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Incentive-compatibility and Coasean invariance in property affairs.

1. Introduction

Legal rules about bundles of rights (or property law) are answers to questions such as those raised by Cooter and Ulen (p. 71): "How are ownership rights established? What can be privately owned? What may owners do with their property? What are the remedies for the violation of property rights?" Answers (legal rules) are drafted subject to, primarily, various philosophical constraints as well as security and economic pragmatism.

Property law is influenced by philosophical views. According to the liberal philosopher John Rawls, as explained by Sen (p. 12), we ought to desire to establish "specific institutions, firmly chosen for the basic structure of society (which) would demand one specific resolution of the principles of justice" but he does not explain "the difficulties in arriving at a unique set of principles to guide institutional choice." Sen questions this Rawlsian notion of "transcendental institutionalism" and he doubts that it is either possible or essential; in turn, he states that there is simply a plurality of philosophical principles (not only Rawls's liberal principles) that justify conflicting property claims. (1) As stated by Cooter and Ulen (pp. 107-110), property has the capability to advance, among other, utilitarianism, justice, liberty and self-expression. More specifically,

On utilitarian grounds, it can be taken from (a person) in principle if the beneficiaries of the expropriation gain more in utility than the owner loses.

On distributive justice grounds, in Aristotle's conception, aristocrats use (wealth) for more worthy ends than do others. (Therefore), redistribution of property would favor the rich and penalize the poor. ... Another school of philosophical thought ... emphasizes a just process for defining and enforcing property rights rather than a just outcome.

On liberty grounds, private property has ... been viewed by some philosophers as a bulwark against the dictatorial authority of governments ... The U.S. Constitution was probably drafted with this idea in mind.

On self-expression grounds, the artist transforms natural objects and makes them the artist's own. ... Creators' rights of ownership ... (extend) beyond art to most of the works of humans.

On natural selection grounds, Eswaran and Neary (2014, p.206), demonstrate that, given evolutionarily stable preferences, "producers value the output more than interlopers do. In this way, natural selection hardwires attachment to the fruits of one's own labor more than attachment to the fruits of someone else's labor. The asymmetry in valuation arises because of the asymmetric role of the contesting individuals in production of the output. Asymmetric valuation generates an innate enforcement mechanism whereby a producer would spend more effort in defense of his output than would an interloper in its attempted appropriation." As the same authors state (p. 221), their setting "provides an evolutionary basis for both the doctrine of first possession and Locke's labor theory of property rights, which are crucial ingredients of the philosophical and legal approaches to property rights."

Property law violations (dubbed negative externalities) are present whenever the well-being of consumers or the production possibilities of firms are negatively affected by the actions of other agents in society. Negative externalities give rise to market failure (which may be corrected through the imposition of standards, taxation and bargaining between the parties involved) and they may range from, among other, bilateral to multilateral and from intellectual to pollution (e.g., environmental, noise, and aesthetic) or from positional to those that involve informational asymmetry. Several specific case examples are instructive.

The often-cited case of Pierson v. Post, 2 Am. Dec. 264 (N.Y. 1805) illustrates an archetypal bilateral dispute. There, the Supreme Court of New York resolved that in order to own an animal, you must physically possess it. The facts of the case are simple: Post and his dogs hunted and pursued a fox along a beach. Pierson was cognizant of the hunt and stepped in just as Post would have succeeded in the chase, ultimately killing and claiming the dead fox for himself. Post argued that his property interest in the fox vested by virtue of the chase itself, thus Pierson violated his property rights by interfering and claiming the fox. The lower court agreed with Post, but on appeal Pierson prevailed. The Court held that while Pierson may have been impolite, he did not violate Post's property rights. The Court went on to explain that one can only own an animal he physically possesses, but an exception may apply when one has mortally wounded the animal and has not given up pursuit. The continued pursuit of an injured animal would, in essence, activate a property right because it shows an unequivocal intention to possess the animal, having already taken some ownership or possessive interest in it through the initial wounding and continued pursuit of the animal. While it may seem unfair to punish Post, despite his efforts, the court reasoned that a bright-line rule preserves peace and order in society. The dissent, however, challenged this notion, asserting that if the hunter is within reach or has a reasonable chance of taking the animal, as was Post, then it should be his. However, the majority was indeed persuaded not just by fairness but also by efficiency. To find that Post had a decisive property interest in the fox by merely chasing it, an intention that could be abandoned at any moment, would cause a flood of litigation.

Conversely in Boomer v. Atlantic Cement Co., property rights proved to be more malleable than the court's hard-lined approach in Pierson v. Post. This case is an example of a more complex multilateral pollution case and is also instructive. Boomer and his neighbors filed suit against Atlantic Cement Company because dirt, smoke, and vibrations spewed from the factory. He argued that this was a private nuisance, as it interfered with the use and enjoyment of his nearby home. The trial court found in favor of Boomer, awarding temporary damages, though the court noted that it is the responsibility of the government to regulate pollution, not the courts. Boomer appealed to get an injunction, but the Appellate Court upheld the trial court decision. Boomer appealed again, still in pursuit of an injunction. The New York Supreme Court partially reversed the lower court's decision, granting permanent damages to Boomer, but not an injunction. The court reasoned that an injunction would be inappropriate because although Boomer undeniably suffered some damage from the operation of the factory, his damages were relatively small compared to the overall societal benefit of Atlantic's continued operation.

This notion of societal value weighed against, and often in favor of, the property interests of private individuals is an important concept as it suggests that though property rights may seem well-articulated by bright-lined rules, there are some circumstances where one's property rights are not so clear and are, in fact, uncertain. Specifically in Ploof v. Putnam, 81 Vt. 471 (1908), Ploof and his family were forced to moor their boat at Putnam's dock on Lake Champlain as a severe storm suddenly approached. Putnam's servant untied Ploof's boat, which resulted in injury to Ploof and his family, as well as damage to the boat. Ploof alleged two counts against Putnam, first that he trespassed against Ploof when his servant negligently released his boat into the storm, and second, that Putnam's servant negligently unmoored the boat. As a general rule, the doctrine of necessity is especially significant in cases where human life is at risk. While the jury demurred both claims, on appeal the Supreme Court of Vermont determined that Putnam's servant acted within the scope of employment and Ploof did, in fact, moor his boat out of necessity to save human life and limb. While normally the law of trespass is fairly cut and dry, such that the use of another's property without permission would violate another's property right, this rule is supple where another's interest in the same property outweighs that of another.

Alternatively in Vincent v. Lake Erie Transportation Co., 124 N.W. 221 (Minn. 1910), a vessel owned by Lake Erie Transportation was moored at Vincent's dock. A storm ensued, causing $500 in damage to the dock. Vincent subsequently sued to recover the damage, alleging that the defendant had trespassed, and a jury found in his favor. Lake Erie Transportation appealed, arguing that it was not liable as its use of the dock was a private necessity. On appeal, the court ruled in favor of Vincent and opined that the defendant could not be liable for trespass, as private necessity is a valid defense. However, the vessel was secured to the dock in order to preserve the vessel, at the expense of the dock. Thus, though the defendant had acted under private necessity, which warranted his temporary use of Vincent's property, the resulting damage was recoverable.

Regarding intellectual property disputes, Hall, Helmers, Rogers, and Sena (2014, p. 376) review "what we know about companies' choices of how to protect their inventions, which is directly linked with the question of how companies appropriate returns to their innovations." According to these authors, when it comes to intellectual property protection, firms choose between formal mechanisms (patents, trademarks, registered designs, and copyright) and informal mechanisms (secrecy, confidentiality agreements, first mover advantage, or complexity.) They point out that patent protection contributes to knowledge spillovers (via imitation) whereas secrecy "may hinder the circulation of new ideas and therefore slow down knowledge spillovers and economic growth". Additionally, they report that "the available empirical evidence ... strongly suggests that only a small fraction of innovative companies relies on patents to protect their inventions" such as biotech firms, while other, such as software companies, do not.

Cooter and Ulen (Chapters 4 and 5), eloquently describe, along with their own, the contributions of Coase (1960), Hobbes (2012) and CalabresiMelamed (1972) that serve as fundamental guiding principles in a society's continuous effort to improve and establish legal rules that relate to property:

(i) According to Coase's invariance theorem, Coase (1960), if property rights are clearly-defined and enforceable and free trades of negative externalities can occur, then private bargaining between property violators and victims will lead to an efficient resolution no matter how property rights are allocated. In other words, when transaction costs (such as search costs, bargaining costs and enforcement costs) are zero, private deals give rise to efficient allocation of resources, irrespective of the legal assignment of property rights.

(ii) Cooter and Ulen offer a corollary of the Coase invariance theorem. According to the Cooter-Ulen corollary to the Coase theorem, when transaction costs are high enough to prevent partially or totally effective private dealings, the efficient allocation of recourses will be a function of clearly-defined property rights.

(iii) Calabresi and Melamed have offered two additional corollaries to the Coase invariance theorem regarding compensation and injunction: (a) according to the first Calabresi-Melamed corollary theorem, when high transaction costs impede cooperation for the resolution of property disputes, awarding compensatory money damages, through the legal system, would be an efficient remedy; and (b) according to the second Calabresi-Melamed corollary theorem, when transaction costs are low, awarding an injunction against a defendant's interference with a plaintiff's property, through the legal system, would be an efficient remedy.

(iv) According to Coase's normative theorem, society ought to structure the legal system in such a way so that obstacles to private dealings are minimized or removed, in other words, the law ought to encourage cooperative agreements between property-disputing agents.

(v) Cooter and Ulen point out that Coase's normative theorem stands in contrast to the philosophical believes of Hobbes who doubts that people are capable of rationally dividing a possible cooperative surplus. According to Hobbes, the law ought to avert coercive pressures and eradicate the harmfulness of disagreements. Hence, according to the normative Hobbes theorem, the law has to be structured in such a way so that injuries caused by failure in private dealings are minimized. The normative Hobbes theorem implies that the law should assign property claims to the entity that values them the most.

The above theorems center on transaction costs such as search costs, bargaining costs, and enforcement costs. Libecap (2014), addresses transaction costs associated with global environmental externalities; in the author's words (p. 428), "in the context of global environmental externality mitigation, four factors raise transactions costs: (1) scientific uncertainty; (2) varying preferences and perceptions; (3) asymmetric information; and (4) lack of compliance and new entry" and stresses that the greater these factors are the less likely it is that there would be agreements on property rights and disputes.

In another seminal contribution Coase (1937) argues that firms exist to minimize transaction costs (to economize on the cost of coordinating economic activity.) Costs of searching markets, inputs, negotiating and signing deals with input suppliers, enforcement of deals, and other such transaction costs give rise to the significance of business firm property boundaries: should the firm own the entire vertical chain associated with the products it produces or just a portion of it? In other words, how many inputs should the firm "make" itself and how many should it "buy" in available markets? How significant are "scale of operations," "input specificity," "frequency of purchase," and "uncertainty"? By and large this contribution of Coase is acknowledged in research that involves the theory of the firm and industrial organization [see Williamson (1985), Kantarelis (2014) and references therein] but, it is ignored by both legal scholars and economists concerned with property issues with the exception of Demsetz (1967) who clearly explains the importance of scale vis-a-vis land ownership settlements and externalities; in his own words:

... land was distributed in randomly sized parcels to randomly selected owners. These owners now negotiate among themselves to internalize any remaining externalities. Two market options are open to the negotiators. The first is simply to try to reach a contractual agreement among owners that directly deals with the external effects at issue. The second option is for some owners to buy out others, thus changing the parcel size owned. Which option is selected will depend on which is cheaper. We have here a standard economic problem of optimal scale. If there exist constant returns to scale in the ownership of different sized parcels, it will be largely a matter of indifference between outright purchase and contractual agreement if only a single, easy-to-police, contractual agreement will internalize the externality. But, if there are several externalities, so that several such contracts will need to be negotiated, or if the contractual agreements should be difficult to police, then outright purchase will be the preferred course of action. The greater the diseconomies of scale to land ownership the more will contractual arrangement be used by the interacting neighbors to settle these differences. Negotiating and policing costs will be compared to costs that depend on the scale of ownership, and parcels of land will tend to be owned in sizes which minimize the sum of these costs. (Compare this with the similar rationale given by R. H. Coase to explain the firm in the "The Nature of the Firm", Economics, New Series, 1937, pp. 386-405.)

Without a doubt, the above theorems as well as Demsetz's analysis, which implies that property rights contribute to more efficient use of resources, serve as fundamental principles in the fields of property law, environmental law, law and economics as well as the business firm and its proprietary domains ranging from physical to intellectual. These authors though do not discuss conditions under which invariance property deals may not materialize due to agents' types (such as strong or weak) and lack of incentive compatibility. For example, in a seller/buyer property deal, both parties may be strong (one asking for a very high market price, the other willing to pay a very low market price) in which case the deal may not be consummated; and if they are both weak, or one weak and the other strong, it is likely that only an incentive-compatible legal ruling (so that the parties do not experience problems associated with asymmetry of information such as adverse selection and moral hazard) can enable the entities to complete the deal. Naturally, the possible types of an agent and the per-type reservation values (threat values) cannot be known with certainty which implies that incentive-compatible legal rulings may contain errors that cause resource misallocation.

Our purpose in this paper is two-fold; firstly, to review the Coasean underpinnings of basic property law and secondly, to propose a broader version of Coase's invariance theorem inclusive of incentive-compatibility. It is our hope that the theorem would be considered more realistic if it is modified to read as follows: when transaction costs (such as search costs, bargaining costs and enforcement costs) are zero, incentive-compatible deals, mediated by the legal system, give rise to efficient allocation of resources, irrespective of the legal assignment of property rights. Coase is not concerned about asymmetry of information issues which may give rise to adverse selection and moral hazard. Our modification of the theorem, as it will be explained below, amounts to incentive-compatibility subject to knowing the probability distribution of the types of the parties involved (e.g., strong or weak) and to appropriate legal rules that eliminate problems associated with asymmetry of information.

In the following sections, we describe the logic of the Coasean invariance theorem and a few possible applications (Section II); we use an example to demonstrate various legal rules subject to Coase, Hobbes and Calabresi-Melamed (Section III); we modify the Coase invariance theorem to include types of agents and incentive compatibility (Section IV); we summarize and conclude in Section V.

2. The Coase Invariance Theorem

Coase (1960) suggested that a solution to the problem of negative externalities due to environmental pollution is not necessary. Assuming that economic agents are free to negotiate--pollutes (victims) can pay the polluter (violator of property rights) to reduce pollution or the polluter can bribe the pollutees to accept more pollution--Coase showed that the same amount of output and pollution would be produced, regardless of which side owned the rights to clean air or water or, in general, property affected. If the polluter owned the right to clean property, the pollutee would pay until the marginal benefit from emission reduction equaled the marginal cost. If the pollutee owned the right to clean property, the polluter would pay until the marginal cost equaled the marginal benefit of less emission. Hence, with zero or insignificant obstacles to bargaining (zero or insignificant bargaining-related transaction costs), the parties involved would reach the same Pareto optimal levels of output and emission. The only dissimilarity would be an equity issue: who pays whom for the right to make use of the property.

To illustrate Coase's invariance prediction, consider two interdependent economic entities X (the polluter) and Y (the pollutee.) For example, following Cooter and Ulen (p. 94), X may be a coal-based electricity firm and Y a laundry firm in the vicinity. The electricity firm may pay, or get paid by the laundry firm, to install scrubbers; alternatively, the laundry firm may pay, or get paid by the electricity firm, to install air filters.

Following Binger and Hoffman (pp. 565-567), let [PI] = profit, TR = total revenue, TC = total cost, x = X's output, y = Y's output, L = labor, P = given output price, w = given wage rate, MP = marginal product, and [partial derivative] = symbol for partial derivative.

(a) Suppose first that, by law, Y has the right to be free from pollution and agrees to let X emit pollutants for a per-unit of x fee (k), to be determined by a competitive market.

Firm Y when it is favored by the law

Given [P.sub.Y], w and k, Y chooses [L.sub.Y] and x to maximize profit as follows:

[[PI].sub.Y] = [TR.sub.Y] - [TC.sub.Y], where

[TR.sub.Y] = [PY.sub.Y] + kx;

y = y([L.sub.Y], x) or, 'y' is a production function in which y depends positively on

[L.sub.Y] and negatively on x; and

[TC.sub.Y] = w[L.sub.Y]. Thus,

[[PI].sub.Y] = [P.sub.Y]y([L.sub.Y], x) + kx - w[L.sub.Y]. (1)

The partial derivatives of (1) with respect to [L.sub.Y] and x are:

[partial derivative][[product].sub.Y]/[partial derivative][L.sub.Y] = [P.sub.Y] [[partial derivative]y/[partial derivative][L.sub.Y]] - w = 0

[partial derivative][[product].sub.Y]/[partial derivative]x = [P.sub.Y] [[partial derivative]y/[partial derivative]x + k = 0

From the second partial,

k = -[P.sub.Y] [partial derivative]y/[partial derivative]x. (2)

Firm X when the law favors Y

Given [P.sub.x], w and k, X chooses [L.sub.x] to maximize profit as follows:

[[PI].sub.X] = [TR.sub.X]--[TC.sub.X], where

[TR.sub.X] = [P.sub.x]X;

x = x([L.sub.X]) or, "x" is a production function in which x depends positively on [L.sub.x]; and

[TC.sub.X] = w[L.sub.X] + k x([L.sub.X]). Thus,

[[PI].sub.X] = [P.sub.x]x([L.sub.x])--w[L.sub.x]--k x([L.sub.x]). (3)

The partial derivative of (3) with respect to [L.sub.x] is:

[partial derivative][[product].sub.X]/[partial derivative][L.sub.X] = ([P.sub.X] - k]) [[partial derivative]x/[partial derivative][L.sub.X]] - w = 0,

from which,



From (2) and (4),


(b) Suppose second that, by law, X has the right to pollute and that Y agrees to pay X a per-unit of ([x.sub.i]--x) bribe (z), to be determined by a competitive market (where [x.sub.i] = some given, agreed upon, initial output level.)

Firm Y when the law favors X

Given [P.sub.Y], w and z, Y chooses [L.sub.Y] and x to maximize profit as follows: [[PI].sub.Y] = [TR.sub.Y] - [TC.sub.Y], where

[TR.sub.Y] = [P.sub.Y]y;

y = y([L.sub.Y], x) or, as above, 'y' is a production function in which y depends positively on LY and negatively on x; and

[TC.sub.Y] = w[L.sub.Y] + z([x.sub.i]--x). Thus,

[[PI].sub.Y] = [P.sub.Y]y([L.sub.Y], x)--w[L.sub.Y]--z([x.sub.i]--x) . (6)

The partial derivatives of (6) with respect to LY and x are:

[partial derivative][[product].sub.Y]/[partial derivative][L.sub.Y] = [P.sub.Y] [[partial derivative]y/[partial derivative][L.sub.Y]] - w = 0

[partial derivative][[product].sub.Y]/[partial derivative]x = ([P.sub.Y] [[partial derivative]y/[partial derivative]x + z = 0

From the second partial,

z = -[P.sub.Y] [partial derivative]y/[partial derivative]x. (7)

Firm X when it is favored by the law

Given [P.sub.x], w and k, X chooses [L.sub.x] to maximize profit as follows:

[[PI].sub.X] = [TR.sub.X] - [TC.sub.X], where

[TR.sub.X] = [P.sub.x]x + z[[x.sub.i]--x([L.sub.x])]

x = x([L.sub.X]) or, as above, 'x' is a production function in which x depends positively on [L.sub.X]; and

[TC.sub.X] = w[L.sub.X]. Thus,

[[PI].sub.X] = [P.sub.x]x + z[[x.sub.i]--x([L.sub.x])]--w[L.sub.x]. (8)

The partial derivative of (8) with respect to [L.sub.x] is:

[partial derivative][[product].sub.X]/[partial derivative][L.sub.X] = ([P.sub.X] - Z) [[partial derivative]x/[partial derivative][L.sub.X]] - w = 0,

from which,

z = [P.sub.X] - w/[partial derivative]x/[partial derivative][L.sub.X] (9)

From (8) and (9),


As it may be seen, equation (10) is identical to equation (5), which proves Coase's invariance prediction.

Equation (2) may be viewed as the polutee's marginal damages (MD) set of points, a positively sloped relationship. Similarly, equation (4) may be viewed as the polluter's marginal abatement cost (MAC) set of points, a negatively sloped relationship. Because emission (e) depends on the amount of x produced, the MD, MAC sets may expressed as functions of "e" and look as those in Figure 1 below. [For more on other possible shapes of the MD/MAC curves as well as more complete analysis see Field (2012)].

Without obstacles to negotiations, X's MAC and Y's MD meet at point B which corresponds to e*, the overall cost minimizing point. At e*, total abatement costs for X equal [e.sub.M]Be* and total damages for Y equal [e.sub.T] Be* . Y would prefer [e.sub.T], the tolerable level of emissions, and X would prefer [e.sub.M], the maximum possible level of emissions, but negotiation would drive them to point e*. Point e* may be selected by regulation authorities to serve as a standard (subject to, of course, all possible ailments discussed above.)

The MAC curve may shift to the left due to "green" technology improvement which, ceteris paribus, will reduce overall emission-related costs for both X and Y. Assuming that regulation authorities desire to enforce e*, enforcement costs will cause the MAC curve to rotate to the right around point [e.sub.M] thus contributing to an increase of the overall emission-related costs for both X and Y.

The MD curve may shift to the left (right) due to an increase (decrease) in the population of firms type Y which will contribute to an increase (decrease) of the overall emission-related costs for both X and Y.


The MAC/MD framework may be utilized to demonstrate the so-called tradable pollution permits. Consider two polluting firms (R and S) whose MAC curves are displayed in Figure 2 and the following two regulation regimes:

(i) Regulation without permits. According to the regulating authority, the two firms should not emit, in total, more than 6 units of the toxic pollutant into the air. Firm R (the firm producing with modern "green" technology) is currently regulated to emit 4 units of the pollutant while firm S (the firm producing with older "less green" technology) is currently regulated to emit 2 units of the same pollutant.

Under these regulation requirements, S's total abatement cost is [TAC.sub.S] = ABC, R's total abatement cost is [TAC.sub.R] = DFG, and the total abatement cost with no permits (NP) is [TAC.sub.NP] = [TAC.sub.S] + [TAC.sub.R].

(ii) Regulation with permits. Alternatively, the regulatory authority may allow firms to negotiate with each other over how much pollutant each is going to emit into the air as long as the total does not exceed the standard of 6 units. Currently, let S emit 2 units and R 4 units; although the total of 6 units satisfies the constraint, under this regulation regime, S and R may agree to the following distribution of emissions: R decreases its emissions from 4 to 3 units and incurs an additional abatement cost of FDLB'; S increases its emission from 2 units to 3 and saves BALB' in abatement cost. When S and R move to B, each emits 3 units for a total of 6, which satisfies the standard. Upon comparison of the respective areas in Figure 2, it is obvious that S saves, in absolute value, more than R pays. Hence, S may keep a portion of its savings and with the remaining compensate R so that both end up with more gains while simultaneously satisfy the regulatory constraint. In other words, S purchases a permit from R to emit more for which, of course, R is amply compensated. Hence, regulation with permits enables both firms to earn more --and society to improve--while, concurrently, firms satisfy the regulatory emission standard. Comparing the outcomes of schemes (i) and (ii), in conjunction with Figure 2, regulation with permits (WP) reduces total abatement costs more than no permit regulation (NP): [TAC.sub.WP] < [TAC.sub.NP].


3. Alternative Legal Rules and Their Impact

The Coase, Hobbes and Calabresi-Melamed theorems may be used in conjunction with a hypothetical numerical example (similar to an example that appears in Cooter and Ulen) to demonstrate the impact of alternative legal rules.

Let there be two agents, a polluter (E) and a pollutee (L); E emits a pollutant which negatively affects L's payoffs. E has available two strategies: abate effluence (A), do not abate effluence (NA); similarly, L has available two strategies: pay E not to pollute or protect against E's effluence (P), do not pay E or do not protect against E's effluence (NP). The matrix below displays the payoffs of the two agents (E plays left, L plays right). Would it be optimal to structure the law so that we achieve the maximum possible for society, in this case, the total payoffs (3150) that correspond to the Nash equilibrium of (NA, P)
            NP         P

E   NA   2500,550   2500,650
    A    980, 880   980, 650

Let us know consider the implications of the following three rules of law and the table below:

Rules of law:

* Rule I: E is free to pollute.

* Rule II: L is entitled to compensatory damages from E.

* Rule III: L is entitled to an injunction forbidding E to pollute.

According to Rule I, it would be optimal for E to adopt strategy NA and make 2500 while it would optimal for L to adopt strategy P and make 650 for a society total of 3150. Hence, society would be indifferent between non-cooperation (Hobbes) or cooperation (Coase).

According to Rule II, L would adopt NP to make 880, the highest possible in that column. E has two choices A or NA. If E chooses A it would make 980; if it chooses NA it will make 2500 and L will make 550. Since L is entitled to compensatory damages from E, E would have the incentive to choose NA and then compensate L for the difference between (880-550) so that it ends up with 2170 and L with 880. Hence, if cooperation is not possible, society would realize a total of 3050 with a leftover of 100. But, if Coasean cooperation is possible, E and L may negotiate to split (evenly or unevenly) the leftover for a total of 3150, the maximum possible that society may realize. (In the table below the left over is evenly split.)

According to Rule III, E cannot pollute. Therefore, E would realize 980 while L will realize 880 for a non-cooperative total of 1860 and a leftover of 1290. But, if Coasean cooperation is possible, E and L may negotiate to split (evenly or unevenly) the leftover for a total of 3150, the maximum possible that society may realize. (In the table below the left over is evenly split.)
              Cooperation not             Leftover
           E                       L

Rule I     2500                    650    0
Rule II    2500-(880-550) = 2170   880    100
Rule III   980                     880    1290

              Cooperation                 Total
              possible                    a la Coase
           E                       L      E+L

Rule I     2500                    650    3150
Rule II    2220                    930    3150
Rule III   1625                    1525   3150

The numerical example demonstrates the power of the Coase invariance theorem when the parties involved do not experience any obstacles to cooperation: in the face of well-defined property rights, no matter how the law is structured, society ends up with the maximum possible which also corresponds to the Nash equilibrium in this case. The example also demonstrates the power of the Hobbes theorem when obstacles to cooperation exist as well as the value of the Calabresi-Melamed compensatory and injunction rules as applied to property rights violations.

4. Information Asymmetry

As the above examples demonstrate, the Coase theorem does not take into consideration the possibility of information asymmetry when parties, in the absence of transaction costs, bargain for prices or compensation. According to the theorem the price or compensation agreed upon by the parties is fair; hence, conveniently, there is no need to address the possibility of information asymmetry.

However, with zero transaction costs and information asymmetry, depending on the type of each negotiating party (strong or weak), (a) a property dispute may not be consummated and (b) a negotiator in a bilateral property dispute, void of incentive-compatibility, may lie and thus receive an exploitative price which, afterwards, may cause costly litigation for all involved. For example, in a bilateral property dispute, one party may be strong and ask for an extremely high price and the other party may be equally strong and offer to pay an extremely low price; in such a case, the parties may not come to an agreement despite zero transaction costs and, since the types of the disputing parties are fixed--not merely obstacles that may be removed or minimized--the normative Coase theorem does not apply either. But even if one party is strong and the other weak, only an incentive-compatible agreement may contribute to the validity of a deal by totally eliminating adverse selection and moral hazard. (2)

According to Myerson (2008, p. 587), in economic life we ought to constantly search for ways to improve the pool of resources and for incentive mechanisms. Hayek (1945) recommended that a social institution (such as the market system) should be viewed as a mechanism for communicating people's information and coordinating people's actions. In a market system, the actions of a market participant depend on information provided by other participants and on the ability of the system to coordinate the participants towards an economic outcome (preferably Pareto optimum). Is information truthful? Do participants have the incentive to lie and/or disobey? If they do, how can we make them tell the truth and obey? Following Myerson, consider the following example: suppose a buyer and a seller (both risk-neutral, and expected profit maximizes) are willing to trade property; their types (known only to them) are "strong" and "weak" each with a probability of 0.5. Obviously, if both the buyer and the seller are strong, trade between the two would not take place. Table 1 below reports threat values, or reservations prices, according to types (buyer: $20, $120; seller: $80, $10). In the cells, numbers to the left of the comma (denoted by pA, pB, pC, pD) correspond to the probabilities that trade will take place in those cells; numbers to the right of the comma (denoted by $A, $B, $C, $D) correspond to dollar figures based on different types.

Consider now a Fifty/Fifty Split bilateral agreement in Table 2 according to which the price agreed upon is half the sum of the corresponding threat values.

Let w = weak seller, s = strong seller, and ws = weak seller who pretends to be strong.

If the seller is weak, her expected profit would be:

E([PI])w = (15 - 10X1X0.5) + (65 - 10)(1)(0.5) = 30.

If the seller is weak but pretends to be strong, her expected profit would be: E([PI])ws = (100 - 10)(1)(0.5) = 45.

Thus, because E([PI])ws > E([PI])w, the seller has the incentive to lie.

Similarly, the buyer has the incentive to lie since her E([PI])w = 37.5 < E([PI])ws = 52.5.

Therefore, given the above setting, the Fifty/Fifty Split bilateral agreement is not incentive compatible which implies that deal cannot be consummated.

Consider now a possible Incentive-Compatible bilateral agreement in conjunction with Table 3. The cells, as above, contain probabilities and prices, where q is a conditional probability of trade applied to the respective cells; the conditional probability for (weak, weak) remains 1. According to Myerson (p. 591), "the probability of trade could also be interpreted as the conditional expected number of objects that the buyer would get in this case, and so q [less than or equal to] 1 here can also be interpreted as a resource constraint, expressing the fact that there is only one object that they can trade; ... for a strong trader to participate in this plan, y must satisfy the participation constraint," in this case y [less than or equal to] 10. Thus, appropriate values of "q" and "y" will generate incentive compatibility.

Proceeding as above, if the seller is weak, her expected profit would be:

E([PI])w = (10 + y - 10)(q)(0.5) + (65 - 10)(1)(0.5) = 0.5qy + 27.5.

If the seller is weak but pretends to be strong, her expected profit would be:

E([PI])ws = (120 - y - 10)(q)(0.5) = 55q - 0.5qy.

Thus, to make honesty an equilibrium, q and y must satisfy the informational constraint

0.5qy + 27.5 [greater than or equal to] 55q - 0.5qy.

Solving for q,

q [less than or equal to] 27.5/(55 - y).

Similarly for the buyer. Therefore, the incentive constraints q [less than or equal to] 27.5/(55 - y) and y [less than or equal to] 10 can generate an infinite number of possible incentive-compatible agreements.

These agreements, of course, need a legal environment within which they may be arbitrated and if needed litigated and enforced. Hence, if informational asymmetry is prevalent, even with zero transaction costs, Coase's invariance prediction may hold only if the property-disputing parties (a) are aware of the role that their uncertain "types" may play (which may cause a deal not to be consummated) and (b) are capable of drafting adverse selection free and moral hazard free incentive-compatible and legally enforceable rules (not an easy task.) Hence, given the theoretical exploration endeavored in this section, Coase's invariance theorem may be stated, more broadly, as follows: when transaction costs (such as search costs, bargaining costs and enforcement costs) are zero, incentive-compatible deals, mediated by the legal system, give rise to efficient allocation of resources, irrespective of the legal assignment of property rights.

5. Summary & Conclusion

We made an attempt in the paper to modify the Coase theorem as applied to property law by bringing into the argument asymmetry of information (ignored by Coase) and point out that, even without transaction costs, uncertainty over the types of property-disputing parties and the difficulty in drafting efficient deals may cause adverse selection and moral hazard or unstable resolutions due to incentive incompatibility. Our argument does not reject the theorem; it serves as a complement by adding the importance of (a) "types" of negotiators and (b) incentive-compatibility in environments characterized by asymmetry in information. Thus, for the theorem's invariance prediction to hold we have to assume zero transaction costs, knowledge of the probability distribution of agents' types, and capability in drafting incentive-compatible agreements.

We would like to conclude by raising some questions for possible future research:

(1) High property taxes in a certain town (primarily to support high quality public education) may cause emigration of low income people to other towns with lower property taxes where high population density may negatively affect the quality of public services (such as public education and sanitation) and contribute to the deterioration of housing as well as to the emergence of gang activity and lawlessness. In this case, could the receiving town, where the underprivileged move, become a tragedy of the commons region due to property rights misallocation which satisfies the utilitarian objectives of some at the expense of everyone else? Could incentive-compatible agreements between privilege and underprivileged members enable society to eradicate such tragedy of the commons and, as Singer (2000, p. 25) points out, build a "bridge between the haves and the have-nots"? In our judgment, Singer (p. 36) thoughtfully guides us on how to select criteria for the effective engineering of incentive-compatible rulings; in his words, "it is the job of the law to manage tensions between competing interests in access and exclusion, change and stability, wealth and equality, liberty and security. The question for us all is: what values should inform us as we choose property rules and institutions? How should the law shape economic and social life?"

(2) Lack of property rights in developing nations, caused by past historic property misallocations owing to asymmetry in information and the resultant deception and exploitation of local populations, have given rise to informal firms which hinder economic development and growth. According to the United Nations (2008, p. 1) "four billion people around the world are robbed of the chance to better their lives and climb out of poverty, because they are excluded from the rule of law due to business informality." Obviously citizens in these countries need property rights or titles. Referencing De Soto (2000), Kantarelis (p.10) states that "informal business firms account for up to about half of economic activity in developing nations ... and are held back by barriers to official recognition: lack of secure property titles, deeds, securities and contracts that describe the economically significant aspects of assets. The lowering of such barriers would improve the ability of firms to borrow against registered and secured property-based collateral; additionally, it would enable them to more easily acquire, and/or merge with, other firms." Unfortunately, the informality problem persists despite the various efforts being made, which indicates how difficult it is to engineer incentive-compatible agreements in order to remove barriers to property ownership. As Singer (p. 91) emphasizes, "[p]roperty is not just about self-interest. It is about creating the ground rules for fair social relationships."


Independent Scholar, Chicago, IL


Assumption College, Worcester, MA

(corresponding author)

Received 23 November 2015 * Received in revised form 11 January 2016

Accepted 11 January 2016 * Available online 10 February 2016


(1.) Sen (p. 12) tells the charming story of three children, Anne, Bob, and Carla, who are arguing over the property rights to a flute. Anne claims ownership of the flute on the basis that she is the only one able to play it; Bob claims it because he, unlike the other children, has no other toys to play with; Carla claims the flute since it was stolen from her after she made it with her own hands. Based on different philosophical beliefs, all three property claims can be taken to be reasonable. Sen's point is that one can produce intuitively believable reasons for assigning property of the flute to any one of the children. Hence, utilitarians--and "for more worthy ends" Aristotelians--would favor Anne, egalitarians Bob, and libertarians Carla. The point here is that there is no reason to assume, as Rawls and most of his followers do, that we have to decide which one of these claims is fairest or most just (Rawls, 1985). Of course, one may wonder: what if the "flute" were a "Stradivarius violin"?

(2.) The problem of getting to share information honestly is called adverse selection. The problem of getting people to act obediently to a plan is called moral hazard.


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Table 1 Bilateral Setting

                                            Buyer's type and
                                            threat value

                                         Strong (0.5)    Weak (0.5)
                                         $20             $120

Seller's type and   Strong (0.5)   $80   [p.sub.A], $A   [p.sub.B], $B
threat value        Weak (0.5)     $10   [p.sub.C], $C   [p.sub.D], $D

Table 2 Fifty/Fifty Split Agreement

                                            Buyer's type and
                                            threat value

                                         Strong (0.5)   Weak (0.5)
                                             $20           $120

Seller's type and   Strong (0.5)   $80   0, No Trade     1, $100
threat value        Weak (0.5)     $10      1, $15        1, $65

Table 3 Incentive-Compatible Split Agreement

                                            Buyer's type and
                                            threat value

                                         Strong (0.5)   Weak (0.5)
                                             $20           $120

Seller's type and   Strong (0.5)   $80    0, No Deal    q, $120-y
threat value        Weak (0.5)     $10     q, $10+y       1, $65
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Author:Anderson, Emily; Kantarelis, Demetri
Publication:Contemporary Readings in Law and Social Justice
Article Type:Essay
Date:Jul 1, 2016
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