Legal Entitlements as Auctions: Property Rules, Liability Rules, and Beyond

106 Yale Law Journal 703 (1997)


*William K. Townsend Professor,

**Lafayette S. Foster, Professor, Yale Law School. Jennifer Brown, Bob Ellickson and Jon Hanson provided helpful comments. Brian




A. Naive Second-Order Liability Rules 12

B. Optimal Second-Order Liability Rules 16

C. Higher-Order Liability Rules As Auction Surrogates 19






The analysis of liability and property rules is undergoing somewhat of a renaissance . Arecent crop of articles have used an option model to distinguish between these two methods of protecting entitlements. A liability rule gives at least one party an option to take an entitlement non-consensually and pay the entitlement owner some exercise price. The difference between liability and property rules is the exercise price -- the damages suffered as a consequence of non-consensual taking. The exercise price of a property rule is so high that no one would ever exercise the option to take non-consensually, while the lower exercise prices of liability rules allow non-consensual transfer.

An implicit part of almost all these analyses is an assumption that liability taking options are themselves protected by property rules. For example, if a liability rule regime gives Calabresi an option to take some entitlement of Melamed for $100, most analysts implicitly assume that after such a taking, Calabresiís interest in the entitlement would be protected by a property rule -- meaning that Melamed (and others) would not have a viable option to take the entitlement back from Calabresi.

Kaplow and Shavell are among the very few that have explicitly tried to defend this assumption. They argue that with regard to certain harmful externalities such as pollution, it becomes impossible as a technological manner to take back an entitlement once the entitlement has been taken (e.g., it is difficult to reclaim a pristine environment after a pollution taking). Moreover, they argue that giving Calabresi a take-back option can lead to an infinite sequence of takings if the damages (the exercise price for the taking option) are set too low: Suppose that under the liability rule damages would be only $75 for taking something worth at least $100 to its owner and to many others. Then if someone takes the thing, which is likely, the owner would wish to take it right back (returning the $75 he received as damages to the taker). Such reciprocal takings are problematic because they will lead inevitably to destructive contests to retain or to take control of things and thus to the use of force. . . .The only apparent solution to the problem of reciprocal takings lies in a mixed system of a liability rule for an initial taking combined with property rule protection of the takerís possessory rights afterwards. Kaplow and Shavellís analysis thus gives explicit justifications for the intuition that protecting liability rules with liability rules would be infeasible or inefficient.

The goal of this essay is to upset, or at least qualify, these justifications -- by showing that regimes with reciprocal taking options can be more efficient than either property or liability rules. To establish this thesis, we will focus almost exclusively on a very stylized nuisance example with two contiguous property owners -- in part because their physical contiguity allows us to analyze the strategic interaction of just two "players," and in part because Kaplow and Shavell have recently argued that in such contexts "there is a prima facie case favoring liability rules over property rules." These authors have nicely formalized the intuition that liability rules have a non-consensual advantage over property rules, because (when properly structured) liability rules can induce takings when the taker on average has a higher valuation than the original entitlement holder. Liability rules thereby come closer to mimicking the allocation that would obtain if efficient trade were possible.

Their insight, however, proves too much. Using their own model, we will show that giving the original entitlement holder a take-back option can likewise induce second-order takings which produce even greater efficiency. Protecting a liability rule option with a liability rule can be more efficient than the traditional liability rule without such a take-back option.

As a matter of nomenclature, we will refer to the traditional liability rule of Calabresi and Melamed is a "first-order" rule because it contemplates at most one non-consensual taking. And by analogy, we will call a regime where the entitlement holder has a take-back option as a "second-order" liability rule, because this rule creates the possibility of two non-consensual takings. Under such a regime, a potential polluter would first have an option to pay the original entitlement owner a predetermined sum for the right to pollute, but (before pollution began) the original owner would have the option to pay the polluter a larger sum to maintain the pollution prohibition. In a second-order liability regime, once the original owner had exercised its take-back option, property-rule protection would henceforth deter the polluter from polluting.

Of course, it is theoretically possible to consider third- or higher-order liability rules which involve a longer series of reciprocal taking options. Most of our analysis will focus on the relative efficiency of second-order liability rules, but we will also show that higher-order liability rules (with multiple-taking options) can implement an efficient auction -- where each taking represents a "bid" signaling a higher valuation. Even though winning bidders normally pay a third party, we will show that bidding to pay other bidders can induce what amounts to an auction with minimum bid increments. An arbitrarily larger number of reciprocal taking options will produce an auction with an arbitrarily small bid increment -- which in the limiting case produces first-best efficiency.

This auction reinterpretion lets us see that liability and property rules are special cases of a larger family of truncated auctions: Traditional (first-order) liability rules are one-round auctions where there is at most one bid; and property rules might even be thought of as creating zero-round auctions (where the minimum opening bid is above a potental takerís highest value). Recast in this way suggests that efficiency-minded lawmakers will want to choose the auction structure (including the courseness of bidding increments and how the auction proceeds are distributed) to minimize a variety of inefficiencies.

For example, administrating a regime with second- or third-order liability rules will not be costless. Introducing taking costs will tend to make lower-order liability rules or even property rules more efficient. However, introducing taking costs qualifies Kaplow and Shavellís conclusion that there is a prima facie case for first-order liability rules with regard to harmful externalities. First-order liability rules are only most efficient for a rather narrow range of possible taking costs: when taking costs are greater than this range, property rules are efficient and when taking costs are less than this range, second- or higher-order liability rules are more efficient.

The claim that reciprocal taking options are unworkable or infeasible is not a priori true: For example, polluters might be allowed to pollute only after first applying for a permit which would establish the polluterís exercise price of polluting, and allow the pollutee to exercise its take-back option by offering to pay some money to purchase an injunction.

The feasibility of reciprocal taking options can be seen in the common law tort defense of necessity, which at times has resembled a second-order liability rule. Jon Hanson has shown that the venerable decision in Vincent v. Lake Erie is a vivid example where the common law protects a liability option with a liability rule. Vincent of course held a ship owner liable for damages when his ship damaged a dock during a storm. The decision is usually characterized as atraditional (first-order) liability rule -- in which a shipowner during a storm has the option (by exposing itself to a damage suit) to take the dock ownerís original entitlement to exclude mooring ships. But Vincentís discussion of an earlier case makes clear that the ship ownerís liability option is itself only protected by aliability rule: In Ploof v. Putnam, the supreme court of Vermont held that where, under stress of weather, a vessel was without permission moored to a private dock at an island in Lake Champlain owned by the defendant, the plaintiff was not guilty of trespass, and that the defendant was responsible in damages because his representative upon the island unmoored the vessel, permitting it to drift upon the shore, with resultant injuries to it. If, in that case, the vessel had been permitted to remain, and the dock had suffered an injury, we believe the shipowner would have been held liable for the injury done.

Vincentís parsing of Ploof v. Putnam describes a classic second-order liability rule: The dock owner holds the intial entitlement; the shipowner (during the exigencies of a storm) has a first- stage option to take but in doing so makes its self liable for injury done; and finally the dock owner has a second-stage option to unmoor the ship -- which causes it to not only give up its cause of action against the ship owner but to expose itself tort liability.

The feasibility of reciprocal taking options can also be seen in an early article of Robert Ellickson. In large part, this essay is inspired by Ellicksoní proposal of what amounts to a second-order liability rule: A landowner who intentionally carries out [unneighborly] activities . . . shall be liable for all damages [but] continuation of the activity may be enjoined by any party willing to compensate the landowner for any losses he suffers from that injunction. Under this regime, the defendant/polluter decides whether to purchase the right to pollute, and the plaintiff/pollutee then decides whether to purchase an injunction to stop the pollution. Ellickson and Hanson, to our knowledge, are the only people who have seriously considered the utility of higher-order liability rules.

The first part of this paper will analyze the relative efficiency of second- (and higher-) order liability rules. In a canonical asymmetric-information model, we will show that second- (and higher) order liability rules dominate first-order liability rules (i) when the taking regime is costlessly administered and (ii) when bargaining is not possible. Part two relaxes this first assumption by considering the relative efficiency of different rules when non-consensual taking is not costless. And part three relaxes the second assumption by considering the effects of bargaining on the rulesí relative efficiency.
See James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U.L. Rev. 440 (1995); Ian Ayres and Eric Talley, Solomonic Bargaining: Dividing A Legal Entitlement To Facilitate Coasean Trade, 104 YALE LAW JOURNAL 1027 (1995) [hereinafter Ayres & Talley I]; Ian Ayres & Eric Talley, Distinguishing Between Consensual and Nonconsensual Advantages of Liability Rules, 105 YALE LAW JOURNAL 235 (1995) [hereinafter Ayres & Talley II]; Louis Kaplow and Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 Harv. L. Rev. 713 (1996) [hereinafter Kaplow & Shavell I]; Louis Kaplow and Steve Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 Yale L. J. 221 (1995) [hereinafter Kaplow & Shavell II]. The property/liability rule distinction originates in Calabresi & Melamed, Property Rules, Liability Rules and Inalienability: One View of the Cathedral, 85 Harv. L. Rev. 1089 (1972). Madeline Morris, The Structure of Entitlements, 78 Cornell L. Rev. 822 (1993). But see Jules L. Coleman & Jody Kraus, Rethinking the Theory of Legal Rights, 95 Yale L. J. 1335 (1986) (arguing that degree of protection from non-consensual taking can be thought of as change the content of the entitlement).

The option framework seem particularly well suited for some nuisance contexts where the taking party intentionally takes the right of anouther -- and hence seems to be consciously choosing, say, to pollute or not pollute. By contrast, negligent tortfeasors do not intentionally take the interest of other parties and might not seem to be affirmatively exercising an option. However, even in the case of negligence, the tortfeasor by choosing her level of care in a sense intentionally chooses a certain probability of taking that comports with the option framework.
See also Krier and Schwab, supra note 1.
Louis Kaplow & Shavell I, supra note 1, at 721.

A fundamental problem of allocating liability rule options for an entitlement is how to handle multiple parties wanting to exercise an option. Ayres & Talley I, supra note 1, at 1088. Kaplow &Shavell, supra note 1, at 733. As opposed to the "reciprocal takings" problems between two parties, this "multiple takers" problem adds substantial complexity to a liability rule regime because the regime would need to specify, inter alia, the priority of option holders and whether the entitlement could be non-concensually transferred among a series of takers. While we will argue below that the possibility of reciprocal takings should not undermine the potential usefulness of liability rule regimes, we do think that multiple-takers problem can undermine their utility. In the nuisance context, the law might be able to avoid or reduce the multiple-takers problem by only granting liability rule options to oneís upwind neighbor (or neighbors). This would created a different type of "mixed" regime, in that the entitlement would be protected by a property rule with regard to all non-neighbors. Environmental factors -- such as physical contiguity or the prevailing direction of wind or water -- may also substantially reduce the number of potential takers. Richard L. Revesz, Rehabilitating Interstate Competition: Rethinking the "Race-to-the-Bottom" Rationale for Federal Environmental Regulation, 67 N.Y.U.L. Rev. 1210 (1992).
Kaplow & Shavell I, supra note 1, at 721.
Kaplow & Shavell I, supra note 1, at 719-720.

Under this schema, a property rule might be referred to as a zero-order liability rule because it allows no non-consensual takings.

For example, infra Table 1, we will consider a third-order liability rule in which the factory can exercise its first-order option by paying $42, the laundry could then exercise the second-order option by paying $58, and factory could then exercise the third-order option by paying $75. Subsequent takings would by definition be deterred by property protection -- meaning that if the factory exercised the third-order option and took control of the entitlement, the laundry (and all others) would be deterred from further non-consensual takings by arbitrarily high damages.

Formally, potential polluters would be deterred from polluting before such court action by high fines for polluting without appropriate agency or judicial permit. As before, property rule protection against certain acts would be necessary to reenforce a reciprocal takings regime. Thus, Kaplow and Shavellís canny observation that it is difficult to take back pollution, once it is emitted does mean that the state could not create a regime where polluters proposed polluting so as to allow pollutees to exercise their take-back option. Indeed, even with regard to pollution, the state could still provide a recipient with a take-back option with regard to prospective pollution.
Vincent v. Lake Erie Trans. Co., 109 Minn. 456, 124 N.W. 221 (Minn. 1910).

Hanson refers to the Vincent standard as a "double-sided" liability rule. Jon Hanson, Double- Sided Liability Rules in Tortious Necessity (manuscript 1996).
Richard A. Epstein, A Common Lawyer Looks at Constitutional Interpretation, 72 B.U.L. Rev. 699, 712
n.40 (1992).
Kaplow & Shavell I, supra note 1, at 757 n. 143.
Vincent, 109 Minn. at 459; 124 N.W. at 222 (citations ommitted).
81 Vt. 471, 71 A. 188 (Vt. 1908).

Robert C. Ellickson, Alternatives to Zoning: Covenants, Nuisance Rules, and Fines as Land Use Controls, 40 U. Chi. L. Rev. 681, 748 (1973). Ellickson described this proposal as a combination of what Calabresi and Melamed called Rules two and four. Rule 2 gives the polluter an option to pollute an pay damages, while rule 4 gives the pollutee an option to enjoin pollution by damages to the polluter. Id. at 738. Calabresi & Melamed, supra note 4, at 1115-23.

By way of contrast, the famous ruling in Spur Industries v. Del E. Webb Development Co., 108 Ariz. 178, 494 P.2d 700 (1972), represents a first-order liability rule in which the polluter has the originl entitlement to pollute, but it is only protected by a liability rule so that the pollutee has the option to stop pollution by paying damages.

But see Madeline Morris, The Structure of Entitlement, 78 Cornell L. Rev. 822, 891-93 (1993) (recognizing possible usefulness of second-order liability rules, but not pursuing when these rules might be efficient).

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