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

Yale Law Journal

Volumn 106, Issue 3, 1996, Pages 703-749

  Ayres, Ian ^a   Balkin, J M ^a  

^a NONE

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EID: 0041463342     PISSN: 00440094     EISSN: None     Source Type: Journal    
DOI: 10.2307/797308     Document Type: Review

References (185)

1. The first two examples are interests in security (Hohfeldian rights proper); the second two are interests in liberty (Hohfeldian privileges). See Wesley N. Hohfeld, Fundamental Legal Conceptions as Applied in Judicial Reasoning, 26 YALE L.J. 710 (1917) [hereinafter Hohfeld, Fundamental Legal Conceptions]; Wesley N. Hohfeld, Some Fundamental Legal Conceptions as Applied in Judicial Reasoning, 23 YALE L.J. 16 (1913). The classification of the entitlement depends on who holds it. If the entitlement is placed in the hands of a polluter, it is a privilege to pollute; if the entitlement rests in the hands of the neighboring landowner, it is a right to be free from pollution.
2. The first two examples are interests in security (Hohfeldian rights proper); the second two are interests in liberty (Hohfeldian privileges). See Wesley N. Hohfeld, Fundamental Legal Conceptions as Applied in Judicial Reasoning, 26 YALE L.J. 710 (1917) [hereinafter Hohfeld, Fundamental Legal Conceptions]; Wesley N. Hohfeld, Some Fundamental Legal Conceptions as Applied in Judicial Reasoning, 23 YALE L.J. 16 (1913). The classification of the entitlement depends on who holds it. If the entitlement is placed in the hands of a polluter, it is a privilege to pollute; if the entitlement rests in the hands of the neighboring landowner, it is a right to be free from pollution.
3. The first two examples are interests in security (Hohfeldian rights proper); the second two are interests in liberty (Hohfeldian privileges). See Wesley N. Hohfeld, Fundamental Legal Conceptions as Applied in Judicial Reasoning, 26 YALE L.J. 710 (1917) [hereinafter Hohfeld, Fundamental Legal Conceptions]; Wesley N. Hohfeld, Some Fundamental Legal Conceptions as Applied in Judicial Reasoning, 23 YALE L.J. 16 (1913). The classification of the entitlement depends on who holds it. If the entitlement is placed in the hands of a polluter, it is a privilege to pollute; if the entitlement rests in the hands of the neighboring landowner, it is a right to be free from pollution.
4. See Guido Calabresi & A. Douglas Melamed, Property Rules, Liability Rules, and Inalienability: One View of the Cathedral, 85 HARV. L. REV. 1089 (1972).
5. See id. at 1092. These assumptions have recently come under critical scrutiny. See Ian Ayres & Eric Talley, Solomonic Bargaining: Dividing a Legal Entitlement to Facilitate Coasean Trade, 104 YALE L.J. 1027 (1995) [hereinafter Ayres & Talley, Solomonic Bargaining]; Ian Ayres & Eric Talley, Distinguishing Between Consensual and Nonconsensual Advantages of Liability Rules, 105 YALE L.J. 235 (1995) [hereinafter Ayres & Talley, Distinguishing]. Calabresi and Melamed also suggested another method of protecting entitlements, called "inalienability," which discouraged the parties from transferring the entitlement either consensually or nonconsensually. See Calabresi and Melamed, supra note 2, at 1092-93. The present Essay does not concern this form of entitlement protection.
6. See id. at 1092. These assumptions have recently come under critical scrutiny. See Ian Ayres & Eric Talley, Solomonic Bargaining: Dividing a Legal Entitlement to Facilitate Coasean Trade, 104 YALE L.J. 1027 (1995) [hereinafter Ayres & Talley, Solomonic Bargaining]; Ian Ayres & Eric Talley, Distinguishing Between Consensual and Nonconsensual Advantages of Liability Rules, 105 YALE L.J. 235 (1995) [hereinafter Ayres & Talley, Distinguishing]. Calabresi and Melamed also suggested another method of protecting entitlements, called "inalienability," which discouraged the parties from transferring the entitlement either consensually or nonconsensually. See Calabresi and Melamed, supra note 2, at 1092-93. The present Essay does not concern this form of entitlement protection.
7. See id. at 1092. These assumptions have recently come under critical scrutiny. See Ian Ayres & Eric Talley, Solomonic Bargaining: Dividing a Legal Entitlement to Facilitate Coasean Trade, 104 YALE L.J. 1027 (1995) [hereinafter Ayres & Talley, Solomonic Bargaining]; Ian Ayres & Eric Talley, Distinguishing Between Consensual and Nonconsensual Advantages of Liability Rules, 105 YALE L.J. 235 (1995) [hereinafter Ayres & Talley, Distinguishing]. Calabresi and Melamed also suggested another method of protecting entitlements, called "inalienability," which discouraged the parties from transferring the entitlement either consensually or nonconsensually. See Calabresi and Melamed, supra note 2, at 1092-93. The present Essay does not concern this form of entitlement protection.
8. See id. at 1092. These assumptions have recently come under critical scrutiny. See Ian Ayres & Eric Talley, Solomonic Bargaining: Dividing a Legal Entitlement to Facilitate Coasean Trade, 104 YALE L.J. 1027 (1995) [hereinafter Ayres & Talley, Solomonic Bargaining]; Ian Ayres & Eric Talley, Distinguishing Between Consensual and Nonconsensual Advantages of Liability Rules, 105 YALE L.J. 235 (1995) [hereinafter Ayres & Talley, Distinguishing]. Calabresi and Melamed also suggested another method of protecting entitlements, called "inalienability," which discouraged the parties from transferring the entitlement either consensually or nonconsensually. See Calabresi and Melamed, supra note 2, at 1092-93. The present Essay does not concern this form of entitlement protection.
9. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
10. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
11. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
12. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
13. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
14. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
15. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
16. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
17. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
18. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3; Ayres & Talley, Distinguishing, supra note 3; Louis Kaplow & Steven Shavell, Property Rules Versus Liability Rules: An Economic Analysis, 109 HARV. L. REV. 713 (1996) [hereinafter Kaplow & Shavell, Economic Analysis]; Louis Kaplow & Steven Shavell, Do Liability Rules Facilitate Bargaining? A Reply to Ayres and Talley, 105 YALE L.J. 221 (1995) [hereinafter Kaplow & Shavell, Reply]; James E. Krier & Stewart J. Schwab, Property Rules and Liability Rules: The Cathedral in Another Light, 70 N.Y.U. L. REV. 440 (1995); Madeline Morris, The Structure of Entitlements, 78 CORNELL L. REV. 822 (1993); see also Symposium, Property Rules, Liability Rules, and Inalienability: A Twenty-Five Year Retrospective, 106 YALE L.J. (forthcoming May 1997) (celebrating 25th anniversary of publication of Calabresi & Melamed, supra note 2); Jason Scott Johnston, Bargaining Under Rules Versus Standards, 11 J.L. ECON. & ORG. 256 (1995).
19. See, e.g., Boomer v. Atlantic Cement Co., 257 N.E.2d 870 (N.Y. 1970) (requiring factory owners to pay permanent damages in compensation for right to pollute). In many business situations, options are the result of a prior bargain, where the option to take at a given price is purchased for some premium. However, in the case of liability rules, the option is the result of preexisting legal rules; the law simply gives parties the right to take in exchange for damages. Both the bargained-for option and the liability rule are examples of what Hohfeld termed a "liability." Hohfeld, Fundamental Legal Conceptions, supra note 1, at 727. A party has a Hohfeldian liability when another party has the right to alter the first party's rights unilaterally. See id. The second party has what Hohfeld called a "power." See id. The person who owns an option alters rights by exercising the option, creating a duty to pay the purchase price. The person who takes under a liability rule alters rights by interfering with the entitlement, creating a duty to pay damages. Hohfeld was careful to point out that having a liability to others (in his sense) is not always a bad thing; sometimes it is to our benefit that others can change our rights unilaterally. See id. at 742. For example, whenever a person makes an offer to us, she changes our bundle of rights, because we now have the right to accept the offer. And when a party destroys a chattel we do not value highly, we may benefit because we have the right to receive damages at the market price, which may be higher than our private valuation. In a world with perfect information and costless bargaining, it is not advantageous to give others unilateral options to purchase, no matter how high the exercise price. It is more efficient to offer to sell the property to the highest bidder. That is one reason why parties normally demand premiums to grant options. But where transaction costs are high, an entitlement holder may prefer to grant options to potential buyers without receiving any premium in return. Such options help ensure that one can reap some profits from the exchange even when one may not be able to transfer consensually to a higher valuing buyer. The analogous insight is that where transaction costs are high, the law can increase efficiency by creating options in the form of liability rules.
20. But see Jules L. Coleman & Jody Kraus, Rethinking the Theory of Legal Rights, 95 YALE L.J. 1335 (1986) (arguing that change in degree of protection from nonconsensual taking changes content of entitlement).
21. The options framework seems particularly well-suited for some nuisance contexts where the taking party intentionally takes the right of another, 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 a negligent tortfeasor chooses a level of care and thus can be said to choose intentionally a certain probability of taking that comports with the options framework.
22. See Calabresi & Melamed, supra note 2, at 1106-10.
23. See id. It might be more accurate to say that scores of legal scholars have interpreted Calabresi and Melamed to be saying that property rules are more efficient when transaction costs are low. See, e.g., Robert P. Merges, Of Property Rules, Coase, and Intellectual Property, 94 COLUM. L. REV. 2655, 2655, 2664 (1994). Just as Coase never formally stated the Coase Theorem in Ronald N. Coase, The Problem of Social Cost, 3 J.L. & ECON. 1 (1960), Calabresi and Melamed never succinctly stated what has been taken to be their primary normative conclusion.
24. See id. It might be more accurate to say that scores of legal scholars have interpreted Calabresi and Melamed to be saying that property rules are more efficient when transaction costs are low. See, e.g., Robert P. Merges, Of Property Rules, Coase, and Intellectual Property, 94 COLUM. L. REV. 2655, 2655, 2664 (1994). Just as Coase never formally stated the Coase Theorem in Ronald N. Coase, The Problem of Social Cost, 3 J.L. & ECON. 1 (1960), Calabresi and Melamed never succinctly stated what has been taken to be their primary normative conclusion.
25. See Coase, supra note 9, at 15.
26. Ayres and Talley argued that liability rules can force entitlement holders to reveal private information about how much they value their entitlements, and hence can facilitate trade. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1032-36. Conversely, Kaplow and Shavell have argued that liability rules may be more efficient even where transaction costs are low because the nonconsensual advantage of liability rules tends to persist when bargaining becomes possible. The extent of these different effects has spurred a lively debate. See Kaplow & Shavell, Reply, supra note 4; Ayres & Talley, Distinguishing, supra note 3; Kaplow & Shavell, Economic Analysis, supra note 4.
27. Ayres and Talley argued that liability rules can force entitlement holders to reveal private information about how much they value their entitlements, and hence can facilitate trade. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1032-36. Conversely, Kaplow and Shavell have argued that liability rules may be more efficient even where transaction costs are low because the nonconsensual advantage of liability rules tends to persist when bargaining becomes possible. The extent of these different effects has spurred a lively debate. See Kaplow & Shavell, Reply, supra note 4; Ayres & Talley, Distinguishing, supra note 3; Kaplow & Shavell, Economic Analysis, supra note 4.
28. Ayres and Talley argued that liability rules can force entitlement holders to reveal private information about how much they value their entitlements, and hence can facilitate trade. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1032-36. Conversely, Kaplow and Shavell have argued that liability rules may be more efficient even where transaction costs are low because the nonconsensual advantage of liability rules tends to persist when bargaining becomes possible. The extent of these different effects has spurred a lively debate. See Kaplow & Shavell, Reply, supra note 4; Ayres & Talley, Distinguishing, supra note 3; Kaplow & Shavell, Economic Analysis, supra note 4.
29. Ayres and Talley argued that liability rules can force entitlement holders to reveal private information about how much they value their entitlements, and hence can facilitate trade. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1032-36. Conversely, Kaplow and Shavell have argued that liability rules may be more efficient even where transaction costs are low because the nonconsensual advantage of liability rules tends to persist when bargaining becomes possible. The extent of these different effects has spurred a lively debate. See Kaplow & Shavell, Reply, supra note 4; Ayres & Talley, Distinguishing, supra note 3; Kaplow & Shavell, Economic Analysis, supra note 4.
30. See Coase, supra note 9.
31. See Kaplow & Shavell, Economic Analysis, supra note 4, at 767-68.
32. Id. at 767.
33. Id. at 767-68.
34. See THE MALTESE FALCON (Paramount Pictures 1941) (portraying valuable chattel encrusted with jewels taken and retaken many times with dramatic consequences).
35. Some types of pollution, however, may be more reversible than one might initially imagine. See William K. Stevens, If It's East of the Mississippi, It's Blanketed in Pollution's Haze, N.Y. TIMES, July 17, 1990, at C4 ("[I]f all human-made sources of air pollution were shut down, 'everything would clear out in three or four days and there would be, on the average, 90-mile visibility'" instead of the current pollution-induced 15-mile visibility) (quoting Dr. John Trijonis of the Santa Fe Research Corporation).
36. See infra text accompanying notes 39-47; Part V. One could even imagine a regime in which the entire transaction took place ex ante. Suppose the law gave the polluter extremely strong incentives (for example, by a threat of imprisonment) to go into court to acquire legal permission before she began polluting. Under such a regime, the polluter would be required to obtain a permit establishing her right to pollute by paying what amounts to an exercise price for pollution. The court would then allow the pollutee to exercise its take-back option by offering to pay money to purchase an injunction. Note that this regime contemplates the use of a property rule to steer the parties into an auction for the entitlement. This point can be generalized. Property rules of some form are inevitable in any system designed to protect legal entitlements. If they are not used to protect the entitlements directly, they will be used to induce parties to participate in the entitlement rules of the legal system.
37. For example, when early American mills flooded, they often only affected a single upstream landowner or at most a small set of landowners. See infra text accompanying notes 123-24 (discussing the New Hampshire Mill Act). The law might be able to avoid or ameliorate the multiple-takers problem in nuisance situations by granting retaking options only to one's upwind neighbor (or neighbors). This would create a "mixed" regime in a different sense than Kaplow and Shavell imagined: The entitlement would be protected by a higher-order liability rule with respect to the upwind neighbor and by a property rule with respect to all others. Environmental factors - such as physical contiguity or the prevailing direction of wind or water - may also substantially limit the number of potential takers. See Richard L. Revesz, Rehabilitating Interstate Competition: Rethinking the "Race-to-the-Bottom" Rationale for Federal Environmental Regulation, 67 N.Y.U. L. REV. 1210, 1222-23 (1992).
38. Handling multiple parties who wish to exercise an option to take is a recurring and fundamental problem for allocating ordinary first-order liability rules, not just higher-order ones. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1088-90; Kaplow & Shavell, Economic Analysis, supra note 4, at 732-37.
39. Handling multiple parties who wish to exercise an option to take is a recurring and fundamental problem for allocating ordinary first-order liability rules, not just higher-order ones. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1088-90; Kaplow & Shavell, Economic Analysis, supra note 4, at 732-37.
40. See infra Part V.
41. In contrast to the reciprocal takings problem involving only two parties, this "multiple takers" problem adds substantial complexity to administering a taking options regime. Such a regime would need to specify, among other things, the priority of option holders and whether the entitlement could be transferred nonconsensually by a series of different takers.
42. Kaplow & Shavell, Economic Analysis, supra note 4, at 721 (emphasis omitted).
43. See id. at 719-20.
44. Under this schema, a property rule might be referred to as a "zero-order" liability rule because it presumes that there will be no nonconsensual takings. We use the term "presume" advisedly. Just as it is theoretically possible to take nonconsensually under a property rule if one were willing to pay the exercise price, a person whose entitlement is protected by a first-order liability rule might, in theory, retake it, if she were willing to pay the exercise price (which might involve going to jail). Sometimes, as Kaplow and Shavell note, the retaking will simply be impossible. See Kaplow & Shavell, Economic Analysis, supra note 4, at 768 (discussing impossibility of reversing harmful externalities). But when it is not impossible, what makes the rule a first-order liability rule is the presumption that no rational person will retake at such a high price. Thus, just as property rules are liability rules in which no one is likely to take nonconsensually, a first-order liability rule can be thought of as a kind of second-order liability rule in which no one is going to exercise the take-back option. A similar point can be made about the relation of second-order liability rules to third-order rules, and so on.
45. For example, we will consider a third-order liability rule in which the factory could exercise the first-order option by paying $42; the laundry could then exercise the second-order option by paying $58; and the factory could then exercise the third-order option by paying $75. See infra Table 2. Subsequent takings would by definition be deterred by property protection - i.e., if the factory exercised the third-order option and took control of the entitlement, the laundry (and all others) would be deterred from further nonconsensual takings by arbitrarily high damages.
46. Our insight that legal rules can be used productively to harness parties' private information has its roots in a larger value-revelation literature. See, e.g., T. Nicolaus Tideman & Gordon Tullock, A New and Superior Process for Making Social Choices, 84 J. POL. ECON. 1145, 1145-46 (1976) (proposing "demand-revealing" solution for problem of strategic maneuvering); see also Saul Levmore, Self-Assessed Valuation Systems for Tort and Other Law, 68 VA. L. REV. 771, 778-79 (suggesting self-assessment solution to problem of property tax collection).
47. Our insight that legal rules can be used productively to harness parties' private information has its roots in a larger value-revelation literature. See, e.g., T. Nicolaus Tideman & Gordon Tullock, A New and Superior Process for Making Social Choices, 84 J. POL. ECON. 1145, 1145-46 (1976) (proposing "demand-revealing" solution for problem of strategic maneuvering); see also Saul Levmore, Self-Assessed Valuation Systems for Tort and Other Law, 68 VA. L. REV. 771, 778-79 (suggesting self-assessment solution to problem of property tax collection).
48. See generally Robert Wilson, Strategic Analysis of Auctions, in 1 HANDBOOK OF GAME THEORY WITH ECONOMIC APPLICATIONS 227 (Robert J. Aumann & Sergiu Hart eds., 1992).
49. Auctions can be implemented with either sealed bidding or open-call bidding, and open-call bidding can be accomplished with either ascending bids (as in so-called "English" auctions) or with descending bids (as in so-called "Dutch" auctions). In "second-price auctions," winning bidders sometimes must only pay the second-highest bid, instead of what they bid themselves. See id. at 230 (describing auction variants).
50. One might think that another important consideration would be the number of possible rounds. In the examples we consider here, however, the parties' maximum valuation of the entitlement is already known. Hence, the number of possible rounds is largely dictated by the size of the bidding increments.
51. For example, in a popular class exercise, a professor offers to auction a $10 bill to the highest bidder - with the important catch that both the first-and second-highest bidders are required to pay. Once the bidding hits $10, the second-highest bidder suddenly realizes that it is better to bid $11 to win the auction (and thereby lose $1) than to come in second and lose $9. For a real world example of this "war of attrition" auction, see Ian Ayres & Peter Cramton, Pursuing Deficit Reduction Through Diversity: How Affirmative Action at the FCC Increased Auction Competition, 48 STAN. L. REV. 761 (1996).
52. We distinguish this from the more familiar situation of an "external auction," where the parties bid for an entitlement owned by another and the winner pays the owner for it.
53. Or, to put it another way, a property rule is like an auction at Sotheby's where the owner really does not want to part with the painting, and thus requires an exceptionally high opening bid. In real life, the auction house will advise (or require) that the initial bid be set lower, because it wants to move merchandise and collect a percentage of the bid. But in this respect the legal system differs from the owner of an auction house; it may have good reasons to respect the desire of the owner not to surrender the chattel except consensually and at the owner's asking price. See infra text accompanying notes 36-38; Part VI.
54. See Kaplow & Shavell, Economic Analysis, supra note 4, at 721.
55. The possibility of inefficient bargaining is dramatized by what economists call bilateral monopoly: Bilateral monopolies, which arise when two parties are locked into dealing with each other . . . can give rise to high negotiation costs that foreclose efficient transfers. Because there is no competitive pressure from outsiders, each party is likely to bargain "strategically" - asking much, offering little, bluffing, threatening to walk away from the deal - in an effort to get as much as possible. . . . "[B]ilateral monopoly is a social problem, because the transaction costs incurred by each party in an effort to engross as much of the profit of the transaction as possible are a social waste. They alter the relative wealth of the parties but do not increase the aggregate wealth of society. A major thrust of the common law . . . is to mitigate bilateral-monopoly problems." JESSE DUKEMINIER & JAMES E. KRIER, PROPERTY 137 n.17 (3d ed. 1993) (quoting RICHARD A. POSNER, ECONOMIC ANALYSIS OF LAW 62 (4th ed. 1992)). Higher-order liability rules may be able to mitigate bilateral monopoly problems in settings that otherwise seem to have low transaction costs.
56. The possibility of inefficient bargaining is dramatized by what economists call bilateral monopoly: Bilateral monopolies, which arise when two parties are locked into dealing with each other . . . can give rise to high negotiation costs that foreclose efficient transfers. Because there is no competitive pressure from outsiders, each party is likely to bargain "strategically" - asking much, offering little, bluffing, threatening to walk away from the deal - in an effort to get as much as possible. . . . "[B]ilateral monopoly is a social problem, because the transaction costs incurred by each party in an effort to engross as much of the profit of the transaction as possible are a social waste. They alter the relative wealth of the parties but do not increase the aggregate wealth of society. A major thrust of the common law . . . is to mitigate bilateral-monopoly problems." JESSE DUKEMINIER & JAMES E. KRIER, PROPERTY 137 n.17 (3d ed. 1993) (quoting RICHARD A. POSNER, ECONOMIC ANALYSIS OF LAW 62 (4th ed. 1992)). Higher-order liability rules may be able to mitigate bilateral monopoly problems in settings that otherwise seem to have low transaction costs.
57. In this respect, an internal auction differs from the familiar "highest bidder" auction that culminates in a consensual trade between the highest bidder and a third party. In these traditional auctions, participation is consensual in the sense that one does not have to bid; only those who participate and win pay proceeds to a third party, producing a result similar to a bargain freely entered into between them. But this case forms only a small class of possible auction regimes. For example, in third party auctions where the penultimate bidder must also pay, the parties may not be able to walk away so easily once the bidding starts. See, e.g., supra note 31 (discussing "war of attrition" auction).
58. See WILLIAM M. LANDES & RICHARD A. POSNER, THE ECONOMIC STRUCTURE OF TORT LAW 31, 36, 42-44 (1987); RICHARD A. POSNER, ECONOMIC ANALYSIS OF LAW 70 (4th ed. 1992).
59. See WILLIAM M. LANDES & RICHARD A. POSNER, THE ECONOMIC STRUCTURE OF TORT LAW 31, 36, 42-44 (1987); RICHARD A. POSNER, ECONOMIC ANALYSIS OF LAW 70 (4th ed. 1992).
60. It is certainly possible to construct examples in which property rules produce better bargaining. But there are no a priori reasons to think that property rules facilitate trade when transaction costs are low.
61. Under the privilege of necessity, a defendant is permitted to commit an intentional tort to another's rights in property or realty to protect a more valuable interest in property or an interest in bodily security or life. See RESTATEMENT (SECOND) OF TORTS §§ 262, 263 & cmt. d (1965). Where the more valuable interest belongs to a large number of persons, for example, where a city must be saved from a fire, the privilege is one of public necessity, and the defendant owes no compensation. See id. § 262 & cmt. d. However, where the more valuable interest belongs only to the defendant or a small number of persons, the privilege is classified as a case of private necessity, and the defendant must still compensate the plaintiff for the harm caused by the invasion. See id. § 263(2) & cmt. e. Because compensation is owed, the privilege is said to be incomplete. However, because the defendant has a privilege, the plaintiff must pay for the damages caused by any self-help she undertakes to avoid the taking. See id. § 263 cmt. b; see also Ploof v. Putnam, 71 A. 188 (Vt. 1908).
62. 124 N.W. 221 (Minn. 1910).
63. See id. at 222.
64. Vincent's discussion of Ploof v. Putnam makes clear that the shipowner's option to take can itself be retaken if damages are paid: 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. Vincent, 124 N.W. at 222. The shipowner's option - a liability rule - is itself protected by a liability rule.
65. Hanson and Stowe refer to the Vincent standard as a "two-sided" liability rule. Jon Hanson & Matt Stowe, Lecture Notes, Torts, Harvard Law School (Fall 1996) (on file with the Yale Law Journal).
66. We emphasize this dual cost because readers are likely to imagine that the total cost of the dock owner's action is the payment of damages. It is important to account for these opportunity costs - foregoing damages created by the other party's previous taking - if we wish to understand how much exercising an option really costs an actor.
67. See Robert C. Ellickson, Alternatives to Zoning: Covenants, Nuisance Rules, and Fines as Land Use Controls, 40 U. CHI. L. REV. 681 (1973). In fact, Ellickson, Hanson, and Stowe, to our knowledge, are the only people who have seriously analyzed the potential utility of higher-order liability rules. In 1980, Mitch Polinsky saw that the law could give both polluters and pollutees a liability option to change the initial amount of legally permissible pollution. See A. Mitchell Polinsky, Resolving Nuisance Disputes: The Simple Economics of Injunctive and Damage Remedies, 32 STAN. L. REV. 1075, 1086-88 (1980). Polinsky opined that this type of regime "has not to my knowledge been considered by legal commentators or the courts. Since this remedy turns out to be unhelpful in most of the situations examined in this article, I will hereafter ignore it." Id. While Polinsky's article included a pathbreaking analysis of first-order liability rules, he never addressed the sequence in which second-order taking options might be exercised. See also Morris, supra note 4, at 822, 891-93 (recognizing possible usefulness of second-order liability rules, but not pursuing question of when these rules might be efficient).
68. See Robert C. Ellickson, Alternatives to Zoning: Covenants, Nuisance Rules, and Fines as Land Use Controls, 40 U. CHI. L. REV. 681 (1973). In fact, Ellickson, Hanson, and Stowe, to our knowledge, are the only people who have seriously analyzed the potential utility of higher-order liability rules. In 1980, Mitch Polinsky saw that the law could give both polluters and pollutees a liability option to change the initial amount of legally permissible pollution. See A. Mitchell Polinsky, Resolving Nuisance Disputes: The Simple Economics of Injunctive and Damage Remedies, 32 STAN. L. REV. 1075, 1086-88 (1980). Polinsky opined that this type of regime "has not to my knowledge been considered by legal commentators or the courts. Since this remedy turns out to be unhelpful in most of the situations examined in this article, I will hereafter ignore it." Id. While Polinsky's article included a pathbreaking analysis of first-order liability rules, he never addressed the sequence in which second-order taking options might be exercised. See also Morris, supra note 4, at 822, 891-93 (recognizing possible usefulness of second-order liability rules, but not pursuing question of when these rules might be efficient).
69. See Ellickson, supra note 45, at 748. Ellickson described this proposal as a combination of two different types of entitlement regimes originally offered by Calabresi and Melamed. See id. at 738. Calabresi and Melamed's "Rule 2" gives the polluter an option to pollute and pay damages, while their "Rule 4" gives the pollutee an option to enjoin pollution by paying damages to the polluter. See Calabresi & Melamed, supra note 2, at 1115-24.
70. In contrast, the "purchased injunction" featured in the famous case of Spur Industries v. Del E. Webb Development Co., 494 P.2d 700 (Ariz. 1972), represents a first-order liability rule. The polluter, in this case the owner of a feed lot, has the original entitlement to pollute. However, this entitlement is only protected by a liability rule. The neighbors have the option to stop pollution by paying damages and purchasing an injunction. Their taking is then protected by a property rule in the form of that injunction. See id. at 705-08. A mortgagor's right of redemption provides yet another example of a second-order rule. Statutes in roughly half of the states give a mortgagor the option to buy back property after a foreclosure sale, by paying the foreclosure sale purchaser the foreclosure sale price. See Michael H. Schill, An Economic Analysis of Mortgagor Protection Laws, 77 VA. L. REV. 489, 495 (1991). The foreclosure sale is often an explicit auction - harnessing the private information of third parties - which allows a nonconsensual taking of the property from the mortgagor See id. at 493. The statutory right of redemption, however, gives the mortgagor a take-back option, which allows the mortgagor to signal a higher (or equivalent) valuation of the property. The right of redemption might be viewed as a way to harness public and private information about the property's value, especially if temporary illiquidity prevents a mortgagor from signalling a high valuation at the time of the foreclosure sale.
71. See supra note 35.
72. See infra Section II.D.
73. The assumption that only two parties are affected obviates the multiple takers problem. See supra text accompanying note 16. If it is common knowledge that no one else in society cares about whether the factory pollutes, then the law might limit the reciprocal taking options to the interested parties. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1084.
74. This hypothetical is not as unrealistic as it might appear. It is strikingly similar to the facts of Copart Industries v. Consolidated Edison Co., 362 N.E.2d 968 (N.Y. 1977): [On a portion of the former Brooklyn Navy Yard, the plaintiff, Copart] conducted a storage and new car preparation business . . . catering to automobile dealers in the metropolitan area of New York City. Adjacent to the navy yard was [defendant Con Edison's] Hudson Avenue plant, engaged in the production of steam and electricity since about 1926. . . . Based on allegations that noxious emissions from defendant's nearby [smoke]stacks caused damage to the exterior of autos stored for its customers such as to require many to be repainted, that reports were received in early 1971 from patrons of paint discoloration and pitting, and that dealers served by plaintiff terminated their business by early May, plaintiff contends that because of said emissions it was caused to cease doing business on May 28, 1971. Id. at 969-70. Copart nicely illustrates the example of a nuisance that primarily affects only one other company; moreover, it is also a case where the legal decision largely determines whether the car preparation business or the power plant continues to operate.
75. In our model, each firm's "valuation" of the entitlement is the lost profits at stake if it cannot operate because it fails to control the decision regarding whether there will be pollution. Thus, a firm's "value" is its willingness to pay for an entitlement it does not currently possess. There may be a difference between this "offering price" and a firm's "asking price" - the price it would accept to surrender an entitlement it owns - because of endowment and wealth effects. Endowment effects are produced by the psychological tendency to value an entitlement more when we already possess it. See Mark Kelman, Consumption Theory, Production Theory, and Ideology in the Coase Theorem, 52 S. CAL. L. REV. 669, 673 (1979). Wealth effects are produced by budget constraints on our ability to pay: We may ask more to surrender an entitlement we own than we could offer to purchase it. See Duncan Kennedy, Cost-Benefit Analysis of Entitlement Problems: A Critique, 33 STAN. L. REV. 387, 401 (1981). In auction settings, however, only offering prices count, because each party bids for an entitlement whose ultimate ownership is in doubt. And because first-and higher-order liability rules are similar to auctions, only willingness to pay will determine whether a firm takes nonconsensually: At each round the parties decide whether or not to take based on their willingness to pay the extra damages. (A symmetrical effect occurs with descending auctions using put options as discussed infra text accompanying notes 90-91; these auctions compare the parties' willingness to accept money in return for surrendering the entitlement (i.e., their asking prices).) First-and higher-order liability rules might tend to mitigate endowment effects, because initial possession does not confer security from nonconsensual taking - initial entitlements are held subject to another person's option. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1101-02. In any event, we assume for purposes of our discussion that offering and asking prices do not differ significantly.
76. In our model, each firm's "valuation" of the entitlement is the lost profits at stake if it cannot operate because it fails to control the decision regarding whether there will be pollution. Thus, a firm's "value" is its willingness to pay for an entitlement it does not currently possess. There may be a difference between this "offering price" and a firm's "asking price" - the price it would accept to surrender an entitlement it owns - because of endowment and wealth effects. Endowment effects are produced by the psychological tendency to value an entitlement more when we already possess it. See Mark Kelman, Consumption Theory, Production Theory, and Ideology in the Coase Theorem, 52 S. CAL. L. REV. 669, 673 (1979). Wealth effects are produced by budget constraints on our ability to pay: We may ask more to surrender an entitlement we own than we could offer to purchase it. See Duncan Kennedy, Cost-Benefit Analysis of Entitlement Problems: A Critique, 33 STAN. L. REV. 387, 401 (1981). In auction settings, however, only offering prices count, because each party bids for an entitlement whose ultimate ownership is in doubt. And because first-and higher-order liability rules are similar to auctions, only willingness to pay will determine whether a firm takes nonconsensually: At each round the parties decide whether or not to take based on their willingness to pay the extra damages. (A symmetrical effect occurs with descending auctions using put options as discussed infra text accompanying notes 90-91; these auctions compare the parties' willingness to accept money in return for surrendering the entitlement (i.e., their asking prices).) First-and higher-order liability rules might tend to mitigate endowment effects, because initial possession does not confer security from nonconsensual taking - initial entitlements are held subject to another person's option. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1101-02. In any event, we assume for purposes of our discussion that offering and asking prices do not differ significantly.
77. In our model, each firm's "valuation" of the entitlement is the lost profits at stake if it cannot operate because it fails to control the decision regarding whether there will be pollution. Thus, a firm's "value" is its willingness to pay for an entitlement it does not currently possess. There may be a difference between this "offering price" and a firm's "asking price" - the price it would accept to surrender an entitlement it owns - because of endowment and wealth effects. Endowment effects are produced by the psychological tendency to value an entitlement more when we already possess it. See Mark Kelman, Consumption Theory, Production Theory, and Ideology in the Coase Theorem, 52 S. CAL. L. REV. 669, 673 (1979). Wealth effects are produced by budget constraints on our ability to pay: We may ask more to surrender an entitlement we own than we could offer to purchase it. See Duncan Kennedy, Cost-Benefit Analysis of Entitlement Problems: A Critique, 33 STAN. L. REV. 387, 401 (1981). In auction settings, however, only offering prices count, because each party bids for an entitlement whose ultimate ownership is in doubt. And because first-and higher-order liability rules are similar to auctions, only willingness to pay will determine whether a firm takes nonconsensually: At each round the parties decide whether or not to take based on their willingness to pay the extra damages. (A symmetrical effect occurs with descending auctions using put options as discussed infra text accompanying notes 90-91; these auctions compare the parties' willingness to accept money in return for surrendering the entitlement (i.e., their asking prices).) First-and higher-order liability rules might tend to mitigate endowment effects, because initial possession does not confer security from nonconsensual taking - initial entitlements are held subject to another person's option. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1101-02. In any event, we assume for purposes of our discussion that offering and asking prices do not differ significantly.
78. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1048; Jennifer Gerarda Brown & Ian Ayres, Economic Rationales for Mediation, 80 VA. L. REV. 323, 336 (1994); Kalyan Chatterjee & William Samuelson, Bargaining Under Incomplete Information, 31 OPERATIONS RES. 835, 837-38 (1983); Peter C. Cramton, Strategic Delay in Bargaining with Two-Sided Uncertainty, 59 REV. ECON. STUD. 205, 208 (1992); Kaplow & Shavell, Economic Analysis, supra note 4; Kaplow & Shavell, Reply, supra note 4, at 227; Roger B. Myerson, Analysis of Two Bargaining Problems with Incomplete Information, in GAME-THEORETIC MODELS OF BARGAINING 115, 116-30 (Alvin E. Roth ed., 1985) [hereinafter GAME-THEORETIC MODELS]; Roger B. Myerson & Mark A. Satterthwaite, Efficient Mechanisms for Bilateral Trading, 29 J. ECON. THEORY 265, 267 (1983).
79. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1048; Jennifer Gerarda Brown & Ian Ayres, Economic Rationales for Mediation, 80 VA. L. REV. 323, 336 (1994); Kalyan Chatterjee & William Samuelson, Bargaining Under Incomplete Information, 31 OPERATIONS RES. 835, 837-38 (1983); Peter C. Cramton, Strategic Delay in Bargaining with Two-Sided Uncertainty, 59 REV. ECON. STUD. 205, 208 (1992); Kaplow & Shavell, Economic Analysis, supra note 4; Kaplow & Shavell, Reply, supra note 4, at 227; Roger B. Myerson, Analysis of Two Bargaining Problems with Incomplete Information, in GAME-THEORETIC MODELS OF BARGAINING 115, 116-30 (Alvin E. Roth ed., 1985) [hereinafter GAME-THEORETIC MODELS]; Roger B. Myerson & Mark A. Satterthwaite, Efficient Mechanisms for Bilateral Trading, 29 J. ECON. THEORY 265, 267 (1983).
80. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1048; Jennifer Gerarda Brown & Ian Ayres, Economic Rationales for Mediation, 80 VA. L. REV. 323, 336 (1994); Kalyan Chatterjee & William Samuelson, Bargaining Under Incomplete Information, 31 OPERATIONS RES. 835, 837-38 (1983); Peter C. Cramton, Strategic Delay in Bargaining with Two-Sided Uncertainty, 59 REV. ECON. STUD. 205, 208 (1992); Kaplow & Shavell, Economic Analysis, supra note 4; Kaplow & Shavell, Reply, supra note 4, at 227; Roger B. Myerson, Analysis of Two Bargaining Problems with Incomplete Information, in GAME-THEORETIC MODELS OF BARGAINING 115, 116-30 (Alvin E. Roth ed., 1985) [hereinafter GAME-THEORETIC MODELS]; Roger B. Myerson & Mark A. Satterthwaite, Efficient Mechanisms for Bilateral Trading, 29 J. ECON. THEORY 265, 267 (1983).
81. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1048; Jennifer Gerarda Brown & Ian Ayres, Economic Rationales for Mediation, 80 VA. L. REV. 323, 336 (1994); Kalyan Chatterjee & William Samuelson, Bargaining Under Incomplete Information, 31 OPERATIONS RES. 835, 837-38 (1983); Peter C. Cramton, Strategic Delay in Bargaining with Two-Sided Uncertainty, 59 REV. ECON. STUD. 205, 208 (1992); Kaplow & Shavell, Economic Analysis, supra note 4; Kaplow & Shavell, Reply, supra note 4, at 227; Roger B. Myerson, Analysis of Two Bargaining Problems with Incomplete Information, in GAME-THEORETIC MODELS OF BARGAINING 115, 116-30 (Alvin E. Roth ed., 1985) [hereinafter GAME-THEORETIC MODELS]; Roger B. Myerson & Mark A. Satterthwaite, Efficient Mechanisms for Bilateral Trading, 29 J. ECON. THEORY 265, 267 (1983).
82. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1048; Jennifer Gerarda Brown & Ian Ayres, Economic Rationales for Mediation, 80 VA. L. REV. 323, 336 (1994); Kalyan Chatterjee & William Samuelson, Bargaining Under Incomplete Information, 31 OPERATIONS RES. 835, 837-38 (1983); Peter C. Cramton, Strategic Delay in Bargaining with Two-Sided Uncertainty, 59 REV. ECON. STUD. 205, 208 (1992); Kaplow & Shavell, Economic Analysis, supra note 4; Kaplow & Shavell, Reply, supra note 4, at 227; Roger B. Myerson, Analysis of Two Bargaining Problems with Incomplete Information, in GAME-THEORETIC MODELS OF BARGAINING 115, 116-30 (Alvin E. Roth ed., 1985) [hereinafter GAME-THEORETIC MODELS]; Roger B. Myerson & Mark A. Satterthwaite, Efficient Mechanisms for Bilateral Trading, 29 J. ECON. THEORY 265, 267 (1983).
83. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1048; Jennifer Gerarda Brown & Ian Ayres, Economic Rationales for Mediation, 80 VA. L. REV. 323, 336 (1994); Kalyan Chatterjee & William Samuelson, Bargaining Under Incomplete Information, 31 OPERATIONS RES. 835, 837-38 (1983); Peter C. Cramton, Strategic Delay in Bargaining with Two-Sided Uncertainty, 59 REV. ECON. STUD. 205, 208 (1992); Kaplow & Shavell, Economic Analysis, supra note 4; Kaplow & Shavell, Reply, supra note 4, at 227; Roger B. Myerson, Analysis of Two Bargaining Problems with Incomplete Information, in GAME-THEORETIC MODELS OF BARGAINING 115, 116-30 (Alvin E. Roth ed., 1985) [hereinafter GAME-THEORETIC MODELS]; Roger B. Myerson & Mark A. Satterthwaite, Efficient Mechanisms for Bilateral Trading, 29 J. ECON. THEORY 265, 267 (1983).
84. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1048; Jennifer Gerarda Brown & Ian Ayres, Economic Rationales for Mediation, 80 VA. L. REV. 323, 336 (1994); Kalyan Chatterjee & William Samuelson, Bargaining Under Incomplete Information, 31 OPERATIONS RES. 835, 837-38 (1983); Peter C. Cramton, Strategic Delay in Bargaining with Two-Sided Uncertainty, 59 REV. ECON. STUD. 205, 208 (1992); Kaplow & Shavell, Economic Analysis, supra note 4; Kaplow & Shavell, Reply, supra note 4, at 227; Roger B. Myerson, Analysis of Two Bargaining Problems with Incomplete Information, in GAME-THEORETIC MODELS OF BARGAINING 115, 116-30 (Alvin E. Roth ed., 1985) [hereinafter GAME-THEORETIC MODELS]; Roger B. Myerson & Mark A. Satterthwaite, Efficient Mechanisms for Bilateral Trading, 29 J. ECON. THEORY 265, 267 (1983).
85. See, e.g., Ayres & Talley, Solomonic Bargaining, supra note 3, at 1048; Jennifer Gerarda Brown & Ian Ayres, Economic Rationales for Mediation, 80 VA. L. REV. 323, 336 (1994); Kalyan Chatterjee & William Samuelson, Bargaining Under Incomplete Information, 31 OPERATIONS RES. 835, 837-38 (1983); Peter C. Cramton, Strategic Delay in Bargaining with Two-Sided Uncertainty, 59 REV. ECON. STUD. 205, 208 (1992); Kaplow & Shavell, Economic Analysis, supra note 4; Kaplow & Shavell, Reply, supra note 4, at 227; Roger B. Myerson, Analysis of Two Bargaining Problems with Incomplete Information, in GAME-THEORETIC MODELS OF BARGAINING 115, 116-30 (Alvin E. Roth ed., 1985) [hereinafter GAME-THEORETIC MODELS]; Roger B. Myerson & Mark A. Satterthwaite, Efficient Mechanisms for Bilateral Trading, 29 J. ECON. THEORY 265, 267 (1983).
86. Our core results do not depend, however, on the uniform distribution assumption. If the firms' profits were normally distributed (with a Gaussian distribution), second-and higher-order liability rules would still produce more efficient equilibria. However, the ensuing auction would not have uniform minimum bidding increments.
87. If the government could determine the relative value of pollution, it might simply allocate the entitlement to the business with the higher valuation.
88. Even if damages are determined ex post, the parties might be able to predict the exercise prices ex ante by applying the applicable damage formula. See Ellickson, supra note 45, at 744 ("If the collective rules were comprehensible, the parties could calculate the damages the plaintiff would collect in litigation from the defendant and the price the plaintiff would have to pay for an injunction."). Even if the government could determine the firms' precise valuations after the fact, it might not want to "tailor" damages based on this more precise information. Where information is asymmetric, tailoring damages to predictions of the firms' actual valuations can encourage inefficient strategic behavior by the parties. Because more now turns on the firms' private information, they may engage in tactics to disguise their real valuations. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1065; Johnston, supra note 4; Kathryn E. Spier, Settlement Bargaining and the Design of Damage Awards, 10 J.L. ECON. & ORG. 84 (1994).
89. Even if damages are determined ex post, the parties might be able to predict the exercise prices ex ante by applying the applicable damage formula. See Ellickson, supra note 45, at 744 ("If the collective rules were comprehensible, the parties could calculate the damages the plaintiff would collect in litigation from the defendant and the price the plaintiff would have to pay for an injunction."). Even if the government could determine the firms' precise valuations after the fact, it might not want to "tailor" damages based on this more precise information. Where information is asymmetric, tailoring damages to predictions of the firms' actual valuations can encourage inefficient strategic behavior by the parties. Because
90. m, both sides can profit from a pollution agreement whereby the mill obtains the right to pollute and makes a payment P to the fishery . . . . The difficulty is that each value is known only to the player himself. William Samuelson, A Comment on the Coase Theorem, in GAME-THEORETIC MODELS, supra note 53, at 321, 326.
91. Because in this example the factory and laundry have the same expected value, the identity of the initial entitlement holder does not affect efficiency.
92. Although $50 of the factory's $75 profits go to the laundry as damages, the firms' joint profit is not affected by this transfer between them.
93. Kaplow & Shavell, Economic Analysis, supra note 4, at 725 (emphasis omitted).
94. Referring to this as a "take-back" option is a little misleading, because readers may mistakenly infer that the factory immediately begins to pollute before the laundry can exercise its right to "take back." But as discussed supra note 18, the factory would not actually begin to pollute until after the laundry had been given a chance to pay to maintain the pollution injunction.
95. As an accounting matter, it is important to decide whether the factory will exercise its option by actually paying the $50 or merely offering to pay if and when the laundry decides not to take back. Throughout this Essay, we will assume that the factory actually pays the first-order exercise price and that the laundry then has the option to retain the entitlement by giving back the $50 plus some additional amount. Whether the factory actually pays or merely makes a firm offer does not affect the model, but making this choice and sticking to it will avoid later confusion. Consider a second-order regime in which the factory has a first-stage option to actually pay $50, followed by the laundry's option to pay $75 to prevent pollution. This is mathematically identical to a second-order regime in which the factory makes a firm offer to pay $50 followed by the laundry's option to refuse this offer and pay $25 to prevent pollution. In the first case, the laundry gets $50 and exercises its option by paying out $75. In the second case, the laundry exercises its option by forgoing the $50 it could have pocketed if it had not exercised the option and paying an additional $25 out-of-pocket. The practical result is the same in each case. In many contexts - such as the situation in Vincent v. Lake Erie - the initial taker will not actually pay at the time of taking, but will expose itself to damages by taking. We adopt the alternative "pay as you take" assumption to highlight the increasing auction bids and the implicit opportunity costs of each taking. However, for interested readers, we will occasionally mention in the footnotes how an alternative Vincent-like auction might be implemented.
96. As discussed supra note 62, this "pay as you take" regime is equivalent to one in which the factory merely offered to pay $50 and the laundry would have to reject the offer and pay $25 to maintain the pollution injunction.
97. The laundry's second-order taking option, however, is protected by a property rule: We assume that the consequences of the factory trying to pollute after the laundry takes back are so dire (i.e., greater than $100) that no factory would trespass on this right.
98. We call this second-order rule "naive" because it does not take into account all of the possible strategic considerations of the parties. See infra Section II.B. When we consider the various ways that the parties can act strategically, the efficiency of the regime is improved and we arrive at the "optimal" second-order rule.
99. As we emphasize below, however, see infra text accompanying note 77, there is an even more efficient way to structure a second-order rule.
100. The factory's expected payoff can be calculated by multiplying the payoff for a particular outcome by the probability that the outcome occurs. If the factory does not take, its payoff is zero. However, 58.33% of the time the factory will take (because, as we shall see shortly, it makes sense for strategic reasons for all factories with valuations greater than $41.67 to take). The most that any factory values the entitlement is $100, so the average valuation of those factories that take is $(100 + 41.67) ÷ 2 or approximately $70.84. If the factory takes, there is a 25% chance that the laundry will take back. The expected payoff to the factory if the laundry fails to take back (which occurs 75% of the time) is $20.84: This number is the expected valuation of those factories that take ($70.84) minus the $50 cost of taking. The expected payoff to a factory if the laundry takes back is the $25 it receives from the laundry. Combining these numbers yields the expression for a factory's expected payoff: .5833 × [(.75) × $20.84 × (.25) × $25] = $12.76. The laundry's expected payoff and the expected joint payoff can be derived analogously.
101. Ellickson developed the idea of purchased injunctions. See Ellickson, supra note 45, at 738-48.
102. As shown in Table 1, the naive rule induces the factory to take 58.33% of the time (i.e., when its valuation is greater than $41.67) and 25% of the laundries then take back (i.e., when their valuation is greater than $75). Accordingly, the probability of two takings is 14.6% (.5833 × .75).
103. See, e.g., Kaplow & Shavell, Reply, supra note 4, at 222-24 (considering bargaining difficulty but not changing exercise prices). Incidentally, this is the problem in the movie THE MALTESE FALCON, supra note 16, and it leads to predictably destructive results.
104. See, e.g., Kaplow & Shavell, Reply, supra note 4, at 222-24 (considering bargaining difficulty but not changing exercise prices). Incidentally, this is the problem in the movie THE MALTESE FALCON, supra note 16, and it leads to predictably destructive results.
105. See supra text accompanying notes 62-64.
106. A factory with a $41.67 valuation is indifferent between taking and not taking. Not taking produces a certain payoff of $0, which equals its expected payoff from taking (.75) × ($41.67 - $50) + (.25) × ($25).
107. i+l).
108. That is because factories with valuations as low as $41.67 and as high as $100 will take. The expected valuation of this group of factories is $70.84.
109. Note that in this case we face no problem of including in our expected value the valuations of factories who will take back after the laundry takes. By assumption, in a second-order regime all second-order takings are dispositive. Because a second-order liability rule is protected by a property rule, factories will not have a (practical) third-order option to retake.
110. The text has attempted to describe the intuitions behind optimally structured liability rules. Although the competing considerations seem complicated, it is actually relatively straightforward to express the joint payoffs mathematically in terms of the first-and second-order exercise prices. One finds the optimum in the usual way, by setting the first-order conditions equal to zero and solving for the unknown exercise price. We verified our calculations with Mathematica.
111. Once again, we could structure the rule so that factories did not have to pay $44.44 in damages initially but merely had to make a firm offer to pay if the laundry declined to take back and pay damages. In such a "take now and pay later" regime, the laundry's second-stage damages would be $22.22. Only laundries with valuations greater than $66.66 would take back, because they would be foregoing the factories' promised payment of $44.44 and committing themselves to pay $22.22.
112. However, the expected payoff to the laundry actually decreases when we move from the naive to the optimal second-order regime, from $51.82 to $50. Both the naive and optimal second-order rules are Pareto superior to the optimal first-order rule. We call the second-order rule "optimal" because it maximizes the panics' joint payoffs and hence is Kaldor-Hicks superior to the naive second-order rule. However, neither is Pareto superior to the other. The Pareto superiority of the optimal second-order rule over the optimal first-order rule can be generalized: Higher-order optimal rules are Pareto superior to all lower-order optimal rules.
113. li=100[i/3(N+1)], ∀ even i
114. The uniformity of the bid increments is an artifact of our uniform distribution assumption. Other distributions of private valuations would produce ascending auctions as well, but the minimum bid increments would not be constant.
115. i
116. 2 ($22.22) is two-thirds the difference between the first and second stage cutoff prices ($33.33).
117. Notice, however, that the laundry's expected profit remains constant at $50 - so that all of the expected efficiency enhancement accrues to the factory. Higher-order liability rules still Pareto dominate lower-order regimes, but only in the weak sense. In the limit, the type-specific expected payoffs for the laundry and the factory are, respectively, formula presented
118. Using L'Hôpital's rule, it is straightforward to show that the limit as N → ∞ of the closed form expression for expected joint payoffs in Table 1 is $66.66.
119. These two results are based on ex ante analysis of the players' expected payoffs - assessed before the laundry and the factory acquire their private information. From an interim perspective - i.e., once the firms have learned their valuations but before they consensually or nonconsensually transfer the entitlement - moving from a lower-to a higher-order liability rule may increase the risk or reduce the expected payoffs for players with particular valuations. The differences between ex ante and interim analysis are discussed more fully in Ayres & Talley, Solomonic Bargaining, supra note 3, and in Brown & Ayres, supra note 53.
120. F) = $277.78 As shown in Table 4, the variance of the laundry's expected payoff decreases monotonically in N, moving asymptotically to $277.78, and the variance of the factory's expected payoff increases monotonically in N, moving asymptotically as well to $277.78.
121. The variance of the laundry's expected payoff under a property rule is $833.33, but only $416.67 under a first-order liability rule. Note that a descending auction compares the parties' willingness to accept payment in return for surrender of the entitlement, whereas the more familiar ascending auction compares their willingness to pay for the entitlement. See supra note 52.
122. See supra Table 4.
123. For example, a property rule eliminates the factory's risk completely, but only by eliminating the chance of any positive payoff.
124. Madeline Morris was the first to point out the possibility of such first-order put liability rules. See Morris, supra note 4, at 851-56.
125. The variance of expected payoffs for the laundry and factory are reversed from the variances reported in Table 4.
126. See Krier & Schwab, supra note 4, at 471.
127. Kaplow and Shavell note that, as Samuelson acknowledges, auctions where the winning bidder pays the losing bidder are often not useful because they would require the initial holder of an entitlement to share too much of the auction proceeds with others. Holders of entitlements might therefore not agree to participate in the auctions (and, if the law required participation, incentives to acquire and improve property would be adversely affected). Kaplow & Shavell, Economic Analysis, supra note 4, at 734 n.66 (citing Samuelson, supra note 57, at 336-37).
128. If the investments are sequential, we might want to give the first investor the entitlement subject to the second investor's call option so that each firm captures the marginal benefit of its investment.
129. Samuelson, for example, suggests that preassigning an entitlement to a particular bidder can impede efficient allocation. See Samuelson, supra note 57, at 325. In contrast, he describes his "rights bidding" mechanism as making the bidders "joint owners of the right" with the opportunity to "share equally" in its value. Id. at 331.
130. This result contrasts with other attempts to improve efficiency by dividing an entitlement among bidders: "Attempts to remedy adverse selection often exacerbate moral hazard. . . . Solomonic entitlements may give bargainers suboptimal prebargaining incentives to make value-enhancing investments." Ayres & Talley, Solomonic Bargaining, supra note 3, at 1085 (citation omitted).
131. Samuelson has proposed a bidding mechanism to allocate entitlements that also has "no seller to collect the proceeds; instead, the proceeds are returned to the parties themselves." Samuelson, supra note 57, at 331. Under what he terms "split-the-difference bidding," the firms would submit sealed bids and the high bidder would receive the entitlement and pay the low bidder one-half the average bid. Samuelson shows that this mechanism can produce efficient allocations, see id. at 331-35, just as we find an Nth-order liability rule would. The potential efficiency of "internal" auctions - where the proceeds of the auctions are shared internally among the bidders - is formalized in the seminal article by Peter Cramton et al., Dissolving a Partnership Efficiently, 55 ECONOMETRICA 615 (1987).
132. Takings costs might be: (i) fixed or variable; and (ii) initially borne by the taking firm, the non-taking firm, or by the general public. The prospect of takings might also induce a variety of ancillary inefficiencies - such as underinvestment in creating or developing the original entitlement - which might be deemed as a fixed cost of a liability regime. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1083-84 (discussing three costs of divided entitlement regimes).
133. If the taking costs of administering a liability rule regime are fixed, then the exercise prices may not be a smoothly increasing function of these costs, but the second result will still hold: Lower order liability rules and/or property rules will become more efficient as these costs become sufficiently high.
134. The optimal exercise prices (not depicted in Table 5) are: TABLE 6. EXERCISE PRICES FOR OPTIMAL SECOND-ORDER LIABILITY RULE AS A FUNCTION OF TAKINGS COSTS (IN $) COST PER TAKING OPTIMAL OPTIMAL FIRST-STAGE SECOND-STAGE EXERCISE PRICE EXERCISE PRICE 0 44.44 66.67 8 48.82 76.61 10 49.33 78.41 12 49.77 80.03 14 49.95 81.54 16 49.99 82.99 Note that the second-order exercise prices plus the takings cost equal the second-order cutoff strategies.
135. The lower-bound estimate of $7.14 is a numeric estimate, because we were not able to calculate a closed-form expression for this third-order cutoff.
136. The intuition is straightforward for why property rules are efficient when taking costs are greater than $50. Under a first-order rule, factories internalize all of the taking costs and the optimal exercise price remains $50 - so factories internalizing the cost of taking will only take when their value is greater than the taking cost plus the exercise price of $50. When the taking cost is less than $50, some range of factories with high valuations will still find it valuable to take and will increase the expected joint payoffs. The choice of optimal exercise prices under a higher-order regime, however, is more complicated. The factory, in making its first taking decision, does not internalize all the costs of its decision, because it might provoke a laundry to take back and consume more resources. Optimally chosen exercise prices try to dampen the firms' incentives to take excessively.
137. See Ayres & Talley, Solomonic Bargaining, supra note 3. But see Kaplow & Shavell, Reply, supra note 4 (conceding that Ayres & Talley provide example with low transaction costs where first-order liability rule is more efficient than property rule, but arguing that liability rule's greater efficiency stems from nonconsensual headstart which persists when bargaining is allowed and not because liability rule "facilitate[s] bargaining"); Ayres & Talley, Distinguishing, supra note 3 (conceding that their initial example does not adequately distinguish between consensual and nonconsensual advantages of liability rules, but providing example where first-order liability rule has no nonconsensual headstart, but becomes more efficient than property rule when bargaining is allowed).
138. See Ayres & Talley, Solomonic Bargaining, supra note 3. But see Kaplow & Shavell, Reply, supra note 4 (conceding that Ayres & Talley provide example with low transaction costs where first-order liability rule is more efficient than property rule, but arguing that liability rule's greater efficiency stems from nonconsensual headstart which persists when bargaining is allowed and not because liability rule "facilitate[s] bargaining"); Ayres & Talley, Distinguishing, supra note 3 (conceding that their initial example does not adequately distinguish between consensual and nonconsensual advantages of liability rules, but providing example where first-order liability rule has no nonconsensual headstart, but becomes more efficient than property rule when bargaining is allowed).
139. See Ayres & Talley, Solomonic Bargaining, supra note 3. But see Kaplow & Shavell, Reply, supra note 4 (conceding that Ayres & Talley provide example with low transaction costs where first-order liability rule is more efficient than property rule, but arguing that liability rule's greater efficiency stems from nonconsensual headstart which persists when bargaining is allowed and not because liability rule "facilitate[s] bargaining"); Ayres & Talley, Distinguishing, supra note 3 (conceding that their initial example does not adequately distinguish between consensual and nonconsensual advantages of liability rules, but providing example where first-order liability rule has no nonconsensual headstart, but becomes more efficient than property rule when bargaining is allowed).
140. Ayres and Talley show, however, that there might be a class of laundries with intermediate values who would not make serious offers to enter into either type of trade. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1053-58.
141. While first-order liability rules induce different types of laundries to "separate" - i.e., to play different strategies that reveal their valuation - they often induce factories to "pool" - i.e., to play the same strategies that conceal their relative valuation. Ayres and Talley suggested that the self-partitioning effect was only likely to facilitate trade when the laundries' private information was the most significant constraint. See id. at 1059-60 ("By effectively forcing the [parties] to reveal information about their valuations, liability rules mitigate the inefficiencies of bargaining under private information."). The trade-facilitating effect is only a possibility. See Ayres & Talley, Distinguishing, supra note 3, at 240.
142. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1038.
143. See Triangle 1 in Figure 1. The laundry's selling both its entitlement and its take-back option for a price less than $44.44 might dominate the laundry's selling just its entitlement - because it discourages nigh-value laundries from strategically offering to sell in order to decrease the likelihood of a factory's taking. Specifically, laundries with valuations above $66.66 might offer to sell their entitlement for a low price - hoping that their offer will be rejected and that the factory (thinking that the laundry has a low value) will be less likely to take. Selling its take-back option makes it more expensive to engage in this behavior, because the high-value laundry cannot take back.
144. See Triangle 2 in Figure 1.
145. See Triangle 3 in Figure 1. The laundry's selling both the entitlement and the take-back option for a price greater than $44.44 is equivalent to the laundry's selling just its take-back option. If the laundry only sells its take-back option, its payoff will be $44.44 from the factory's nonconsensual taking plus whatever it earns from selling its take-back option (say $x). This transaction is equivalent to selling the entitlement and take-back option immediately for $44.44 + $x. The factory would like to stop low-value laundries from pooling with high-value laundries in accepting these offers, but the same incentives to pool occur in either case.
146. As discussed above, factories may strategically choose to take even when their valuation is below the first-order exercise price because they hope to profit if the laundry takes back. The factory's decision to act strategically turns crucially on its belief about the laundry's likelihood of taking back. If the factory is certain that the laundry's valuation is above $66.66, then all factories will take. If the factory is certain that the laundry's valuation is below $66.66, then only factories with valuations above $44.44 will take. Knowing this, laundries may choose to send false signals about their valuation. For example, a laundry with a low valuation might signal a high valuation by making an offer to buy the factory's option. This would increase the chance that the factory will take. The laundry hopes that the factory will reject the offer and take nonconsensually because it will then pay the laundry in damages more than the laundry valued the entitlement. Analogously, laundries that valued the entitlement greatly might be willing to make offers to sell their entitlement for less than $44.44. This would signal a low value and consequently reduce the chance that factories would take nonconsensually.
147. To put it another way, any offer from a factory to buy a laundry's take-back option credibly signals that the factory's valuation is greater than $66.66, while any offer to sell its taking option signals that the factory's valuation is less than $66.66. The factory has a third type of bargain available to it: It can offer to buy the laundry's entitlement and take-back option for less than $44.44. This offer does not, however, signal the factory's value. High-value factories might well try to pool with low-value factories to buy the laundry's entitlements on the cheap.
148. We can generalize this point: In any Nth-order liability rule, the party with the last or Nth option will be able to act strategically with respect to the exercise of this option. The party with the next to the last ((N-1)th) option will not, because the Nth taking is protected by a property rule. This removes the practical option to retake.
149. Serious offers to enter into the third type of trade (namely, to buy the laundry's entitlement and lake-back option for less than $44.44) do not, however, signal the factory's value. High-value factories might well try to pool with low-value factories to buy laundries' entitlements on the cheap.
150. See, e.g., supra note 110 and accompanying text.
151. For example, a factory with a high valuation might offer to buy a laundry's entitlement for less than $44.44. This type of trade could only be socially beneficial if a factory had a valuation below $33.33. Nevertheless, a factory with a high valuation would pursue it not to create value but to transfer value.
152. The generic offering incentives of the firms either to separate (self-partition), to mimic behavior hoping for acceptance, or to mimic behavior hoping for rejection amount to the following for the three types of trade: (i) The laundry might sell its entitlement (and its take-back option) for a price less than $44.44. Factories: Factories with high and intermediate valuations (greater than $33.33) might mimic factories with low valuations (less than $33.33) by offering to buy the laundry's entitlement; these factories hope for acceptance. Laundries: Laundries with high and intermediate valuations (greater than $33.33) would never accept an offer to sell for less than $44.44, but might mimic offers made by laundries with low valuations (less than $33.33) to reduce the chance that the factory will take; these laundries hope for rejection. (ii) The laundry could buy the factory's taking option. Factories: Factories with low valuations (less than $33.33) might mimic factories with intermediate valuations (between $33.33 and $66.66) by offering or accepting offers to sell their take-back option; these factories hope for acceptance. Factories with high valuations (greater than $66.66) will self-partition by refusing to offer (or accept an offer) to sell their take-back option. Laundries: Laundries with high valuations (greater than $66.66) might mimic the behavior of laundries with intermediate valuations (between $33.33 and $66.66) by trying to buy factories' taking options; these laundries hope for acceptance. Laundries with low valuations (less than $33.33) might mimic laundries with intermediate valuations (between $33.33 and $66.66) by offering to purchase the take-back option to increase the chance that factories will take; these laundries hope for rejection. (iii) The laundry could sell its entitlement and its take-back option for a price greater than $44.44. Factories: Only factories with high valuations (greater than $66.66) would self-partition by offering (or accepting an offer) to buy their take-back option. Laundries: Laundries with low and intermediate valuations (less than $66.66) would mimic the behavior of laundries with high valuations (greater than $66.66) by offering to sell their take-back option; these laundries hope for acceptance.
153. In game-theoretic terms, the participation constraints on any bargaining equilibrium ensure that the payoffs from trade will never be less than the payoffs when trade is not allowed.
154. After relaxing our initial assumption that takings are costless in Part II, we would have preferred to analyze bargaining in the shadow of costly nonconsensual takings. Unfortunately, solving such a model has proven so far to be beyond our analytic grasp.
155. A similar result has been shown for first-order liability rules. See Ayres & Talley, Distinguishing, supra note 3, at 242-51.
156. See supra text accompanying note 56.
157. On the other hand, it may be easier for juries to assess damages for events that have already occurred than to assess damages for events that did not actually occur. Moreover, while praising the general structure of Vincent as an example of a second-order liability rule, we are concerned that the measure of second-order damages will not account for the dock owner's opportunity cost, i.e., the damages the dock owner could have collected if it had not unmoored the ship. Failing to deduct first-order damages (the damage to the dock if the ship is moored) could artificially inflate the cost of retaking, thus turning the current Vincent rule into a first-order liability rule. If total second-order damages are too great, they may deter dock owners from exercising their second-order takings option (that is, unmooring the boat). For another context in which courts have failed to account properly for opportunity costs, see Ian Ayres, Analyzing Stock Lock-ups: Do Target Treasury Sales Foreclose or Facilitate Takeover Auctions?, 90 COLUM. L. REV. 682 (1990).
158. Ayres and Talley (and others) have shown that tailored damages can actually increase the obstacles for Coasean trade because more turns on the parties' private information about what the tailored damages will be. See supra note 56.
159. 1868 N.H. Laws, ch. 20, § 3 (set out in Head v. Amoskeag Mfg. Co., 113 U.S. 9, 10-11 (1885)); see also Head, 113 U.S. at 20 (relating history of statute).
160. Richard Epstein interpreted these statutory damages as ensuring a division of the surplus brought about by the forced exchange. See RICHARD A. EPSTEIN, TAKINGS: PRIVATE PROPERTY AND THE POWER OF EMINENT DOMAIN 174 (1985). We think that they are more consistent with Kaplow and Shavell's theory, described in the text.
161. To understand just a few of the complexities, imagine a multibidder ascending auction analogous to the optimal fourth-order liability rule described in Table 2. If one of the bidders takes at the third stage, whom would she pay?
162. "NIMBY" situations are collective action problems in which no party wants to absorb costs that would benefit all of the others, but each would like someone else to absorb these costs. The initials stand for "Not In My Back Yard."
163. See generally Michael O'Hare, "Not on My Block You Don't": Facility Siting and the Strategic Importance of Compensation, 25 PUB. POL'Y 407 (1977); Gerald R. Faulhaber & Daniel E. Ingberman, Markets vs. Governments: The Political Economy of NIMBY (1996) (unpublished manuscript, on file with authors).
164. See Samuelson, supra note 57, at 337.
165. For example, at one extreme, the law might force the winning bidders to pay their nominal bids to the losing bidder; at another extreme, the winning bidders would only need to contribute pro rata to paying the losing bidder's bid.
166. See MICHAEL O'HARE ET AL., FACILITY SITING AND PUBLIC OPPOSITION (1983); Lawrence S. Bacow & James R. Milkey, Overcoming Local Opposition to Hazardous Waste Facilities: The Massachusetts Approach, 6 HARV. ENVTL. L. REV. 265 (1982); Robert Cameron Mitchell & Richard T. Carson, Property Rights, Protest, and the Siting of Hazardous Waste Facilities, 76 AM. ECON. REV. 285 (1986).
167. See MICHAEL O'HARE ET AL., FACILITY SITING AND PUBLIC OPPOSITION (1983); Lawrence S. Bacow & James R. Milkey, Overcoming Local Opposition to Hazardous Waste Facilities: The Massachusetts Approach, 6 HARV. ENVTL. L. REV. 265 (1982); Robert Cameron Mitchell & Richard T. Carson, Property Rights, Protest, and the Siting of Hazardous Waste Facilities, 76 AM. ECON. REV. 285 (1986).
168. See MICHAEL O'HARE ET AL., FACILITY SITING AND PUBLIC OPPOSITION (1983); Lawrence S. Bacow & James R. Milkey, Overcoming Local Opposition to Hazardous Waste Facilities: The Massachusetts Approach, 6 HARV. ENVTL. L. REV. 265 (1982); Robert Cameron Mitchell & Richard T. Carson, Property Rights, Protest, and the Siting of Hazardous Waste Facilities, 76 AM. ECON. REV. 285 (1986).
169. This point has been recognized repeatedly in the literature. See, e.g., Anthony T. Kronman, Specific Performance, 45 U. CHI. L. REV. 351, 352 (1978); Thomas S. Ulen, The Efficiency of Specific Performance: Toward a Unified Theory of Contract Remedies, 83 MICH. L. REV. 341, 375-76 (1984).
170. This point has been recognized repeatedly in the literature. See, e.g., Anthony T. Kronman, Specific Performance, 45 U. CHI. L. REV. 351, 352 (1978); Thomas S. Ulen, The Efficiency of Specific Performance: Toward a Unified Theory of Contract Remedies, 83 MICH. L. REV. 341, 375-76 (1984).
171. Currently, the promisee has the option to "await performance" for a "commercially reasonable time." U.C.C. § 2-610 (1990).
172. See Ellickson, supra note 45, at 738-48.
173. Judges could implement this scheme by instructing a jury to determine ordinary expectation damages (without knowledge of the attempted modification), and then simply adding the enhancement to the jury's award.
174. See, e.g., Oliver Hart & John Moore, Incomplete Contracts and Renegotiation, 56 ECONOMETRICA 755 (1988); Thomas J. Miceli, Contract Modification When Litigating for Damages Is Costly, 15 INT'L REV. L. & ECON. 87 (1995); William P. Rogerson, Efficient Reliance and Damage Measures for Breach of Contract, 15 RAND J. ECON. 39 (1984); Steven Shavell, The Design of Contracts and Remedies for Breach, 99 Q.J. ECON. 121 (1984).
175. See, e.g., Oliver Hart & John Moore, Incomplete Contracts and Renegotiation, 56 ECONOMETRICA 755 (1988); Thomas J. Miceli, Contract Modification When Litigating for Damages Is Costly, 15 INT'L REV. L. & ECON. 87 (1995); William P. Rogerson, Efficient Reliance and Damage Measures for Breach of Contract, 15 RAND J. ECON. 39 (1984); Steven Shavell, The Design of Contracts and Remedies for Breach, 99 Q.J. ECON. 121 (1984).
176. See, e.g., Oliver Hart & John Moore, Incomplete Contracts and Renegotiation, 56 ECONOMETRICA 755 (1988); Thomas J. Miceli, Contract Modification When Litigating for Damages Is Costly, 15 INT'L REV. L. & ECON. 87 (1995); William P. Rogerson, Efficient Reliance and Damage Measures for Breach of Contract, 15 RAND J. ECON. 39 (1984); Steven Shavell, The Design of Contracts and Remedies for Breach, 99 Q.J. ECON. 121 (1984).
177. See, e.g., Oliver Hart & John Moore, Incomplete Contracts and Renegotiation, 56 ECONOMETRICA 755 (1988); Thomas J. Miceli, Contract Modification When Litigating for Damages Is Costly, 15 INT'L REV. L. & ECON. 87 (1995); William P. Rogerson, Efficient Reliance and Damage Measures for Breach of Contract, 15 RAND J. ECON. 39 (1984); Steven Shavell, The Design of Contracts and Remedies for Breach, 99 Q.J. ECON. 121 (1984).
178. Uncertainty about whether one will be able to pay or receive a reported price can induce people to speak more honestly. See Ayres & Talley, Solomonic Bargaining, supra note 3, at 1030.
179. We must offer an important caveat to this analysis. Buyers might make an inflated offer (i.e., an offer that exceeds their private values for performance) if they know that changed circumstances have rendered the seller's performance impossible. If a buyer is confident that her firm offer will be rejected, this scheme will fail to harness the buyer's information. Consequently, courts or legislatures might have to impose some good faith or reasonableness requirement on the buyer's offer to insure that the offer is reasonably related to the buyer's actual valuation. This good faith review would not be necessary when the seller's performance was possible - particularly if the goods exist, and it is merely a question of to whom the seller is going to sell.
180. Original contract provisions that give promisees a limited right to inflate damages might not be enforceable if courts characterized the enhanced damages as penalties, see Eric L. Talley, Note, Contract Renegotiation, Mechanism Design, and the Liquidated Damages Rule, 46 STAN. L. REV. 1195, 1196 (1994), or if courts characterized the provisions as violating the prohibition against introducing evidence of settlement negotiations,
181. see FED. R. EVID. 408.
182. At a minimum, we are proposing that there should be no immutable rule against such a renegotiation mechanism. It is a more difficult question, however, to determine whether the default rule governing contract renegotiation should be our proposal as opposed to, for example, the U.C.C.'s good faith standard or the common law's preexisting duty rule. The text implicitly treats our proposal as the governing default, but for now we are agnostic aboul whether it might make more sense for parties to have to "opt in" affirmatively to our renegotiation scheme rather than forcing them to "opt out." For a fuller discussion of appropriate default choice, see Ian Ayres & Robert Gertner, Filling Gaps in Incomplete Contracts: An Economic Theory of Default Rules, 99 YALE L.J. 87 (1989),
183. and Ian Ayres & Robert Gertner, Strategic Contractual Inefficiency and the Optimal Choice of Legal Rules, 101 YALE L.J. 729 (1992).
184. We qualify our endorsement of Vincent because it is not clear that common law courts are striving to set first-or second-order damages in accordance with our dispositive takings principle. See supra text accompanying notes 73-75 (discussing dispositive takings principle).
185. See, e.g., Kaplow & Shavell, Economic Analysis, supra note 4.