain the effects of laws, to assess which legal rules are economically efficient, and to predict which legal rules will be promulgated.-Relationship to other disciplines and...

 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. This is a tautology
Tautology (logic)
In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...

, but an illuminating one. It reveals that corrective taxation is not the only way to internalize negative externalities.

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. Most economists believe that wealth effects are small, however.

Equivalence version

Steven N. S. Cheung
Steven N. S. Cheung
Steven Ng-Sheong Cheung , a Hong Kong born economist, specializes in the fields of transaction costs and property rights. Known for his work on private property rights and transaction costs, he achieved his fame with an economic analysis on China open-door policy after 1980s...

 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 resources allocation, and the assumption of private property rights is not necessary. Therefore, zero transaction costs and private property rights cannot logically coexist

In his UCLA dissertation and in subsequent work, Steven N. S. Cheung
Steven N. S. Cheung
Steven Ng-Sheong Cheung , a Hong Kong born economist, specializes in the fields of transaction costs and property rights. Known for his work on private property rights and transaction costs, he achieved his fame with an economic analysis on China open-door policy after 1980s...

 (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 [see the work of Arthur C. Pigou] 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
Agency cost
An agency cost is an economic concept that relates to the cost incurred by an entity associated with problems such as divergent management-shareholder objectives and information asymmetry...

 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

The Coase Theorem has been used by jurists and legal scholars in the analysis and resolution of disputes involving both contract law 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
Learned Hand
Billings Learned Hand was a United States judge and judicial philosopher. He served on the United States District Court for the Southern District of New York and later the United States Court of Appeals for the Second Circuit...

 of Second Circuit Court of Appeals in his decision, United States v. Carroll Towing Co.
United States v. Carroll Towing Co.
United States v. Carroll Towing Co. 159 F.2d 169 is a decision from the 2nd Circuit Court of Appeals that proposed a test to determine the standard of care for the tort of negligence...

159 F.2d 169 (2d. Cir. 1947). Judge Hand's holding resolved simply that liability
Legal liability
Legal liability is the legal bound obligation to pay debts.* In law a person is said to be legally liable when they are financially and legally responsible for something. Legal liability concerns both civil law and criminal law. See Strict liability. Under English law, with the passing of the Theft...

 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
A tort, in common law jurisdictions, is a wrong that involves a breach of a civil duty owed to someone else. It is differentiated from a crime, which involves a breach of a duty owed to society in general...

 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:
  1. 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.
  2. 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
    Specific performance
    Specific performance is an order of a court which requires a party to perform a specific act, usually what is stated in a contract. It is an alternative to award/ for awarding damages, and is classed as an equitable remedy commonly used in the form of injunctive relief concerning confidential...

    : they prefer monetary awards.
  3. 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.
  4. 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 V.) 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
Applied economics
Applied economics is a term that refers to the application of economic theory and analysis. While not a field of economics, it is typically characterized by the application of economic theory and econometrics to address practical issues in a range of fields including labour economics, industrial...

 that neglect this crucial assumption
In logic an assumption is a proposition that is taken for granted, as if it were true based upon presupposition without preponderance of the facts...


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. (This is the conclusion of Coase's original paper, making him the first 'critic' of using the theorem as a practical solution.) Economist James Meade
James Meade
James Edward Meade CB, FBA was a British economist and winner of the 1977 Nobel Memorial Prize in Economic Sciences jointly with the Swedish economist Bertil Ohlin for their "Pathbreaking contribution to the theory of international trade and international capital movements."Meade was born in...

 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.

Meade could be seen as an example of what Coase himself called "blackboard economists"—the finding of inefficiencies in rational choice models and the immediate presumption that public action is required—without ever examining the real world data to examine if the private market has actually failed to correct the inefficiency. Cheung also shows how Meade demonstrates this practise yet again.

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. (Though these problems do not preclude a free market
Free market
A free market is a competitive market where prices are determined by supply and demand. However, the term is also commonly used for markets in which economic intervention and regulation by the state is limited to tax collection, and enforcement of private ownership and contracts...

 Coasian solution.)

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.

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
Bargaining Problem
The two person bargaining problem is a problem of understanding how two agents should cooperate when non-cooperation leads to Pareto-inefficient results. It is in essence an equilibrium selection problem; Many games have multiple equilibria with varying payoffs for each player, forcing the players...

, negotiation
Negotiation is a dialogue between two or more people or parties, intended to reach an understanding, resolve point of difference, or gain advantage in outcome of dialogue, to produce an agreement upon courses of action, to bargain for individual or collective advantage, to craft outcomes to satisfy...

, and game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

 (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
David M. Kreps
David Marc "Dave" Kreps is a game theorist and economist and professor at the Graduate School of Business at Stanford University. He is known for his analysis of dynamic choice models and non-cooperative game theory, particularly the idea of sequential equilibrium, which he developed with Stanford...

, also the Chainstore paradox
Chainstore paradox
Chainstore paradox is a concept that purports to refute standard game theory reasoning.-The chain store game:A monopolist has branches in 20 towns. He faces 20 potential competitors, one in each town, who will be able to choose IN or OUT. They do so in sequential order and one at a time...

). Second, the information assumptions required to apply Coase's theorem correctly to yield an efficient result are complete information
Complete information
Complete information is a term used in economics and game theory to describe an economic situation or game in which knowledge about other market participants or players is available to all participants. Every player knows the payoffs and strategies available to other players.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
Common knowledge
Common knowledge is knowledge that is known by everyone or nearly everyone, usually with reference to the community in which the term is used. Common knowledge need not concern one specific subject, e.g., science or history. Rather, common knowledge can be about a broad range of subjects, including...

. When this is not the case, Coasian solutions predictably yield highly inefficient results due to perverse incentive
Perverse incentive
A perverse incentive is an incentive that has an unintended and undesirable result which is contrary to the interests of the incentive makers. Perverse incentives are a type of unintended consequences.- Examples :...

s—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
Ultimatum game
The ultimatum game is a game often played in economic experiments in which two players interact to decide how to divide a sum of money that is given to them. The first player proposes how to divide the sum between the two players, and the second player can either accept or reject this proposal. ...

, 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.

In response to Hahnel and Sheeran, Holt [2011] demonstrates
that precommitment in a Coase-Theorem Bargaining Game Leads to a Mutual Preference for Hiring the Government as an Arbitrator.

Hahnel R and Sheeran KA. 2009. Misinterpreting the Coase Theorem. Journal of Economic Issues. Vol 43. No 1. March. pp 215–238.

Holt G. 2011. Precommitment in a Coase-Theorem Bargaining Game Leads to a Mutual Preference for Hiring the Government as an Arbitrator: A Corollary to Hahnel and Sheeran (2009).
Journal of Economic Issues. Vol. 45 No. 3. September. p 733.

External links

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