PROPERTY RIGHTS AND PROPERTY LAW orthcoming in Polinsky Shavell eds, Handbook of Law and Economics DEAN LUECK AND THOMAS J MICELIE Abstract. This chapter examines the economics of property rights and property law. It shows how the economics of property rights can be used to understand fundamental features of property law and related extra-legal institutions. The chapter examines both the rationale for legal doctrine, and the effects of legal doctrine regarding the exercise, enforcement, and transfer of rights. It also examines various property rights regimes including open access, private ownership, common property, and state property. The guiding questions are: How are property rights established? What explains the variation in the types of property rights? What governs the we argue that property rights and property law can be best understood as a system of societal use and transfer of rights? And, how are property rights enforced? In answering these questio rules designed to maximize social wealth. They do this by creating incentives for people to maintain and invest in assets, which leads to specialization and trade DRAFT OF AUGUST 17, 2004: DO NOT CITE OR QUOTE WITHOUT PERMISSION KEYWORDS: PROPERTY RIGHTS. OWNERSHIP TRANSACTION COSTS. EXTERNALITY JLE CODES: D23. D62K11 K23 s Lueck: University of Arizona. Miceli: University of Connecticut. We are grateful for the comments of Doug Allen, Tom Hazlett, Eric Rasmussen, lan Wills, as well as participants in the Law and Economics Handbook Conference at Stanford Law School, the European School for New Institutional Economics, and a workshop at the University of Michigan. Lueck was supported by the Cardon Endowment for Agricultural and Resource Economics
* Lueck: University of Arizona. Miceli: University of Connecticut. We are grateful for the comments of Doug Allen, Tom Hazlett, Eric Rasmussen, Ian Wills, as well as participants in the Law and Economics Handbook Conference at Stanford Law School, the European School for New Institutional Economics, and a workshop at the University of Michigan. Lueck was supported by the Cardon Endowment for Agricultural and Resource Economics. PROPERTY RIGHTS AND PROPERTY LAW [Forthcoming in Polinsky & Shavell eds., Handbook of Law and Economics] DEAN LUECK AND THOMAS J. MICELI* Abstract. This chapter examines the economics of property rights and property law. It shows how the economics of property rights can be used to understand fundamental features of property law and related extra-legal institutions. The chapter examines both the rationale for legal doctrine, and the effects of legal doctrine regarding the exercise, enforcement, and transfer of rights. It also examines various property rights regimes including open access, private ownership, common property, and state property. The guiding questions are: How are property rights established? What explains the variation in the types of property rights? What governs the use and transfer of rights? And, how are property rights enforced? In answering these questions we argue that property rights and property law can be best understood as a system of societal rules designed to maximize social wealth. They do this by creating incentives for people to maintain and invest in assets, which leads to specialization and trade. DRAFT OF AUGUST 17, 2004: DO NOT CITE OR QUOTE WITHOUT PERMISSION. KEYWORDS: PROPERTY RIGHTS, OWNERSHIP, TRANSACTION COSTS, EXTERNALITY. JLE CODES: D23, D62, K11, K23
Lueck 8 Miceli- Property Lato 1. Introduction This chapter examines the economics of property rights and property law. The purpose is to show how the economics of property rights can be used to understand fundamental features of property law and related extra-legal institutions. The chapter will examine both the rationale for, and the effects of, legal doctrine. The guiding questions are: How are property rights established? What explains the variation in the types of property rights? What governs the use and transfer of rights? And, how are property rights enforced? In answering these questions we argue that property rights and property law can be best understood as a system of societal rule designed to maximize social wealth. They do this by creating incentives for people to maintain and invest in assets, which leads to specialization and trade 1. 1. Property rights and Property Law Property rights have been a subject of discussion among philosophers as well as political and legal scholars long before economists began to examine their origins and consequences Property rights were discussed and implicitly understood by ancient Greek and Roman writers, but it is perhaps Hobbes (1651)who first discusses property in a manner recognizable to modern economists. Indeed Hobbes''state of nature can be viewed as open access dissipation. A wide range of Enlightenment thinkers such as Blackstone(1766), Hume(1739-1740), Locke(1690), and Smith(1776)also discussed property rights. Though they varied in their treatments all considered property rights as fundamental social institutions for creating wealth and preventing We define property rights as the ability (or expected ability) of an economic agent to use an asset (Allen 1999, Barzel 1997, Shavell 2004). As Demsetz(1967)notes in one of the classic early economic analyses, property rights represent a social institution that creates incentives to efficiently use assets, and to maintain and invest in assets. They may or may not be enforced by courts and because the actions of courts are costly, legal rights are but a subset of economic property rights. In addition to law(and statutorily-based regulations enforced by administrative agencies), property rights may be enforced by custom and norms(e.g, Ellickson 1991), and by markets through repeated transactions Property law is the body of court enforced rules governing the establishment, use, and transfer of rights to land and those assets attached to it such as air minerals water. and wildlife Intellectual property law similarly details the conditions under which the courts enforce rights to intellectual assets. In this framework, virtually all, if not all, branches of law are property rights law. Labor law defines the courts role in enforcing rights to one's labor, contract law defines the rights of contracting parties, and so on. Because the economics of property rights originated with a focus on rights to land and associated natural resources(e.g. fisheries, pastures, water) the Enforcement may also be by violence as with the Mafia( Gambetta 1993) 2 Merrill and Smith(2002)and Arruniada(2003), however, argue that the in rem nature of property (real rights versus in personam'use rights typical in contracts) is an important distinction that property rights economists have overlooked since Coase(1960). Merrill and Smith(2002, p. 375)argue that '[t]he simplifying assumptions [of of property' They cite doctrines like the numerus clausus principle, and Arrunada notes the important of title p economists] introduce blind spots that can limit the ability of law and economics scholars to explain the institutio systems as in rem enforcement institutions
Lueck & Miceli – Property Law 1 1. Introduction This chapter examines the economics of property rights and property law. The purpose is to show how the economics of property rights can be used to understand fundamental features of property law and related extra-legal institutions. The chapter will examine both the rationale for, and the effects of, legal doctrine. The guiding questions are: How are property rights established? What explains the variation in the types of property rights? What governs the use and transfer of rights? And, how are property rights enforced? In answering these questions we argue that property rights and property law can be best understood as a system of societal rules designed to maximize social wealth. They do this by creating incentives for people to maintain and invest in assets, which leads to specialization and trade. 1.1. Property Rights and Property Law Property rights have been a subject of discussion among philosophers as well as political and legal scholars long before economists began to examine their origins and consequences. Property rights were discussed and implicitly understood by ancient Greek and Roman writers, but it is perhaps Hobbes (1651) who first discusses property in a manner recognizable to modern economists. Indeed Hobbes’ ‘state of nature’ can be viewed as open access dissipation. A wide range of Enlightenment thinkers such as Blackstone (1766), Hume (1739-1740), Locke (1690), and Smith (1776) also discussed property rights. Though they varied in their treatments all considered property rights as fundamental social institutions for creating wealth and preventing strife. We define property rights as the ability (or expected ability) of an economic agent to use an asset (Allen 1999, Barzel 1997, Shavell 2004). As Demsetz (1967) notes in one of the classic early economic analyses, property rights represent a social institution that creates incentives to efficiently use assets, and to maintain and invest in assets. They may or may not be enforced by courts and because the actions of courts are costly, legal rights are but a subset of economic property rights. In addition to law (and statutorily-based regulations enforced by administrative agencies), property rights may be enforced by custom and norms (e.g., Ellickson 1991), and by markets through repeated transactions.1 Property law is the body of court enforced rules governing the establishment, use, and transfer of rights to land and those assets attached to it such as air, minerals, water, and wildlife.2 Intellectual property law similarly details the conditions under which the courts enforce rights to intellectual assets. In this framework, virtually all, if not all, branches of law are ‘property rights law.’ Labor law defines the court’s role in enforcing rights to one’s labor, contract law defines the rights of contracting parties, and so on. Because the economics of property rights originated with a focus on rights to land and associated natural resources (e.g. fisheries, pastures, water) the 1 Enforcement may also be by violence as with the Mafia (Gambetta 1993). 2 Merrill and Smith (2002) and Arruñada (2003), however, argue that the in rem nature of property (‘real rights’ versus in personam ‘use rights’ typical in contracts) is an important distinction that property rights economists have overlooked since Coase (1960). Merrill and Smith (2002, p. 375) argue that ‘[t]he simplifying assumptions [of economists] introduce blind spots that can limit the ability of law and economics scholars to explain the institution of property.’ They cite doctrines like the numerus clausus principle, and Arruñada notes the important of title systems as in rem enforcement institutions
Lueck 8 Miceli-Property Lato link between 'property law and property rights' is firmly established. This chapter will develol (e.g, contracts, torts) the literature has become so specialized that the connection to the caseg this link by examining property rights generally and property law in particular. Yet, much of th analysis in this chapter is applicable to topics elsewhere in the handbook, though in many conomics of property rights might seem faint The economic analysis of property law is substantially less well developed than the economic analysis of contract law or tort law(for example, there is no generally applicable model), and this chapter reflects this state of the discipline. The economics of property rights, however, developed but mostly without a focus on property law. The disconnection between the Demsetz's(1998)recent entry"Property Rights"in the The New Palgrave Dictionae pl economics of property rights and the economics of property law is longstanding. For example, Economics and the Law makes absolutely no mention of property law, and much of the economics of property rights literature remains ignorant of property law. Similarly, property law scholarship often is ignorant of economics. This is not to say there has not been important work in property law with strong economic underpinnings(e.g, Ellickson 1993, Epstein 1985 Heller 1998, Merrill 1986, Rose 1990), but it is clear that economics has not yet penetrated property law as it has penetrated contract and tort law. While it is common for courses in contract law and tort law to be taught using economics as the guiding framework, an economics- based course in property law is almost unheard of. In part, this chapter seeks to break down this division by bringing the two literatures together 1. 2. Property Rights, Transaction Costs, and the Coase Theorem The economics of property law begins with Coase( 1960), who provides a property rights externalities as a source of market failure requiring government intervention to force the en perspective on the problem of externalities, or social cost. Prior to Coase, economists viewed responsible party to curtail the harmful activity. Consider Coase's famous example of the rancher and farmer with adjacent plots of land. The rancher's cattle stray onto the farmer's land causing crop damage. If the ranchers profit, r(h), and the amount of crop damage, d(h), are functions of the rancher's herd size, h, then the first-best optimal herd size, h*, maximizes r(h) -d(h). That is, h"solves r (h=d (h). This is also the choice that would be made by a single party acting as both the farmer and rancher, Coase's'sole owner' solution. First-best then is synonymous with the zero transaction cost outcome. With separate parties, however, and the absence of a contract between the farmer and the rancher or some type of government intervention(a tax, fine, or regulation), the rancher would choose the herd size to maximize r(h). This results in too many cattle because the rancher adds cattle until (h)=0, which implies h> h*. Thus, the rancher must pay a tax(or face liability) for the damage from straying cattle, or he will expand his herd beyond the efficient(first-best)size s The main exception to this is a deep theoretical literature on takings which is examined in section 8 Merrill and Smith(2001)note this also An exception is Dwyer and Menell (1998) Another important, though little known early property rights contribution is that of Alchian (1965) We assume that <0 and d 20, ensuring a unique optimum
Lueck & Miceli – Property Law 2 link between ‘property law’ and ‘property rights’ is firmly established. This chapter will develop this link by examining property rights generally and property law in particular. Yet, much of the analysis in this chapter is applicable to topics elsewhere in the handbook, though in many cases (e.g., contracts, torts) the literature has become so specialized that the connection to the economics of property rights might seem faint. The economic analysis of property law is substantially less well developed than the economic analysis of contract law or tort law (for example, there is no generally applicable model), and this chapter reflects this state of the discipline. The economics of property rights, however, is well developed but mostly without a focus on property law.3 The disconnection between the economics of property rights and the economics of property law is longstanding. For example, Demsetz’s (1998) recent entry “Property Rights” in the The New Palgrave Dictionary of Economics and the Law makes absolutely no mention of property law, and much of the economics of property rights literature remains ignorant of property law.4 Similarly, property law scholarship often is ignorant of economics. This is not to say there has not been important work in property law with strong economic underpinnings (e.g., Ellickson 1993, Epstein 1985, Heller 1998, Merrill 1986, Rose 1990), but it is clear that economics has not yet penetrated property law as it has penetrated contract and tort law. While it is common for courses in contract law and tort law to be taught using economics as the guiding framework, an economicsbased course in property law is almost unheard of. 5 In part, this chapter seeks to break down this division by bringing the two literatures together. 1.2. Property Rights, Transaction Costs, and the Coase Theorem The economics of property law begins with Coase (1960), who provides a property rights perspective on the problem of externalities, or ‘social cost.’6 Prior to Coase, economists viewed externalities as a source of market failure requiring government intervention to force the responsible party to curtail the harmful activity. Consider Coase’s famous example of the rancher and farmer with adjacent plots of land. The rancher’s cattle stray onto the farmer’s land causing crop damage. If the rancher’s profit, π(h), and the amount of crop damage, d(h), are functions of the rancher’s herd size, h, then the first-best optimal herd size, h*, maximizes π(h)−d(h). That is, h* solves π′(h)=d′(h). 7 This is also the choice that would be made by a single party acting as both the farmer and rancher, Coase’s ‘sole owner’ solution. First-best then is synonymous with the zero transaction cost outcome. With separate parties, however, and the absence of a contract between the farmer and the rancher or some type of government intervention (a tax, fine, or regulation), the rancher would choose the herd size to maximize π(h). This results in too many cattle because the rancher adds cattle until π′(h)=0, which implies hr > h*. Thus, the rancher must pay a tax (or face liability) for the damage from straying cattle, or he will expand his herd beyond the efficient (first-best) size. 3 The main exception to this is a deep theoretical literature on takings which is examined in section 8. 4 Merrill and Smith (2001) note this also. 5 An exception is Dwyer and Menell (1998). 6 Another important, though little known early property rights contribution is that of Alchian (1965). 7 We assume that π″0, ensuring a unique optimum
Lueck 8 Miceli-Property Lato Note that this solution to the externality problem embodies a particular assignment of property rights--namely, that the farmer has the right to be free from crop damage. Another way to say this is that the farmer is labeled as the "cause"of the harm and therefore must face liability. And if the property right(or the legal liability rule) is structured properly, the rancher will purchase the right to impose crop damage up to the point where the marginal profit from the last steer just equals the marginal damage, yielding an efficient herd size Coase's critique of this conventional, or"Pigovian, perspective on externalities is not that it is wrong per se, but that it is incomplete. To illustrate, suppose that the rancher initially has the economic(and legal) right to impose crop damage without penalty. According to the Pigovian view, this would result in an excessive herd size because the rancher would expand the herd to h. But note that the farmer would be willing to pay up to d(h), his marginal damage, for each steer that the farmer removes from the herd in order to avoid crop damage, while the rancher would accept any amount greater than his marginal profit, T(h). Thus, if transaction costs are zero, the parties will contract to reduce the herd to the efficient size. In other words, the farmer will purchase the rights to the straying cattle, the reverse of what happened under the Pigovian solution. The outcome in both cases is therefore first-best. This conclusion has become known as the Coase Theorem, which can be stated in general terms as follows: When transaction costs are zero, the allocation of resources will be efficient regardless of the initial assignment of property rights Coase challenged two assumptions implicit in the Pigovian view: first, that there is a unique cause of the harm, and second, that government intervention is necessary to internalize the externality. Coase noted that in general, and in the specific farmer-rancher example, the cause of harm is'reciprocalin the sense that if either party is removed, the harm disappears. Second, by noting that well defined ownership can lead to transactions, the private contracting as well as government regulation and taxation i ange of solutions extends to 1.3. The Impact of Transaction Costs: When Does Law Matter? Although there has been debate among economists and legal scholars on the significance of the Coase Theorem and its implications, Coase(1960, 1988)has been clear on this issue. Economic and legal institutions are important and have impacts because transaction costs are not zero and This tradition is attributed to A C. Pigou's The Economics of Welfare(1932) Stigler(1987)takes credit for calling this proposition the"Coase Theorem. Stigler also recounts a famous dinner at the home of Aaron Director where Coase convinced a formidable group of scholars (including Milton Friedman and Stigler) that his analysis was indeed correct. Typically economists have argued that the Coase Theorem is conditioned on the size of wealth effects. Barzel notes that the standard example of rights shifting without compensation itself violates the assumption of zero e (1997), however, argues that wealth effects are likely to be trivial and not a condition of the Coase Theorem transaction costs. This is because zero transaction costs means that a rights shift would have to be accompanied by a payment to the original rights holder In technical terms Coase points out that most interesting actions(n) depend on the inputs of both parties(a, b);that is,y=f(a, b). This"bilateral externality is discussed in section 7.1 This'contractualapproach is discussed in section 4.4
Lueck & Miceli – Property Law 3 Note that this solution to the externality problem embodies a particular assignment of property rights--namely, that the farmer has the right to be free from crop damage. Another way to say this is that the farmer is labeled as the “cause” of the harm and therefore must face liability. And if the property right (or the legal liability rule) is structured properly, the rancher will purchase the right to impose crop damage up to the point where the marginal profit from the last steer just equals the marginal damage, yielding an efficient herd size. Coase’s critique of this conventional, or “Pigovian,” perspective on externalities is not that it is wrong per se, but that it is incomplete.8 To illustrate, suppose that the rancher initially has the economic (and legal) right to impose crop damage without penalty. According to the Pigovian view, this would result in an excessive herd size because the rancher would expand the herd to hr . But note that the farmer would be willing to pay up to d′(h), his marginal damage, for each steer that the farmer removes from the herd in order to avoid crop damage, while the rancher would accept any amount greater than his marginal profit, π′(h). Thus, if transaction costs are zero, the parties will contract to reduce the herd to the efficient size. In other words, the farmer will purchase the rights to the straying cattle, the reverse of what happened under the Pigovian solution. The outcome in both cases is therefore first-best. This conclusion has become known as the Coase Theorem9 , which can be stated in general terms as follows: When transaction costs are zero, the allocation of resources will be efficient regardless of the initial assignment of property rights.10 Coase challenged two assumptions implicit in the Pigovian view: first, that there is a unique cause of the harm, and second, that government intervention is necessary to internalize the externality. Coase noted that in general, and in the specific farmer-rancher example, the cause of harm is ‘reciprocal’ in the sense that if either party is removed, the harm disappears.11 Second, by noting that well defined ownership can lead to transactions, the range of ‘solutions’ extends to private contracting as well as government regulation and taxation.12 1.3. The Impact of Transaction Costs: When Does Law Matter? Although there has been debate among economists and legal scholars on the significance of the Coase Theorem and its implications, Coase (1960, 1988) has been clear on this issue. Economic and legal institutions are important and have impacts because transaction costs are not zero and 8 This tradition is attributed to A.C. Pigou’s The Economics of Welfare (1932). 9 Stigler (1987) takes credit for calling this proposition the “Coase Theorem.” Stigler also recounts a famous dinner at the home of Aaron Director where Coase convinced a formidable group of scholars (including Milton Friedman and Stigler) that his analysis was indeed correct. 10 Typically economists have argued that the Coase Theorem is conditioned on the size of wealth effects. Barzel (1997), however, argues that wealth effects are likely to be trivial and not a condition of the Coase Theorem. He notes that the standard example of rights shifting without compensation itself violates the assumption of zero transaction costs. This is because zero transaction costs means that a rights shift would have to be accompanied by a payment to the original rights holder. 11 In technical terms Coase points out that most interesting actions (Y) depend on the inputs of both parties (a,b); that is, Y = f(a,b). This ‘bilateral’ externality is discussed in section 7.1. 12 This ‘contractual’ approach is discussed in section 4.4
Lueck 8 Micelli-Property Lazo thus property rights are not perfectly defined (Allen 1999, Barzel 1997). 3The Coase Theorem thus stresses the role of transaction costs in shaping the institutions, including law, that determines the allocation of resources. Seen as the costs of defining and enforcing property rights, transaction costs include enforcement costs, measurement costs, and moral hazard costs (Allen 1998) But Coase's insight goes further. Not only does the law matter for efficiency, as Demsetz(1972) explicitly points out, but the law itself is an economic choice, also expected to be driven by economic forces. Indeed, Coase's(1960)discussion of nuisance law suggests an economic logic to the law in its assignment of property rights among various parties to these disputes, but its relevance extends beyond the study of externalities. It is concerned with the larger question of how property rights are established, the types of property rights regimes that are allowed, and the rules that govern the use and transfer of property rights. In this sense, property law is a complement to markets. This is the real contribution of Coase, and it will emerge as a theme throughout this chapter in a wide range of property law settings 1. 4. Outline of chapter The remainder of the chapter is organized as follows. Section 2 develops the basic economic models of property rights that guide the analysis throughout the chapter. Section 3 examines the origin of rights. Section 4 follows with an analysis of the changes in property rights, or what has become known as the evolution of rights. Section 5 then examines various forms of voluntary of title by adverse possession and theft. Section 7 examines various means of internal go ers exchange, including markets, leases, and inheritance. Section 6 examines involuntary transfers externalities. Section 8 considers issues related to state(collective)ownership, as opposed to private ownership, of property, including the optimal scale of ownership and takings. Section 9 considers restrictions on the alienability of property. Finally Section 10 concludes. Each section is a mix of formal and informal theory and application to law and related institutions Throughout we try to make clear that the goal of the chapter is to use economics to illuminate the rationale for and effects of property law doctrine. Where possible we summarize the empirical literature or explain empirical applications. The sections are not symmetric, simply because the literature is not symmetric 2. Basic Property rights models Before examining property law doctrine it is appropriate to first examine the predominant types of property rights regimes and their economic structure. In this section we both describe the various types of property and examine the implications of these regimes for the use of and Many scholars have called a case of zero transaction costs a Coasian world but Coase(1988, p 174)claims"The world of zero transaction costs has often been described as a Coasian world. nothing could be further from the truth. It is the world of modern economic theory, one which I was hoping to persuade economists to leave In another path breaking article, Coase(1937)uses a similar transaction cost argument to explain the boundary between markets and firms. Barzel and Kochin(1992)note the link between Coase's property rights and transaction costs theories Because of its focus on specific assets, we make little use of theproperty rights theory of the firm'(e.g, Hart an Moore 1990)which has become important in the economics of organization
Lueck & Miceli – Property Law 4 thus property rights are not perfectly defined (Allen 1999, Barzel 1997).13 The Coase Theorem thus stresses the role of transaction costs in shaping the institutions, including law, that determines the allocation of resources. Seen as the costs of defining and enforcing property rights, transaction costs include enforcement costs, measurement costs, and moral hazard costs (Allen 1998). But Coase’s insight goes further. Not only does the law matter for efficiency, as Demsetz (1972) explicitly points out, but the law itself is an economic choice, also expected to be driven by economic forces.14 Indeed, Coase’s (1960) discussion of nuisance law suggests an economic logic to the law in its assignment of property rights among various parties to these disputes, but its relevance extends beyond the study of externalities. It is concerned with the larger question of how property rights are established, the types of property rights regimes that are allowed, and the rules that govern the use and transfer of property rights. In this sense, property law is a complement to markets. This is the real contribution of Coase, and it will emerge as a theme throughout this chapter in a wide range of property law settings. 1.4. Outline of Chapter The remainder of the chapter is organized as follows. Section 2 develops the basic economic models of property rights that guide the analysis throughout the chapter. Section 3 examines the origin of rights. Section 4 follows with an analysis of the changes in property rights, or what has become known as the evolution of rights. Section 5 then examines various forms of voluntary exchange, including markets, leases, and inheritance. Section 6 examines involuntary transfers of title by adverse possession and theft. Section 7 examines various means of internalizing externalities. Section 8 considers issues related to state (collective) ownership, as opposed to private ownership, of property, including the optimal scale of ownership and takings. Section 9 considers restrictions on the alienability of property. Finally Section 10 concludes. Each section is a mix of formal and informal theory and application to law and related institutions. Throughout we try to make clear that the goal of the chapter is to use economics to illuminate the rationale for and effects of property law doctrine. Where possible we summarize the empirical literature or explain empirical applications. The sections are not symmetric, simply because the literature is not symmetric.15 2. Basic Property Rights Models Before examining property law doctrine it is appropriate to first examine the predominant types of property rights regimes and their economic structure. In this section we both describe the various types of property and examine the implications of these regimes for the use of and 13 Many scholars have called a case of zero transaction costs a ‘Coasian world’ but Coase (1988, p.174) claims ‘The world of zero transaction costs has often been described as a Coasian world. Nothing could be further from the truth. It is the world of modern economic theory, one which I was hoping to persuade economists to leave.’ 14 In another path breaking article, Coase (1937) uses a similar transaction cost argument to explain the boundary between markets and firms. Barzel and Kochin (1992) note the link between Coase’s property rights and transaction costs theories. 15 Because of its focus on specific assets, we make little use of the ‘property rights theory of the firm’ (e.g., Hart and Moore 1990) which has become important in the economics of organization
Lueck Miceli-Property Lato investment in assets The models used in this section are fundamental to the later sections of the chapter that examine specific issues and legal doctrine As we noted above, there first systematic analysis of property rights began with the Enlightenment writers(.g, Blackstone, Hume, Locke, Smith), but the formal modeling of the economics of property rights began with Frank Knight's(1924)analysis of public and private roads. Knight showed that a public road with no charge for access would be overused compared to the private road because users would not face the full cost of their actions. Gordon(1954 further developed Knight's preliminary model-establishing the now famous"average product rule' for input use --in the context of an open ocean fishery where no one could be excluded Gordons model was completed with Cheungs(1970) paper, which fully characterized the Nash equilibrium for an open access resource Our analysis of various property rights regimes will use a common set of notation in which a fixed asset(e.g, plot of land )is used in conjunction with a variable input()in order to produce a market output (Y=f(x)). If the input is available at a market wage of w, then the first-best use of the input(x*()must maximize r=f(x)-wx and satisfy the first-order necessary condition flx)=w. The first-best value of the land is thus*=R*(r* t)edt, where r is the discount rate.We start with sS, or a complete lack of rights, and th examine private property rights, common property, and mixed property rights regimes 2.1 Assume there are n individuals who have unrestricted assess to a resource such as a piece of land, and that output from the land(e.g, beef from grazing animals)is given by Y=fir) where x, is the effort of the i h individual, f(>0 andf(<0, and the opportunity cost of effort is the market wage, w. 9 Each person's objective is to maximize his own rent subject to the constraint of open access, which means that each user can only capture(and own) the output proportion to his share or error This means each person must solve the following constrained maximization problem maxR=f(x)-wx subject to f=|x/∑:x/∑mx) Scott(1955) similarly shows the dissipation under open access and the private property solution In law, since Roman times, open access resources have been called res nullius, or things unowned his production function captures the effect of competing users of the open access asset and is standard in the literature. Also, note that while ownership of the land is absent each person is assumed to have perfect ownership themselves, their labor, and the product derived from the open access asset This is a standard assumption but might be modified to explicitly distinguish use effort from violence effort
Lueck & Miceli – Property Law 5 investment in assets. The models used in this section are fundamental to the later sections of the chapter that examine specific issues and legal doctrine. As we noted above, there first systematic analysis of property rights began with the Enlightenment writers (e.g., Blackstone, Hume, Locke, Smith), but the formal modeling of the economics of property rights began with Frank Knight’s (1924) analysis of public and private roads. Knight showed that a public road with no charge for access would be overused compared to the private road because users would not face the full cost of their actions. Gordon (1954) further developed Knight’s preliminary model – establishing the now famous ‘average product rule’ for input use -- in the context of an open ocean fishery where no one could be excluded.16 Gordon’s model was completed with Cheung’s (1970) paper, which fully characterized the Nash equilibrium for an open access resource. Our analysis of various property rights regimes will use a common set of notation in which a fixed asset (e.g., plot of land) is used in conjunction with a variable input (x) in order to produce a market output (Y= f(x)). If the input is available at a market wage of w, then the first-best use of the input (x*(w)) must maximize R = f(x) – wx and satisfy the first-order necessary condition f’(x) = w. The first-best value of the land is thus 0 * *( *, ) rt V R x t e dt ∞ − = ∫ , where r is the discount rate.17 We start with open access, or a complete lack of property rights, and then, in turn, examine private property rights, common property, and mixed property rights regimes.18 2.1. Open Access Assume there are n individuals who have unrestricted assess to a resource such as a piece of land, and that output from the land (e.g., beef from grazing animals) is given by 1 ( ) n i i Yf x = = ∑ where xi is the effort of the i th individual, f’(⋅) > 0 and f’’(⋅) < 0, and the opportunity cost of effort is the market wage, wi. 19 Each person’s objective is to maximize his own rent subject to the constraint of open access, which means that each user can only capture (and own) the output in proportion to his share of effort.20 This means each person must solve the following constrained maximization problem: max ( ) i i i i ii x R = − f x wx (2.1) subject to 1 1 ( ) n n i ii i i i f x xf x = = = ⎡ ⎤ ⎣ ⎦ ∑ ∑ 16 Scott (1955) similarly shows the dissipation under open access and the private property solution. 17 Each period’s rent can be viewed as a steady state outcome. 18 In law, since Roman times, open access resources have been called res nullius, or things unowned. 19 This production function captures the effect of competing users of the open access asset and is standard in the literature. Also, note that while ownership of the land is absent each person is assumed to have perfect ownership of themselves, their labor, and the product derived from the open access asset. 20 This is a standard assumption but might be modified to explicitly distinguish use effort from violence effort
Lueck miceli Assuming that all users are homogeneous (w;=wi, for all i*j), the Nash open access equilibrium is x=x(n, wl,..., w,, which must satisfy the first-order necessary condition ()f Equation(2.2), as Cheung shows, is indeed identical to Gordons asserted average product equilibrium, but only in the limiting case of an infinite number of users with unrestricted access. Thus, in the limit as n>o, (2.2) becomes =1 I X which states that the open access equilibrium level of effort occurs where the average product equals the wage. More importantly, this limiting case also implies that rents are completel dissipated;or that,2iR-Eialr'(xa)-wxa]=0. Similarly, the present value of the asset is also zero; that is, voa= R(xo, De"dt=0 In this framework, the absence of property rights leads to overuse of the asset and complete dissipation of its value. Complete dissipation is a limiting result, however, of the assumption of homogeneous users. If users are heterogeneous, dissipation under open access will be incomplete, and infra-marginal (low cost)users will earn rents(Libecap 1989). The presence rent under open access may be an important factor in preventing the establishment of rights to the open access resource because those earning rents will have incentives to maintain the open access regime 2. 2 Private Property rights Private ownership, as Knight first noted is the straightforward solution to the open access problem. Under the conditions of the Coase Theorem, the owner faces the full value and opportunity cost of asset use, he chooses the first-best level of use(x* y=0. The Coase Theorem also implies that, as long as property rights are well defined the organization of the asset s use will not matter: the owner may use the land himself, he may hire inputs owned by others, input owners may hire(or rent) the asset, or there may be a sharing arrangement between the asset owner and the input owners. In fact, under the conditions of zero transaction costs, any property regime(e.g, common property, state ownership) would generate the first -best use of the asset This has been the starting point with Knight, Gordon and Cheung quation (2.2)is actually a weighted average of average and marginal products. Brooks et al. (1999)show that Cheung's(1970)equilibrium holds in a dynamic setting 2Hardin's(1968)famously named"tragedy of the commons"is a popularized version of this literature This was well understood by Hobbs, Bentham, Locke and Blackstone long ago
Lueck & Miceli – Property Law 6 Assuming that all users are homogeneous21 (wi = wj, for all i ≠ j), the Nash open access equilibrium is x = xoa(n, w1, …, wn), which must satisfy the first-order necessary condition ( ) ( ) 1 , 1 1 ( ) 1 1 '( ) 1,..., . n n i i n i i i i i f x n f x wi n n n x = = = ⎛ ⎞ − ⎜ ⎟ = == ⎝ ⎠ ∑ ∑ ∑ (2.2) Equation (2.2), as Cheung shows, is indeed identical to Gordon’s asserted average product equilibrium, but only in the limiting case of an infinite number of users with unrestricted access.22 Thus, in the limit as n→ ∞, (2.2) becomes 1 1 ( ) , n i i n i i f x w x = = ⎛ ⎞ ⎜ ⎟ = ⎝ ⎠ ∑ ∑ (2.3) which states that the open access equilibrium level of effort occurs where the average product equals the wage. More importantly, this limiting case also implies that rents are completely dissipated; or that, 1 1 () 0 n n i oa oa i i i R f x wx = = = −= ⎡ ⎤ ∑ ∑ ⎣ ⎦ . Similarly, the present value of the asset is also zero; that is, 0 ( , ) 0. oa oa rt V R x t e dt ∞ − = = ∫ In this framework, the absence of property rights leads to overuse of the asset and complete dissipation of its value.23 Complete dissipation is a limiting result, however, of the assumption of homogeneous users. If users are heterogeneous, dissipation under open access will be incomplete, and infra-marginal (low cost) users will earn rents (Libecap 1989). The presence of rent under open access may be an important factor in preventing the establishment of rights to the open access resource because those earning rents will have incentives to maintain the open access regime. 2.2 Private Property Rights Private ownership, as Knight first noted is the straightforward solution to the open access problem.24 Under the conditions of the Coase Theorem, the owner faces the full value and opportunity cost of asset use, he chooses the first-best level of use (x* Voa =0. The Coase Theorem also implies that, as long as property rights are well defined the organization of the asset’s use will not matter: the owner may use the land himself, he may hire inputs owned by others, input owners may hire (or rent) the asset, or there may be a sharing arrangement between the asset owner and the input owners. In fact, under the conditions of zero transaction costs, any property regime (e.g., common property, state ownership) would generate the first-best use of the asset. 21 This has been the starting point with Knight, Gordon and Cheung, 22 Equation (2.2) is actually a weighted average of average and marginal products. Brooks et al. (1999) show that Cheung’s (1970) equilibrium holds in a dynamic setting. 23 Hardin’s (1968) famously named “tragedy of the commons” is a popularized version of this literature. 24 This was well understood by Hobbs, Bentham, Locke and Blackstone long ago
Lueck 8 Miceli-Property Lato Not only does private ownership create incentives for optimal resource use, it also creates incentives for optimal asset maintenance and investment. With open access, no user has any incentive to use inputs that have a future payoff. To see the effect on investment, consider a slightly modified version of the model above. Let future output be Yr+/=f(xv), where xr is current investment, available at a market wage of w, and the interest rate is r:. The first-best use of the input(x,)must maximize R=f(xv/(1+ry-wa, and satisfy the first-order necessary conditionf'lxy/(+r)=wr. This outcome is generated under perfect private ownership. Now let r be the probability of expropriation(because of imperfect property rights)of the future output so that(1-rm) is the probability the investor's output remains intact. The solution to the investment problem(x, )is now to maximize R=f(xv/(1-77(+r)/-wxr which must satisfy(xv/( T)/(1+r)=wr. This clearly implies less investment(x, <x'). Pure open access means that no investor could claim future output(T=1), so x =0, and the rent from investment also equals zero In a recent article, Heller( 1998)identifies a situation in which a large number of uncoordinated individuals have the right to exclude users, thus creating a regime in which assets are under-used because each rights holder can exercise a"veto'over use. Because of the incentive to under use rather than over use the asset, Heller labeled this the anti-commons'and argues that many of the development problems in post-communist Europe are plagued with this problem of too many owners.Buchanan and Yoon(2000) formalize Heller's idea and give it additional application cases where competing bureaucracies can stifle development by exercising veto rights. De Sotos(2000) documentation of the difficulties of operating in an economy heavily laden with overlapping bureaucracies is a similar application(as discussed in Section 5. 1. 2). In a similar application, Anderson and Lueck(1992) study 'fractionated ownership of land on American Indian reservations. They found that divided ownership of agricultural landamong large numbers of heirs to the original owner )led to dramatic reductions in the value of agricultural itput It is not clear that the anti-commons phenomenon can usefully be regarded as a distinct property regime. The lack of investment incentives does not stem fromto much ownership, but simply from severely divided interests in which unanimous agreement is required for decision. In this sense, the anti-commons is like open access too many people have access and thus no one can gain from optimal use. The difference seems to be that the decisions considered are investment decisions, so the anti-commons can be viewed as open investment problem. The same land or apartments governed by too many will be overused while investment will be suboptimal 2 Writing before Adam Smith, Wm. Blackstone( Book ll, Chapter 1, 1765)recognized this and wrote: 'And the art of agriculture, by a regular connexion and consequence, introduced and established the idea of a more permanent property in the soil, than had hitherto been received and adopted. It was clear that the earth would not produce he I fruits in sufficient quantities, without the assistance of tillage: but who would be at the pains of tilling it, if another might watch an opportunity to seize upon and enjoy the product of his industry, art, and labor? This is based on the detailed analysis of Bohn and Deacon(2000) Heller and Eisenberg(1998)also call open access a problem of too many owners, whereas the economic models xamined above characterize this as a lack of ownership
Lueck & Miceli – Property Law 7 Not only does private ownership create incentives for optimal resource use, it also creates incentives for optimal asset maintenance and investment. With open access, no user has any incentive to use inputs that have a future payoff.25 To see the effect on investment, consider a slightly modified version of the model above.26 Let future output be Yt+1 = f(xt), where xt is current investment, available at a market wage of w, and the interest rate is r. The first-best use of the input ( * t x ) must maximize R = f(xt)/(1+r) – wtxt and satisfy the first-order necessary condition f’(xt)/(1+r) = wt. This outcome is generated under perfect private ownership. Now let π be the probability of expropriation (because of imperfect property rights) of the future output, so that (1-π) is the probability the investor’s output remains intact. The solution to the investment problem ( t x π ) is now to maximize R = f(xt) [(1-π)/(1+r)] – wtxt which must satisfy f’(xt) [(1- π)/(1+r)] = wt. This clearly implies less investment ( * t t x x π < ). Pure open access means that no investor could claim future output (π = 1), so oa t x = 0, and the rent from investment also equals zero. In a recent article, Heller (1998) identifies a situation in which a large number of uncoordinated individuals have the right to exclude users, thus creating a regime in which assets are under-used because each rights holder can exercise a ‘veto’ over use. Because of the incentive to under use rather than over use the asset, Heller labeled this the ‘anti-commons’ and argues that many of the development problems in post-communist Europe are plagued with this problem of ‘too many owners.’ Buchanan and Yoon (2000) formalize Heller’s idea and give it additional application in cases where competing bureaucracies can stifle development by exercising veto rights. De Soto’s (2000) documentation of the difficulties of operating in an economy heavily laden with overlapping bureaucracies is a similar application (as discussed in Section 5.1.2). In a similar application, Anderson and Lueck (1992) study ‘fractionated’ownership of land on American Indian reservations. They found that divided ownership of agricultural land (among large numbers of heirs to the original owner) led to dramatic reductions in the value of agricultural output. It is not clear that the anti-commons phenomenon can usefully be regarded as a distinct property regime. The lack of investment incentives does not stem from ‘too much ownership’, but simply from severely divided interests in which unanimous agreement is required for decision.27 In this sense, the anti-commons is like open access: too many people have access and thus no one can gain from optimal use. The difference seems to be that the decisions considered are investment decisions, so the anti-commons can be viewed as open access investment problem. The same land or apartments governed by ‘too many’ will be overused while investment will be suboptimal. 25 Writing before Adam Smith, Wm. Blackstone (Book II, Chapter 1, 1765) recognized this and wrote: ‘And the art of agriculture, by a regular connexion and consequence, introduced and established the idea of a more permanent property in the soil, than had hitherto been received and adopted. It was clear that the earth would not produce her 1`fruits in sufficient quantities, without the assistance of tillage: but who would be at the pains of tilling it, if another might watch an opportunity to seize upon and enjoy the product of his industry, art, and labor?’ 26 This is based on the detailed analysis of Bohn and Deacon (2000). 27 Heller and Eisenberg (1998) also call open access a problem of ‘too many owners,’ whereas the economic models examined above characterize this as a lack of ownership
Lueck 8 Miceli-Property Lato The empirical literature on private property rights is of two types. First, there is a literature that private property. This rather small literature is dominated by studies on natural resources and attempts to measure the dissipation from open access and to compare resource use to that und especially of fisheries where open access regimes have been common(e.g, Agnello and Donnelly 1975, Bottomley 1963). These studies have estimated the deadweight losses from open access use and compared levels of asset use in open access regimes with those of private property and other limited access regimes. Second there is a recent and growing literature on the effects of property rights security on resource use and investment. Much of this literature has focused on the investment effects of differences in legal title to land. In his survey article Besley (1998 )notes that the econometric evidence for positive investment effects of more secure rights in developing countries is quite limited. These studies suffer, however, from data limitations(on oth measures of investment and measures of property rights security)and from potential property rights endogeneity. We expect more investment with better defined rights, but as we discuss in section 4, the choice of property rights regime can itself be influenced by investment levels or other correlated variables. Thus the econometric issue is how to find an instrument for property rights variables to isolate the effect of rights on investment. Still there is some compelling evidence for the importance of property rights in the cases of natural resource use (Bohn and Deacon 2000), American Indian reservation agriculture(Anderson and Lueck 1992), and urban residential land(Miceli et al. 2002) 2.3. Common Property rights In modern social science the term commons common property originated in the analysis of what is now called open access. Yet, in law and custom common property has long meant, in stark contrast to open access, exclusive ownership by a group. Common property regimes have been well documented, especially for natural resource stocks in less developed economies (Bailey 1992, McKay and Acheson 1987, Ostrom 1990), and their details have been studied in many settings(e.g, Acheson 1988, Dahlman 1980, Eggertson 1992, Stevenson 1991). Ma writers on common property have noted the gains from group enforcement of rights to the resource(Ellickson 1993, McKay and Acheson 1987, Ostrom 1990, and Stevenson 1991), and we examine common ownership to take this empirical feature into account Common property is best viewed as an intermediate case between open access and private ownership. Common property may arise out of explicit private contracting(e. g, unitized oil reservoirs, groundwater districts)or out of custom(e.g, common pastures and forests; it may have legal(e. g, riparian water rights)or regulatory(e. g, hunting and fishing regulations) bases that have implicit contractual origins. Contracting to form common property effectively creates a group that has exclusive rights to the resource( eggertsson 1992, Lueck 1994). Acting together There is also a property rights literature that focuses on differences between private and regulated firms(e.g bublic utilities)that we do not discuss here We return to this issue in the context of the choice of title system in section 5.1.1 Indeed Hardins(1968)famous paper incorrectly characterizes the common pastures of English villages as op access resources when the historical record shows clearly that they were common property (e.g, Dahlman 1980, Smith 2000) Further evidence that common property regimes are productive is seen from the disasters that have occurred when they have been dismantled by the state(effectively creating open access )as in the forests of Nepal and Thailand Ostrom 1990)
Lueck & Miceli – Property Law 8 The empirical literature on private property rights is of two types.28 First, there is a literature that attempts to measure the dissipation from open access and to compare resource use to that under private property. This rather small literature is dominated by studies on natural resources and especially of fisheries where open access regimes have been common (e.g., Agnello and Donnelly 1975, Bottomley 1963). These studies have estimated the deadweight losses from open access use and compared levels of asset use in open access regimes with those of private property and other limited access regimes. Second, there is a recent and growing literature on the effects of property rights security on resource use and investment. Much of this literature has focused on the investment effects of differences in legal title to land. In his survey article Besley (1998) notes that the econometric evidence for positive investment effects of more secure rights in developing countries is quite limited. These studies suffer, however, from data limitations (on both measures of investment and measures of property rights security) and from potential property rights endogeneity.29 We expect more investment with better defined rights, but as we discuss in section 4, the choice of property rights regime can itself be influenced by investment levels or other correlated variables. Thus the econometric issue is how to find an instrument for property rights variables to isolate the effect of rights on investment. Still there is some compelling evidence for the importance of property rights in the cases of natural resource use (Bohn and Deacon 2000), American Indian reservation agriculture (Anderson and Lueck 1992), and urban residential land (Miceli et al. 2002). 2.3. Common Property Rights In modern social science the term ‘commons’ or ‘common property’ originated in the analysis of what is now called open access. Yet, in law and custom common property has long meant, in stark contrast to open access, exclusive ownership by a group.30 Common property regimes have been well documented, especially for natural resource stocks in less developed economies (Bailey 1992, McKay and Acheson 1987, Ostrom 1990), and their details have been studied in many settings (e.g., Acheson 1988, Dahlman 1980, Eggertson 1992, Stevenson 1991). Many writers on common property have noted the gains from group enforcement of rights to the resource (Ellickson 1993, McKay and Acheson 1987, Ostrom 1990, and Stevenson 1991), and we examine common ownership to take this empirical feature into account.31 Common property is best viewed as an intermediate case between open access and private ownership. Common property may arise out of explicit private contracting (e.g., unitized oil reservoirs, groundwater districts) or out of custom (e.g., common pastures and forests); it may have legal (e.g., riparian water rights) or regulatory (e.g., hunting and fishing regulations) bases that have implicit contractual origins. Contracting to form common property effectively creates a group that has exclusive rights to the resource (Eggertsson 1992, Lueck 1994). Acting together 28 There is also a property rights literature that focuses on differences between private and regulated firms (e.g., public utilities) that we do not discuss here. 29 We return to this issue in the context of the choice of title system in section 5.1.1. 30 Indeed Hardin’s (1968) famous paper incorrectly characterizes the common pastures of English villages as open access resources when the historical record shows clearly that they were common property (e.g., Dahlman 1980, Smith 2000). 31 Further evidence that common property regimes are productive is seen from the disasters that have occurred when they have been dismantled by the state (effectively creating open access) as in the forests of Nepal and Thailand (Ostrom 1990)
Lueck miceli individuals can realize economies of enforcing exclusive rights to the asset. Equation (2.2) mplies that waste can be reduced simply by restricting access to the asset A contracting model can illustrate how common property can limit waste from the rule of capture.Contracting to form common property effectively creates a group that has exclu only to the group's size and the joint effort to exclude outsiders. In this setting, individuals ns rights to the resource. We assume that(contractual)agreement among group members pertains acting together can realize economies of enforcing exclusive rights to the asset, so we also assume the costs of excluding(or policing) non-members can be represented as p(n), where p'(n) 0. a simple and customary method of allocating use of common property is a rule that grants equal access to all members of the group(Ostrom 1990). Equal sharing of the asset avoids the explicit costs of measuring and enforcing individual effort(or use) but still creates an incentive for over use.Effort is not explicitly part of the common property contract'so each member chooses his own effort(xi) as he captures his share of the assets output(Y=f(xv again)in competition with other group members. The size of the group is chosen to maximize the wealth of the group subject to the constraint of aggregate effort(X )by members operating in a common property regime, and in recognition of the costs of excluding outsiders. Optimal group size is a tradeoff between increased resource use with a larger group and increased enforcement costs associated with a smaller group. Formally the problem is maxR=/∑mx(n)-∑m(wx(m)-p(m, where x f is the individuals solution to the problem in equation(2. 1). The optimal group size, no determines total effort and must satisfy the first-order necessary condition B0-∑((∑x)-)∠ dnp(n)=0 Equation (2.5)states that the gain from an additional member in terms of a marginal reduction in policing costs must equal the marginal reduction in aggregate rent from overuse of the resource The net present value of the common property resource is thus V=L R(x, ne"dt>0,where vs>y>v=0. While the value of an asset governed by common property is less than its first-best value, it could have greater value than private property depending on the magnitude of the policing cost and overuse effects The model is based on Lueck(1994). Also see Caputo and lueck(1994)and wagner(1995). Others us evolutionary game theory models(e.g. Sethi and Somanathan 1996) Common property might also be viewed as an output sharing contract with moral hazard. In this framework group members shirk as in a principal-agent model(see Lueck 1994). Evidence of both types of common property asset sharing(e. g, share access to a pasture)and output sharing(e.g share the cheese produced from cattle on the common pasture)-are found in the empirical literature Total effort is given by X =xne
Lueck & Miceli – Property Law 9 individuals can realize economies of enforcing exclusive rights to the asset. Equation (2.2) implies that waste can be reduced simply by restricting access to the asset. A contracting model can illustrate how common property can limit waste from the rule of capture.32 Contracting to form common property effectively creates a group that has exclusive rights to the resource. We assume that (contractual) agreement among group members pertains only to the group's size and the joint effort to exclude outsiders. In this setting, individuals acting together can realize economies of enforcing exclusive rights to the asset, so we also assume the costs of excluding (or policing) non-members can be represented as p(n), where p'(n) 0. A simple and customary method of allocating use of common property is a rule that grants equal access to all members of the group (Ostrom 1990). Equal sharing of the asset avoids the explicit costs of measuring and enforcing individual effort (or use) but still creates an incentive for over use.33 Effort is not explicitly part of the common property ‘contract’ so each member chooses his own effort (xi) as he captures his share of the asset’s output (Y = f(Σxi) again) in competition with other group members. The size of the group is chosen to maximize the wealth of the group subject to the constraint of aggregate effort (Xc ) by members operating in a common property regime, and in recognition of the costs of excluding outsiders. Optimal group size is a tradeoff between increased resource use with a larger group and increased enforcement costs associated with a smaller group. Formally the problem is 1 1 max ( ( )) ( ( )) ( ) c n n c i i n i i i R f x n wx n p n = = =−− ∑ ∑ , (2.4) where c i x is the individual’s solution to the problem in equation (2.1). The optimal group size, nc determines total effort34 and must satisfy the first-order necessary condition 1 1 ( ( ) ) ' '( ) 0. c n n i i i i i R dx f x w pn n dn = = ∂ ⎡ ⎤ = − −= ∂ ∑ ∑ ⎢ ⎥ ⎣ ⎦ (2.5) Equation (2.5) states that the gain from an additional member in terms of a marginal reduction in policing costs must equal the marginal reduction in aggregate rent from overuse of the resource. The net present value of the common property resource is thus 0 ( , ) 0, c c rt V R x t e dt ∞ − = > ∫ where V* > Vc > Voa = 0. While the value of an asset governed by common property is less than its first-best value, it could have greater value than private property depending on the magnitude of the policing cost and overuse effects. 32 The model is based on Lueck (1994). Also see Caputo and Lueck (1994) and Wagner (1995). Others use evolutionary game theory models (e.g. Sethi and Somanathan 1996). 33 Common property might also be viewed as an output sharing contract with moral hazard. In this framework group members shirk as in a principal-agent model (see Lueck 1994). Evidence of both types of common property – asset sharing (e.g., share access to a pasture) and output sharing (e.g. share the cheese produced from cattle on the common pasture) – are found in the empirical literature. 34 Total effort is given by 1 c n c c i i X x = = ∑
