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UBC Theses and Dissertations

Imperfect information, legal institutions and externalities Bennett, Nancy D. 1975

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IMPERFECT INFORMATION, LEGAL INSTITUTIONS, AND EXTERNALITIES by NANCY D. BENNETT B.A., Columbia University, 1970 M.A., Simon Fraser University, 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Economics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1975 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may b e g r a n t e d b y t h e H e a d o f my D e p a r t m e n t o r b y h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a D a t e 6 CC* K7*T i Chairman: G. Christopher Archibald ABSTRACT Externalities have presented a d i f f i c u l t y in the attainment of Pareto optimal competitive equilibria in decentralized market economies. An externality can be said to exist whenever technological interdepen-dencies between economic agents give rise to a divergence between social marginal cost and private marginal cost. The problem is that we have not thoroughly explored the question of why externalities persist. That i s , why are externalities not internalized optimally in a market system? Why do markets f a i l ? This thesis approaches these questions by examining the sources of market failure. One source of market failure, transaction costs, is the focus of the thesis. The assumption that transaction costs are zero is relaxed. One particular type of transaction cost, imperfect technological infor-mation, i s examined to see i f the inclusion of this transaction cost i n an otherwise competitive model can explain the persistence of specific classes of externalities. The externalities considered are private external diseconomies, i.e., interdependencies between agents that affect individuals separately. I do not consider externalities that have public good attributes. We cannot fu l l y discuss transaction costs without considering the effect of the institutions existing in an economy on these costs. This i i t h esis examines the r e l a t i o n s h i p between one i n s t i t u t i o n , the l e g a l system, and imperfect information. The l e g a l system comprises the set of i n d i v i d u a l r i g h t s , common and statutory laws, court system, and l e g a l services markets which e x i s t i n a decentralized economy. The thesis e n t a i l s a t h e o r e t i c a l examination of the persistence of p r i v a t e external diseconomies, given imperfect information. F i r s t , a taxonomy of l e g a l r i g h t s i s formulated. The importance of r i g h t s i s established by showing that the assignment of rights influences resource a l l o c a t i o n by a f f e c t i n g the equilibrium point attained given any type of e x t e r n a l i t y (private or public) and zero transaction costs. A geometric bargaining model provides a counter-example to the "Coase theorem". But t h i s model i s too general to deal with s p e c i f i c e x t e r n a l i t y and imperfect information cases. Imperfect information i n the context of e x t e r n a l i t i e s i s defined e x p l i c i t l y and.models employed to show that under c e r t a i n information/ e x t e r n a l i t y cases, p r i v a t e markets e i t h e r may not a r i s e to a l l o c a t e resources, or, i f markets do e x i s t , they may operate i n e f f i c i e n t l y . The markets examined are p r i v a t e insurance markets as they'are one type of i n s t i t u t i o n economic theory predicts would a r i s e to i n t e r n a l i z e e x t e r n a l i t i e s i n the case of imperfect information. I t i s found that insurance, as a market a l l o c a t i o n mechanism, may not i n t e r n a l i z e c e r t a i n types of e x t e r n a l i t i e s when information i s imperfect. The l e g a l system i s then examined i n greater d e t a i l as an example of a nonmarket a l l o c a t i o n mechanism. In p a r t i c u l a r , formal models are used to investigate the e f f e c t of s p e c i f i c l i a b i l i t y laws and due care standards on the attainment of Pareto optimal resource a l l o c a t i o n , given p r i v a t e e x t e r n a l i t i e s and imperfect information. I t i s found that l e g a l l i a b i l i t y rules do not i n general lead to optimal e q u i l i b r i a . In c e r t a i n cases however, l i a b i l i t y laws may improve s o c i a l welfare by providing incentives f o r the p a r t i e s involved i n the e x t e r n a l i t y to a l t e r t h e i r behavior responsible for the e x t e r n a l i t y . In contrasting p r i v a t e insurance markets and l e g a l rules with respect to the information each requires to operate and the e q u i l i b r i a attainable ( i f they e x i s t ) , i t i s found that l e g a l rules may be superior to private insurance markets. This r e s u l t occurs because l e g a l rules require l e s s precise information than do insurance markets and may also be able to a f f e c t the behavior of a l l p a r t i e s involved i n the e x t e r n a l i t y . Insurance generally covers only the p a r t i e s damaged by the e x t e r n a l i t y . In summary, t h i s thesis provides a t h e o r e t i c a l r a t i o n a l e for one type of market f a i l u r e due to e x t e r n a l i t i e s and points out a nonmarket method of improving s o c i a l welfare when exter-n a l i t i e s e x i s t . i v TABLE OF CONTENTS PAGE •..I. Introduction i 1 I I . The Role of Legal I n s t i t u t i o n s i n the Operation of Markets A. Introduction: A Taxonomy of Rights 11 B. The Importance of P r i o r Rights i n the Operation of Perfect Markets 18 1. The "Coase Theorem" 18 2. The E f f e c t of P r i o r Rights on Attainable E q u i l i b r i a 23 I I I . Imperfect Information: Operation of Contingent Markets with E x t e r n a l i t i e s A. Introduction 36 B. The Operation of Contingent Markets with Stochastic E x t e r n a l i t i e s 51 C. The Operation of Contingent Markets with Information E x t e r n a l i t i e s 66 IV. I n s t i t u t i o n a l Response to Imperfect Information: L i a b i l i t y Laws and Legal Rules A. Introduction 85 B. A l t e r n a t i v e L i a b i l i t y Rules 98 C. The E f f e c t s of L i a b i l i t y Rules on Nonmarket E q u i l i b r i a 107 1. S t r i c t L i a b i l i t y on A 110 2. S t r i c t L i a b i l i t y on G 114 3. L i a b i l i t y on G, Independent of A 118 4. L i a b i l i t y on G, Dependent on A 121 5. Negligence-Contributory Negligence 124 V PAGE D. Conclusion 130 V. Conclusion . . . . ; • 137 VI. Bibliography. •• 139 v i LIST OF TABLES PAGE Table I: Technological Information Cases ...... 45 Table I I : Legal L i a b i l i t y Rules 105 Table I I I : Optimal Care Levels f o r G 121 Table IV: Optimal Care Levels f o r A 123 Table V: E q u i l i b r i a under Negligence-Contributory Negligence Rule .... 125 Table VI: Due Care Standards for Negligence-Contributory Negligence i 126 v i i LIST OF FIGURES PAGE Figure I 29 Figure II 29 Figure I II 30 Figure IV ^.......... 31 Figure V 113 Figure VI . ... 117 Figure VII . 117 Figure VIII .. .; • 117 Figure IX • ; ... . 119 Figure X i . . . ; . 120 Figure XI • 120 Figure XII • .; 121 Figure XIII 122 Figure XIV 128 Figure XV • 135 v i i i ACKNOWLEDGMENTS I wish to thank G. Christopher Archibald, David Donaldson, and Anthony D. Scott f o r t h e i r h e l p f u l comments and c r i t i c i s m s . I would also l i k e to thank Richard G. Harris f o r bringing to my attention a number of useful references for t h i s thesis and for the many discussions with him about my to p i c . F i n a l l y , I wish to acknowledge the Canada Council and the Un i v e r s i t y of B r i t i s h Columbia f o r providing me with f i n a n c i a l support. 1 I. INTRODUCTION I t i s generally believed that e x t e r n a l i t i e s i n h i b i t the attainment of an optimal a l l o c a t i o n of resources given the assumptions of the p e r f e c t l y competitive model. That t h i s conclusion i s accepted un-equivocally by most economists i s s u r p r i s i n g , because there i s no cl e a r d e f i n i t i o n of what an e x t e r n a l i t y i s and why i t e x i s t s when a l l p e r f e c t competition assumptions are met. Terms l i k e market f a i l u r e , non-a p p r o p r i a b i l i t y , p u b l i c goods and bads, s p i l l o v e r s , etc. pervade the l i t e r a t u r e . These terms attempt to convey the notion that e x t e r n a l i t i e s are things or a c t i v i t i e s that are excluded i n the operation of the competitive p r i c e system. The t r a d i t i o n a l l i t e r a t u r e does not deal with the question of why e x t e r n a l i t i e s are excluded from competitive markets. The treatment of e x t e r n a l i t i e s i n economic theory has ignored what I consider the fundamental question: why do we observe e x t e r n a l i t i e s ? Instead, t r a d i t i o n a l e x t e r n a l i t y considerations concentrate on p o l i c y issues; what actions can be taken to i n t e r n a l i z e e x t e r n a l i t i e s . There i s a s u r f e i t of a r t i c l e s dealing with the e f f i c i e n c y and optimality of p o l i c i e s to i n t e r n a l i z e e x t e r n a l i t i e s : taxes and subsidies, merger, regulations, and quotas. Emphasis on the cure i s premature when we do not know the cause of the problem. This thesis attempts to provide a t h e o r e t i c a l r a t i o n a l e f o r the existence and persistence of a s p e c i f i c type of e x t e r n a l i t y ; a p r i v a t e , inter-personal or i n t e r - f i r m external diseconomy. I t i s not possible to examine a l l types of e x t e r n a l i t i e s , so I s h a l l therefore concentrate on p a r t i c u l a r examples. Before defining the cases I s h a l l be concerned 2 with, I would l i k e to examine a general d e f i n i t i o n of e x t e r n a l i t y , point out some of i t s weaknesses, then introduce what I f e e l i s a major cause of the persistence of s p e c i f i c types of e x t e r n a l i t i e s , namely, trans-action costs. A prevalent d e f i n i t i o n i n the l i t e r a t u r e suggests that an e x t e r n a l i t y e x i s t s when the u t i l i t y of an i n d i v i d u a l or a firm's p r o f i t i s dependent upon a c t i v i t i e s generated by another i n d i v i d u a l or firm. The affe c t e d agent i s assumed to be unable to con t r o l the a c t i v i t i e s . This d e f i n i t i o n i s due to a number of people, in c l u d i n g Meade (1952) and Buchanan and Stubblebine (1962). I t has been u t i l i z e d i n most of the e x t e r n a l i t y l i t e r a t u r e with varying degrees of mathematical rigour. The " a c t i v i t i e s " , never c l e a r l y defined, are assumed to be incompletely p r i c e d i n competi-t i v e markets or not p r i c e d at a l l . A c t i v i t y i s a general term that i s interpreted according to the case at hand. For example, an a c t i v i t y can e n t a i l the use of a factor of production (land, water, a i r ) , or be derived from a good (neighbour's flower garden) of bad (noise, s t i n k ) . I pre f e r to view incompletely p r i c e d a c t i v i t i e s using Pigou's terminology (1932). E x t e r n a l i t i e s w i l l a r i s e when technological interdependencies are com-bined with a divergenceebetween p r i v a t e marginal costs (or products) and s o c i a l marginal costs (or products). Some component of the e x t e r n a l i t y may thus be pr i c e d , but the p r i c e i s not necessa r i l y equivalent to the s o c i a l marginal value of the a c t i v i t y . The important aspect of the d e f i n i t i o n i s the assertion that exter-n a l i t i e s are unpriced or i n s u f f i c i e n t l y p r i c e d . Herein l i e s ; one. o f t h e shortcomings of the d e f i n i t i o n . The a c t i v i t y i s assumed to be unpriced. \ 3 Therefore, markets f o r the exchange of the goods or factors that generate e x t e r n a l i t i e s do not e x i s t or operate imperfectly by assumption. The term market f a i l u r e may be used, following Bator (1958) to describe t h i s s i t u a -t i o n , i . e . , the non-existence or i n e f f i c i e n t operation of c e r t a i n markets i n the competitive framework. 1 The problem with the t r a d i t i o n a l exter-n a l i t y l i t e r a t u r e i s that i t gives i n s u f f i c i e n t explanation f or the i n e f f i c i e n c y or non-existence of markets where there are e x t e r n a l i t i e s . We observe that c e r t a i n markets do not e x i s t or work imperfectly. Methodologically, should the non-existence or imperfection of markets be an assumption or a hypothesis i n a model? I would argue that market f a i l u r e should be derived from a set of i n i t i a l conditions, such as assumptions about the behavior of economic agents, the i n s t i t u t i o n s a f f e c t i n g economic behavior, technological r e l a t i o n s h i p s , and so on. The t r a d i t i o n a l l i t e r a t u r e generally ignores these i n i t i a l conditions and assumptions, trea t s market f a i l u r e as an (or the) assumption, then proceeds to analyze methods of p r i c i n g e x t e r n a l i t i e s optimally. I think that the fundamental explanation f o r the presence of e x t e r n a l i t i e s i s that lesstthan a f u l l set of markets operate i n an 2 economy. I f there are n goods i n the economy, then i n theory (n - 1) markets w i l l e x i s t . What I ask i s why c e r t a i n markets, those inv o l v i n g 1 Market f a i l u r e was analyzed by Bator (1958), but never i n a rigorous fashion. Bator's c l a s s i f i c a t i o n i s too broad and not useful f o r my an a l y s i s . My i n t e r e s t i n the market f a i l u r e approach emanates from a stimulating paper by Arrow (1969). 2 E x t e r n a l i t i e s are not the only r e s u l t of an economy that operates l e s s than a f u l l set of markets. Other examples are the lack of futures markets and c e r t a i n markets for risk-bearing. 4 e x t e r n a l i t i e s , do not e x i s t . Consider an economy with sets of markets for a l l possible present and future goods. A l l goods can be exchanged through markets i n t h i s economy. For example, i n d i v i d u a l s would pay fo r the r i g h t to view each other's gardens, to dump garbage i n the r i v e r , to blow smoke i n people's faces, etc. Perhaps the f i r s t thing one would notice i n such an economy i s that s u b s t a n t i a l amounts of resources are being devoted to the operation of markets. Processes of gathering and as s i m i l a t i n g information, monitoring agents' actions, and enforcing the rules under which markets operate would be extensive, and one might guess, very c o s t l y . One might ask i f the use of the resources to operate markets i s warranted. In the r e a l world, we do not observe at any point i n time, a l l possible markets i n operation. One reason why a pr i v a t e , unregulated market may not e x i s t i s that there e x i s t transaction costs of operating the market. 1 Transaction costs are a function of the i n s t i t u t i o n a l c h a r a c t e r i s t i c s of an economy. As Arrow (1969, p. 48) has noted, "market f a i l u r e i n general and e x t e r n a l i t i e s i n p a r t i c u l a r are r e l a t i v e to the mode of economic organization". Market f a i l u r e i s not a techno-l o g i c a l phenomenon, nor i s i t absolute. Technology w i l l determine the 1 Of course, markets may f a i l f o r other reasons, namely when goods are consumed p u b l i c a l l y . Many e x t e r n a l i t i e s have pu b l i c good a t t r i b u t e s . Smoke p o l l u t i o n , f o r example, w i l l be a pu b l i c bad because once the p o l l u t i o n i s generated, many i n d i v i d u a l s consume i t simultaneously. There i s a vast amount of l i t e r a t u r e on the r e l a t i o n s h i p between exter-n a l i t i e s and pu b l i c goods. I do not wish to enter t h i s taxonomic debate. My thesis w i l l concentrate on pri v a t e e x t e r n a l i t i e s to avoid the added complexities introduced by pu b l i c goods. In addition, I w i l l examine only external diseconomies as they are em p i r i c a l l y more s i g n i -f i c a n t than external economies and present a more complex (and hence, interesting) set of problems. 5 method of producing goods, but i t does not determine which goods are marketed. I t could be argued that there e x i s t technological r e l a t i o n -ships between e x t e r n a l i t i e s and goods or factors that lead to j o i n t consumption or production. In a dynamic economy, the degree of j o i n t -ness w i l l vary with the state of the technology. The non-marketing of c e r t a i n goods j o i n t l y produced or consumed i s not a function of tech-nology, but rather due to transaction costs. Transaction cost i s a general term and we must examine the sources of these costs. Transaction costs can be defined as the costs i n terms of r e a l resources consumed of exchanging t i t l e to ownership of a commodity (goods or factors) (Demsetz, 1968, p. 35). Other possible synonomous terms include contracting costs and marketing costs. What gives r i s e to these costs? In general cases of e x t e r n a l i t y , there are two major sources of transaction costs. F i r s t , excluding non-buyers from consuming c e r t a i n commodities may be t e c h n o l o g i c a l l y impossible or require a large expenditure of resources. This cost i s known as non-a p p r o p r i a b i l i t y . 1 An example i s p o l l u t i o n abatement. D i r t y a i r i s shared by a large number of i n d i v i d u a l s who have no a b i l i t y i n d i v i d u a l l y to a l t e r the amount and q u a l i t y of the a i r they consume. The costs of monitoring agents' behavior could also be included i n t h i s category. I s h a l l not deal with e x t e r n a l i t i e s that p e r s i s t because of non-appropriability, but focus on another type of transaction cost. I s h a l l concentrate on transaction costs that a r i s e from uncertainty and imperfect information. This category i s somewhat general and can 1 Non-appropriability i s also a necessary condition for the existence of p u b l i c goods. 6 include f o r example, the costs of negotiating a contract, and the costs of obtaining information about the p r i c e s or q u a l i t y of a good, i n d i v i -duals' preference orderings, or technological r e l a t i o n s h i p s between j o i n t l y produced or consumed goods. We could also consider incentive problems; what i s necessary to induce agents to reveal information? Information, or the lack of i t , i s an extremely important source of transaction costs. There i s some debate whether transaction costs are a function of information or the reverse. I pre f e r , following Arrow (1969), to consider transaction cost the general category, with informa-t i o n problems a contributory source of the costs. When dealing with models incorporating transaction costs, one has to c l e a r l y specify the information structure f o r a l l economic agents involved. We must now ask how i n s t i t u t i o n s can influence transaction costs. , This question cannot be answered without an examination of l e g a l rules and property r i g h t s . I s h a l l therefore focus my attention .on l e g a l i n s t i t u t i o n s , i . e . , the set of common and statutory laws and the l e g a l system which enacts and enforces these laws i n a decentralized economy. Rights have an important e f f e c t on.information costs. I f r i g h t s are non-existent or non-exclusive for. a p a r t i c u l a r resource, or good, a common property s i t u a t i o n e x i s t s and the.market for that resource or good may f a i l . T r a n s f e r a b i l i t y of ri g h t s w i l l also a f f e c t costs. I f a r i g h t f o r the exchange of a good i s non-transferable, the market f o r that used good does not e x i s t . Where t r a n s f e r a b i l i t y r i g h t s e x i s t but are co s t l y , only c e r t a i n subsets of markets may operate. T r a n s f e r a b i l i t y and e x c l u s i v i t y i n turn depend on l e g a l i n s t i t u t i o n s which have the task of d e l i n e a t i n g and enforcing r i g h t s , for example, the determination of l i a b i l i t y laws. Operation of l e g a l i n s t i t u t i o n s i s not c o s t l e s s , and these transaction costs w i l l a f f e c t the operation of markets. Demsetz (1966, 1969) and others (of the "Chicago school") have argued that markets for e x t e r n a l i t i e s w i l l not e x i s t when the transaction costs of operating these markets are too high. This assertion i s i n v a l i d without an examination of the e f f e c t s of l e g a l rules and i n s t i t u t i o n s on trans-action costs. Costs that are "too high" under one set of i n s t i t u t i o n s may be low enought to make the market work with other sets of i n s t i t u -tions or r i g h t s . A question a r i s e s at t h i s point as to whether transactionucosts can be reduced by government control of the exchange of goods. That i s , given that there are costs of operating markets p r i v a t e l y , can c e n t r a l c o n t r o l by government e f f i c i e n t l y a l l o c a t e resources with l e s s cost than the market? To show that government con t r o l i s l e s s c o s t l y requires, f o r example, that government has more information, can p o l i c e r i g h t s with les s cost, or, because of i t s s i z e , can pool r i s k s and operate insurance markets. I t cannot be assumed that c e n t r a l i z e d government con t r o l of resource a l l o c a t i o n i s superior to decentralized p r i v a t e market a c t i v i t y . The assumption of competitive e q u i l i b r i a i n a l l possible markets presents some d i f f i c u l t i e s i n my a n a l y s i s . I t may not be a v a l i d 1 Any v e r i f i c a t i o n of the s u p e r i o r i t y of government con t r o l over p r i v a t e market operation i s hampered by the lack of an economic theory of government. No c l e a r l y defined objective function e x i s t s for e i t h e r consumption or,production a c t i v i t i e s of governments. Without some empirical evidence, we are l e f t only with assumptions about the government's a b i l i t y to minimize transaction costs. 8 assumption when transaction costs e x i s t . The t r a d i t i o n a l e x t e r n a l i t y l i t e r a t u r e argues that given any type of e x t e r n a l i t y , competitive equi-l i b r i a e x i s t , but the r e s u l t i n g e q u i l i b r i a may not be Pareto optimal. I f transaction costs are zero, what Negishi (1972) and others have im-p l i c i t l y shown i s that e x t e r n a l i t i e s w i l l not p e r s i s t i n competitive markets. 1 Markets would be c o s t l e s s l y set up or emerge to i n t e r n a l i z e a l l e x t e r n a l i t i e s , and we would observe Pareto optimal resource a l l o c a t i o n s . Systems of taxes and subsidies, bargaining, merger, and so on are equiva-l e n t to implementing markets i n these t r a d i t i o n a l e x t e r n a l i t y models. But, why would these p o l i c i e s even be necessary i n a world of costless trans^ actions? Without some form of transaction cost, for example, imperfect information, l e g a l r e s t r i c t i o n s on l i a b i l i t y claims, government interven-t i o n i n markets, we would not expect to observe e x t e r n a l i t i e s i n competitive markets. The assumption of competitive e q u i l i b r i a thus precludes exter-n a l i t i e s and the assumption of transaction costs may preclude p e r f e c t competition. When one considers c e r t a i n transaction costs e x p l i c i t l y (for example, imperfect information), competitive e q u i l i b r i a may be 2 incompatible with e f f i c i e n t and optimal e q u i l i b r i a . In addition, 1 This conclusion does not hold i f e x t e r n a l i t i e s give r i s e to noncon-v e x i t i e s i n production or consumption p o s s i b i l i t y sets. See Arrow (1969) and S t a r r e t t (1972) for a discussion of e x t e r n a l i t i e s and nonconvexity. See Negishi (1972) for a proof of the conclusion i n a general equilibrium model. Papers by Ledyard (1971) and Osana (1972) have shown that under c e r t a i n assumptions about the nature of exter-n a l i t i e s and information i n the economy, the welfare theorems may hold. Also see Camacho (1970). No one, to my knowledge, has e x p l i c i t l y examined the welfare theorems under d i f f e r e n t transaction cost assumptions. 2 See Chapter I I I , part C of t h i s t h e s i s . 9 transaction costs may lead to nonconvexities which can prevent the attainment of competitive market e q u i l i b r i a . Transaction costs may thus give r i s e to market f a i l u r e due to e x t e r n a l i t i e s . The t r a d i t i o n a l e x t e r n a l i t y l i t e r a t u r e has not considered transaction costs e x p l i c i t l y . Their c o r r e c t i v e solutions imply the creation of markets, but the solutions t e l l us l i t t l e about the f e a s i -b i l i t y and optimality of the r e s u l t i n g e q u i l i b r i a . The costs of operating these c o r r e c t i v e p o l i c i e s and the types of transaction costs that give.vrise to market f a i l u r e due to e x t e r n a l i t i e s are ignored. By examining the pos-s i b l e types of transaction costs that give r i s e to e x t e r n a l i t i e s , one adds both a more r e a l i s t i c dimension to the analysis of the problem and a more consistent t h e o r e t i c a l framework for analysis. The t r a d i t i o n a l l i t e r a t u r e does not give a s a t i s f a c t o r y explanation f o r the persistence of exter-n a l i t i e s . As Crocker (1973, p. 563) has noted To assert that a r e s u l t i s e f f i c i e n t because i t i s the outcome that would occur with omnipresent markets a f t e r having i n i t i a l l y made a set of assumptions inexorably leading to the conclusion that a market i s the only form of economic <•-J. peraL, -\ cooperation that leads to e f f i c i e n t outcomes i s not very enlightening. I f markets are i n f a c t c o s t l y , t h i s sort of reasoning does not provide any obvious conclusions about the e f f i c i e n c y of markets or of any other i n s t i t u t i o n s as modes of a l l o c a t i o n and economic cooperation. The approach to e x t e r n a l i t i e s o u t l i n e d i n t h i s introduction gives r i s e to a number of i n t e r e s t i n g and, as yet, unanswered problems. One could develop p a r t i a l and general equilibrium models of markets with transaction costs and e x t e r n a l i t i e s under a v a r i e t y of assumptions about transaction costs and i n s t i t u t i o n s . From these models, one could then t 10 develop and evaluate a l t e r n a t i v e methods of i n t e r n a l i z i n g e x t e r n a l i t i e s and apply the analysis to " r e a l world" problems. This t h e s i s concentrates on one p a r t i c u l a r aspect of the problem of e x t e r n a l i t i e s and transaction costs, the e f f e c t s of imperfect information on market and nonmarket a l l o c a t i o n mechanisms with e x t e r n a l i t i e s . I s h a l l deal with p r i v a t e external diseconomies. I do not consider cases where e x t e r n a l i t i e s are p u b l i c i n nature. Examples of the type of e x t e r n a l i t i e s I s h a l l examine include upstream-downstream p o l l u t i o n , . d e f e c t i v e products that i n j u r e i n d i v i d u a l s , and i n d u s t r i a l p o l l u t a n t s that a f f e c t i n d i v i d u a l workers. The t h e s i s i s structured as follows. Chapter. TI considers the r o l e of l e g a l i n s t i t u t i o n s i n the operation' of competitive markets. A taxonomy, of l e g a l r i g h t s i s formulated, and the impact, of one type of these r i g h t s on resource, a l l o c a t i o n w i t h . t r a d i t i o n a l e x t e r n a l i t i e s i s examined. Exter-n a l i t i e s are treated generally i n t h i s chapter, as I wish, to point out.the l i m i t a t i o n s of the t r a d i t i o n a l analysis and the need'to choose s p e c i f i c e x t e r n a l i t y cases f o r formal analysis... Chapter I I I defines e x t e r n a l i t i e s i n the context of imperfect information as a s p e c i f i c transaction.cost, and examines the f e a s i b i l i t y of using p r i v a t e insurance markets to. i n t e r n a l i z e e x t e r n a l i t i e s i n a decentralized economy. As the r e s u l t s in.Chapter III with regard to insurance markets are. rather pessimistic,.Chapter IV con-siders the use of the legal, system as a nonmarket al l o c a t i o n , mechanism, concentrating on the use of l i a b i l i t y r u l e s to i n t e r n a l i z e e x t e r n a l i t i e s . The general r e s u l t s and.implications of the t h e s i s are summarized i n Chapter V. 11 I I . THE ROLE OF LEGAL INSTITUTIONS IN THE OPERATION OF MARKETS A. Introduction: A Taxonomy of Legal Rights I t has been asserted that the assignment of property r i g h t s and l e g a l i n s t i t u t i o n s i n general have no e f f e c t on the a l l o c a t i o n of resources and operation of markets (or exchange processes) i n a competi-t i v e economy (e.g., Furubotn and Pejovich (1972), Coase (1960), Demsetz (1966,1967)). The only way i n which these i n s t i t u t i o n s are assumed to influence economic decision-making i s through t h e i r d i s t r i b u t i v e e f f e c t s . Rights are only supposed to a f f e c t the l e v e l and d i s t r i b u t i o n of income and can thus be ignored i n models concerned with a l l o c a t i v e e f f i c i e n c y when a l l competitive assumptions are met. 1 I f , however, t h i s assertion i s i n c o r r e c t , and r i g h t s do a f f e c t resource a l l o c a t i o n , then models which abstract from consideration of r i g h t s and other l e g a l constraints may y i e l d predictions that are i n v a l i d i n c e r t a i n cases. Two questions a r i s e . F i r s t , i s the assertion that r i g h t s do not a f f e c t resource a l l o c a t i o n v a l i d ? Secondly, i f a l t e r n a t i v e assignments of r i g h t s a f f e c t the r e l a t i v e p r i c e s of goods and/or fact o r s , how and when should l e g a l variables be introduced i n t o economic models? I t i s my i n t e n t i o n to show that l e g a l i n s t i t u t i o n s do a f f e c t resource a l l o c a t i o n , and that i t i s necessary to include an e x p l i c i t consideration of r i g h t s i n any attempt to explain the existence and persistence of e x t e r n a l i t i e s . 1 A d i s t u r b i n g consequence of the assertion that property r i g h t s do not a f f e c t competitive e q u i l i b r i a i s that t h i s assertion can be interpreted to imply the optimality of e x i s t i n g r i g h t s and used to j u s t i f y the status quo. 12 Let me f i r s t note that the enti r e argument concerning the symmetry (or n e u t r a l i t y or invariance) of ri g h t s i n the context of a f u l l set of markets with zero transaction costs i s of l i t t l e relevance to the prob-lem of e x t e r n a l i t y . As noted i n Chapter I, we cannot assume the existence of e x t e r n a l i t i e s i n a world where a l l the assumptions of per f e c t competi-t i o n are met. The presence of c e r t a i n types of r i g h t s and l i a b i l i t y r ules suggests that the competitive assumption (or requirement) of univers a l markets (Arrow (1969)) may be v i o l a t e d . What i s missing i n most economists' discussion of l e g a l i n s t i t u t i o n s i s a systematic d e f i n i -t i o n and analysis of these i n s t i t u t i o n s . The term "property r i g h t " i s , for example, used by economists to mean a v a r i e t y of things and i s often not defined at a l l . I t i s neither appropriate nor meaningful to i n s e r t r i g h t s or laws in t o competitive models without sp e c i f y i n g what r i g h t s are or how they r e l a t e to the necessary and s u f f i c i e n t conditions f o r the existence of p e r f e c t l y competitive markets. A r t i c l e s such as those by Furubotn and Pejovich (1972), Coase (1960), and Demsetz (1966) are subject to t h i s c r i t i c i s m , and we must thus be suspicious of t h e i r assertions and "theorems". Before considering the e f f e c t of l e g a l i n s t i -tutions on the generation of e x t e r n a l i t i e s , I f i n d i t necessary to discuss the possible rol e s of these i n s t i t u t i o n s i n the competitive model. This task w i l l begin with a b r i e f taxonomic discussion of l e g a l i n s t i t u t i o n s . The following c l a s s i f i c a t i o n of l e g a l i n s t i t u t i o n s i s not exhaustive. I am only considering the c i v i l l e g a l procedures ( e s s e n t i a l l y the law of torts) that can a f f e c t the operation of markets and the existence of e x t e r n a l i t i e s . Becker (1968), S t i g l e r (1970), and others have examined 13 the e f f e c t s of criminal law on the production of crime and i l l e g a l a c t i v i t i e s . I do not wish to consider these t o p i c s , although i t could be argued that criminal laws p e r t a i n to e x t e r n a l i t y s i t u a t i o n s . My analysis s i m p l i f i e s many l e g a l concepts and does not deal with the i n t r i c a t e and subtle nuances of the law. The i n t e n t i o n i s not to incorporate a l l aspects of l e g a l systems i n t o economic an a l y s i s , but rather to consider someggeneral and abstract p r i n c i p l e s of law as they apply to the behavior of economic agents and the operation of markets. 1 Most laws act as constraints on economic agents' choice sets. Posner (1972, p. 393) defines a law as a "command backed by the coercive power of the state". Although i t i s conceivable that people derive u t i l i t y (either p o s i t i v e or negative) from laws, I do not f e e l that the treatment of laws as arguments of u t i l i t y functions w i l l a i d i n an analysis of the existence of markets f o r goods. The d e r i v a t i o n of demand functions f o r laws would not resolve the d i f f i c u l t i e s that e x t e r n a l i t i e s pose f o r decentralized economies. Although i n d i v i d u a l s do not demand laws i n my a n a l y s i s , they may require adjudication to obtain an assign-ment of r i g h t s . Adjudication i n turn requires l e g a l s e r v i c e s , and 2 i n d i v i d u a l s may thus demand l e g a l services (a derived demand). In my 1 I also wish to ignore at t h i s point, the d i f f i c u l t and p r i o r problems of r a t i o n a l i z i n g the emergence of laws, l e g a l i n s t i t u t i o n s , and governments that enact these laws. See part A of Chapter IV f o r a b r i e f discussion of some of the problems of determining r i g h t s . For the purposes of t h i s chapter, I merely assume that the necessary l e g a l i n s t i t u t i o n s e x i s t and r i g h t s are defined. 2 c:In Chapter IV, I consider some possible e f f e c t s of the l e g a l services market on the determination of r i g h t s . 14 analysis, laws must therefore enter economic models as constraints on behavior and choice. The type and nature of the constraint depends upon the law under consideration and the economic assumptions d e f i n i n g agents' environments and behavior. Certain laws make sense only under s p e c i f i c assumptions about the state of the world. I propose the following taxonomy. 1 Laws as constraints can be p a r t i t i o n e d i n t o two categories: p r i o r r i g h t s and contingent r i g h t s . P r i o r r i g h t s comprise those laws which govern the ex ante d i s t r i b u t i o n and use of resources. They are necessary for the operation of an economic system. In an i d e a l world, analogous to the world depicted by Arrow and Debreu (1951, 1954, 1959), p r i o r r i g h t s should s a t i s f y four conditions. They must be comprehensive, exclusive, transferable, and 2 enforceable, to allow f o r the possible e f f i c i e n t operation of markets. Comprehensiveness means that p r i o r r i g h t s must be defined over a l l commodities. The d e f i n i t i o n of commodity becomes c r u c i a l i n t h i s context. To make any sense, r i g h t s must cover both the p h y s i c a l a t t r i -butes of commodities and the services rendered by commodities as d i s t i n c t e n t i t i e s . For example, labour services and the actual workers are separate commodities. Workers have the r i g h t to s e l l t h e i r services but _ This taxonomy i s not exhaustive; c l e a r l y other c l a s s i f i c a t i o n s of laws and l e g a l rules are poss i b l e . 2 The f i r s t three conditions are discussed by Posner (1972) i n a d i f f e r e n t context, and are modified somewhat to f i t my taxonomy. Also see Cheung (1970). Note that i f p r i o r r i g h t s do not s a t i s f y the four conditions, markets may s t i l l e x i s t , but may function i n e f f i c i e n t l y . In these cases, market f a i l u r e may s t i l l e x i s t . 15 not themselves. Firms may own (de facto) the r i g h t to emit p o l l u t i o n (a negative commodity s e r v i c e ) , but they do not a c t u a l l y own the p h y s i c a l commodity being p o l l u t e d ( a i r , water, e t c . ) . The laws that a f f e c t com-prehensiveness of p r i o r r i g h t s could be c a l l e d property laws and these laws give r i s e to property r i g h t s . This use o f the term i s more s p e c i f i c than the somewhat i n e x p l i c i t d e f i n i t i o n s of property r i g h t s given i n the t r a d i t i o n a l l i t e r a t u r e . One function of p r i o r r i g h t s i s thus the d e l i m i -t a t i o n of i n i t i a l endowments, that i s , wealth, i n the form of ownership of property: p h y s i c a l commodities and commodity ser v i c e s . P r i o r r i g h t s must be exclusive. Two d i f f e r e n t agents (or sets of agents) cannot possess the same r i g h t to property at the same time. The i n e f f i c i e n c i e s r e s u l t i n g from the non-exclusive ownership of resources have been the subject of considerable study (common property resources). The t h i r d condition f o r p r i o r r i g h t s i s that they should be transferable. The law of contracts a f f e c t s exchange of p r i o r r i g h t s . Contract laws enable owners of property r i g h t s to make and set the conditions of exchange of the commodities under t h e i r c o n t r o l , i . e . , they help to define markets and are a necessary condition for the existence of markets. Laws of contracts can impose constraints on the terms of exchange. In an i d e a l world where r i g h t s correspond to a l l commodities, laws of contract must also e x i s t to govern the exchange of the commodity and the r i g h t to use that commodity. The s p e c i f i c i t y of contracts w i l l depend upon the other assumptions of any model. For example, i f information i s p e r f e c t and there i s no uncertainty as to d e f a u l t i n the terms of trade, p r o v i s i o n need not be made to spe c i f y recourse f o r breach of contract. I t would be 16 known with c e r t a i n t y at the i n i t i a t i o n of exchange that a l l terms would be met. Or, agents may write contingent contracts that c l e a r l y e s t a b l i s h the rules i n cases of default. I t i s important to note that the imposi-t i o n of p r i o r r i g h t s may not be s u f f i c i e n t to handle a l l decision-making problems of agents. P r i o r r i g h t s must be enforceable by the l e g a l system i f they are to have any e f f e c t on i n d i v i d u a l s ' behavior. But r i g h t s must not only be enforceable, they must also be enforced. In summary, p r i o r r i g h t s w i l l specify the exclusive ownership and rules of exchange f o r a l l commodities i n an Arrow-Debreu so r t of world. Contingent r i g h t s p e r t a i n to those laws which are necessary i n an imperfectly informed world to determine the d i s t r i b u t i o n of property r i g h t s a f t e r an unforseen event occurs. The existence of contingent r i g h t s thus implies, that one or more of the p r i o r r i g h t s ' conditions are not met. L i a b i l i t y rules and the adjudication process are the means by which l e g a l i n s i t u t i o n s determine the assignment of contingent r i g h t s . More s p e c i f i c a l l y , contingent or ex post r i g h t s apply to a world where recontracting e x i s t s and i s necessary. In an Arrow-Debreu world with p r i o r r i g h t s , a l l decisions are taken and a l l contracts made once-for-a l l . Uncertainty and imperfect information do not present problems i f contracts can be written to cover a l l uncertain events and contingent claims. There i s no need f o r contingent l i a b i l i t y or f a u l t laws that determine r i g h t s i n the case of unforseen events or i f contracts are broken. A world where a l l p r i o r r i g h t s e x i s t i s s t a t i c : there i s no unforseen technological change without appropriate insurance markets; and there i s no need ever to redefine r i g h t s . Contingent r i g h t s apply 17 to an imperfect world where contingent contracts cannot be made ex ante because agents lack information. I t i s assumed that contingent r i g h t s are necessary because transact t i o n costs e x i s t i n the operation of contingent claims markets. As noted i n Chapter I, the a c q u i s i t i o n and dissemination of information i s a transaction cost. There would be no need f o r contingent r i g h t s or l e g a l i n s t i t u t i o n s to define these r i g h t s i f information were perf e c t . P r i v a t e markets f o r r i s k bearing would a r i s e to handle uncertain events given the d e l i m i t a t i o n of p r i o r r i g h t s . The question i s why insurance markets do not tend to operate when information i s imperfect, that i s , when p r i o r r i g h t s are i n e f f e c t i v e . Chapter I II examines t h i s question i n d e t a i l . This chapter confines i t s anafysis-to p r i o r r i g h t s . One might also say that the determination of new r i g h t s f a l l s i n t o the contingent r i g h t category. New r i g h t s , l i k e new goods, are d i f f i c u l t to deal with. Simply de f i n i n g p r i o r r i g h t s over a l l possible commodities does not solve the problem adequately. The existence of contingent r i g h t s also necessitates a l e g a l adjudication system; some method of assigning claims and r i g h t s a f t e r the occurrence of an unforseen event. Bargaining i s not necessarily a f e a s i b l e nor e f f i c i e n t method of deter-mining r i g h t s when transaction costs are not zero. There are two basic ways of introducing adjudication into economic ana l y s i s . The f i r s t , exemplified by Landes (1971) and Martin (1972), introduces a court or l i t i g a t i o n system, whereelawyers, judges, and j u r i e s are given objective functions. These groups are assumed to deter-mine r i g h t s a f t e r an event on the basis of the evidence given by the 18 agents involved i n a r i g h t s dispute and on c e r t a i n prescribed sets of common and statutory law. Determination of r i g h t s by t h i s approach i s p r o b a b i l i s t i c and d i f f i c u l t to model. A second, more rigorous approach i s taken by Diamond (1974a, 1974b) and Green (1974a). They are concerned with the e f f e c t of s p e c i f i c l i a b i l i t y r u l e s on agents' behavior. They examine the optimality of l i a b i l i t y systems and attempt to formulate imperfect information problems by r e l a t i n g agents' a c t i v i t i e s p r i o r to the unforseen event to l e g a l standards f o r these a c t i v i t i e s . They f i n d that only c e r t a i n types of l i a b i l i t y rules and standards can lead to e f f i c i e n t e q u i l i b r i a . Chapter IV modifies Diamond's and Green's models to deal with c e r t a i n types of e x t e r n a l i t i e s . Given t h i s b r i e f discussion of r i g h t s , I s h a l l examine the e f f e c t of p r i o r r i g h t s on resource a l l o c a t i o n i n t h i s chapter, then consider i n Chapters III and IV market and nonmarket methods of analyzing contingent r i g h t s ( r e s p e c t i v e l y ) . B. The Importance of P r i o r Rights i n the Operation of Perfect  Markets 1. The "Coase theorem" Coase argued, i n h i s discussion of the e f f e c t of property r i g h t s on resource a l l o c a t i o n with e x t e r n a l i t i e s , that " I t i s necessary to know whether the damaging business i s l i a b l e or not f o r damage caused since without the establishment of t h i s i n i t i a l d e l i m i t a t i o n of r i g h t s there can 19 be no market transactions to tr a n s f e r and recombine them. But the u l t i -mate r e s u l t (which maximizes the value of production) i s independent of the l e g a l p o s i t i o n i f the p r i c i n g system i s assumed to work without cost" .(•lf60> p. 8). This statement and Coase's p a r t i a l equilibrium example of the cows and corn has been interpreted by many economists w r i t i n g about e x t e r n a l i t y problems to mean that the assignment of property r i g h t s does not matter i n the p r e s c r i p t i o n of solutions f o r e x t e r n a l i t i e s from an a l l o c a t i v e standpoint. P r i o r r i g h t s must be assigned to one party, but i t i s then asserted that the e f f i c i e n t equilibrium points reached by al t e r n a t i v e assignments of property r i g h t s are i d e n t i c a l regardless of who possesses the r i g h t . I w i l l c a l l t h i s a s s e rtion the "Coase theorem". I t can be shown that the "Coase theorem" does not i n general lead to the conclusion that e f f i c i e n t equilibrium points are unaffected by v a r i a b l e property r i g h t s . Coase's r e s u l t i s a s p e c i a l case. There i s no guarantee that h i s s o l u t i o n w i l l be obtained under our usual assumptions made i n u t i l i t y and p r o f i t maximization models. There has been considerable debate over what Coase d i d and di d not ac t u a l l y say. The question i s whether the "Coase theorem"-was a c t u a l l y asserted by Coase. His p a r t i a l equilibrium example concluded that the same equilibrium point i s attained independent of the assignment of p r i o r r i g h t s to the farmer or the rancher. The problem i s that Coase had no formal model and h i s arguments were based on many i m p l i c i t assump-ti o n s . In dealing with a problem such as e x t e r n a l i t i e s which do not f i t n i c e l y i n t o the competitive framework, one has to maKe e x p l i c i t assump-tions about agents' behavior, and what constitutes an equilibrium. Coase 20 and many of h i s followers have f a i l e d to specify the objective functions of the p a r t i e s involved i n an e x t e r n a l i t y , the behavioral assumptions, and the poss i b l e e q u i l i b r i a . Coase must make the following assumptions to obtain the r e s u l t s indicated i n h i s cows and corn example: pe r f e c t competition i n a l l markets, pe r f e c t d i v i s i b i l i t y of a l l factors of production and products, zero transaction costs (in the assignment of ri g h t s and bargaining process), and the existence of rents. His example considers only two firms who both operate i n d i f f e r e n t competitive f a c t o r and product markets (yet both firms earn re n t s ) . A l l other firms i n the two indus-t r i e s are unaffected by the e x t e r n a l i t y (straying c a t t l e i n Coase's case). The two firms bargain p r i v a t e l y and the s o l u t i o n attained i s assumed to have no e f f e c t on r e l a t i v e p r i c e s i n the respective i n d u s t r i e s of both firms. Coase therefore' has a very p a r t i a l type of ana l y s i s . He did acknowledge that the assignment of p r i o r r i g h t s would matter when transaction costs were considered. He d i d not elaborate formally on how transaction costs a f f e c t resource a l l o c a t i o n , nor on the r e l a t i o n s h i p between e x t e r n a l i t i e s and transaction costs. He i m p l i c i t l y recognized the importance of property r i g h t s as p r i o r r i g h t s that are necessary f o r the operation of markets, but he d i d not explain c l e a r l y how ri g h t s a f f e c t resource a l l o c a t i o n . I w i l l not reproduce Coase's numerical example, but s h a l l i n d i c a t e some of the problems with his a n a l y s i s . Note that e x t e r n a l i t i e s appear as mysterious aberrations i n Coase's a n a l y s i s . We do not know how an ex t e r n a l i t y could p o s s i b l y a r i s e i n a world which s a t i s f i e s ; Coase's 21 i m p l i c i t assumptions. Coase thus helped to e s t a b l i s h the t r a d i t i o n a l e x t e r n a l i t y framework (discussed i n Chapter I ) . He merely assumed that e x t e r n a l i t i e s e x i s t , yet incorporates assumptions inconsistent with the presence of e x t e r n a l i t i e s . One can c r i t i c i z e Coase on many grounds; h i s "model" i s imprecise, e.g., were both firms maximizing p r o f i t s before the change i n the l e g a l r u l e , i s there free entry and e x i t , what happens i f the e x t e r n a l i t y and ri g h t s p e r t a i n to a factor that i s paid i t s marginal product (does not earn r e n t s ) , what happens i n a general equilibrium context, etc. The assumption of rents f o r example, i s c r u c i a l to Coase's a n a l y s i s . Once the assignment of r i g h t s i s made, Coase's bargaining method requires the party without the ri g h t s to pay the party with the r i g h t s i f he wishes an increase (or decrease) i n the l e v e l of the good generating the exter-n a l i t y . This t r a n s f e r must be a pure rent i f we are to leave r e l a t i v e prices unaffected and keep both firms i n t h e i r respective i n d u s t r i e s i n t h i s p a r t i a l equilibrium world. The f i r m without the r i g h t s must be earning rents p r i o r to the tr a n s f e r . I f not, and he was i n long run equilibrium p r i o r to the introduction of the e x t e r n a l i t y , the payment to the other f i r m (or e f f e c t of the e x t e r n a l i t y i f he i s the damaged party) w i l l eventually drive him out of the industry as h i s average costs w i l l be greater than the competitive product p r i c e p r e v a i l i n g i n the industry. I would also l i k e to discuss b r i e f l y the problem o f choosing an o r i g i n i n the ana l y s i s . I t i s important to recognize that i n most r e a l world e x t e r n a l i t y cases, p r i o r r i g h t s reside de facto with the agent generating the e x t e r n a l i t y . I f t h i s were not so, we would not observe 22 the external e f f e c t . The o r i g i n a l p o s i t i o n i n any e x t e r n a l i t y case, the status quo, thus has a p o s i t i v e l e v e l of the e x t e r n a l i t y (e.g., a p o l l u -tant) and the r i g h t s vested with the p o l l u t e r . Coase and others discussing property r i g h t s take the status quo as the o r i g i n i n any s i t u a t i o n , then discuss whether a l t e r i n g the r i g h t s a f f e c t s resource a l l o c a t i o n . In Coasei's farmer-rancher example there e x i s t s , no matter who i s l i a b l e , a p o s i t i v e number of cows capable of stomping crops. Coase makes the argu-ment that the e x t e r n a l i t i e s are r e c i p r o c a l i n the sense that not harming one of the agents involves harming the other. Reciprocity, however, makes sense only i f we s t a r t from a status quo p o s i t i o n where the e x t e r n a l i t y already e x i s t s . The status quo p o s i t i o n i s thus not defined properly with regard to p r i o r r i g h t s . P r i o r r i g h t s should cover (by d e f i n i t i o n ) the i n i t i a l determination of endowments. I f the p o l l u t e e has the r i g h t s to water i n a c e r t a i n l o c a l e , then a. p r i o r i there i s no water p o l l u t i o n . Ownership of r i g h t s s p e c i f i e s that the p o l l u t e r must pay the owner of the water r i g h t s to engage i n a c t i v i t i e s that p o l l u t e the water. I f the p o l l u t e r owns the r i g h t s to the water, a p o s i t i v e amount of water p o l l u -t i o n e x i s t s and the p o l l u t e e must pay i f he wants to decrease the amount of p o l l u t i o n . Thus the equivalent set of a l t e r n a t i v e property r i g h t s i s e i t h e r a status quo with zero p o l l u t i o n i n which the p o l l u t e r must pay to increase the amount of p o l l u t i o n , or a status quo with p o s i t i v e p o l l u -t i o n i n which the p o l l u t e e must pay to decrease the amount of p o l l u t i o n . 1 1 -Of course t h i s r i g h t s assignment i s s t i l l not s p e c i f i c enough as i t says nothing about the enforcement of one 1s r i g h t s . We must therefore assume that the p r i o r r i g h t s convey the power to compel the other party to pay e i t h e r to increase of decrease the p o l l u t i o n , and that there are 23 The choice of property r i g h t s determines the choice of the o r i g i n . By introducing v a r i a b l e p r i o r r i g h t s , Coase has thus created an environment that requires some form of bargaining theory to derive a determinate s o l u t i o n or solutions. My basic quarrel with Coase i s that he sketched only one poss i b l e r e s u l t , using a very s p e c i f i c and p a r t i a l example. Many of h i s followers (Turvey (1962), Davis and Whinston (1962)) then interpreted Coase's example to mean that a l t e r n a t i v e delimitations of p r i o r r i g h t s would y i e l d i d e n t i c a l equilibrium points under more general models. Thus one d i d not have to worry about who had the r i g h t s . This g e n e r a l i z a t i o n of Coase i s i n v a l i d . I f one i n t e r p r e t s Coasef as saying that e f f i c i e n t a l l o c a t i o n s can be reached with a p r i o r r i g h t on ei t h e r the a f f l i c t e d or generating party (given Coase's assumptions), but that the actual equilibrium point reached with any given r i g h t i s d i f f e r e n t , then I would accept the "theorem". But Coase i n no way proves t h i s assertion. 2. The E f f e c t of P r i o r Rights on Attainable E q u i l i b r i a I s h a l l now reformulate the Coase argument and present a model that attempts to preserve the Coasian framework, yet c l e a r l y d i s t i n -guishes between the set of attainable e q u i l i b r i a and the equilibrium point a c t u a l l y reached under a l t e r n a t i v e assignments of p r i o r r i g h t s . no information or uncertainty problems. S t a r r e t t (1972) has also recognized the importance of the choice of o r i g i n i n e x t e r n a l i t y cases. He was not concerned with the invariance of property r i g h t s and derived e f f i c i e n t e q u i l i b r i a without d i s t i n g u i s h i n g between the equilibrium points. 24 The question i s , w i l l the p r i o r r i g h t that allows no e x t e r n a l i t y and requires that the generator must pay the v i c t i m to engage i n an a c t i v i t y that gives r i s e to an e x t e r n a l i t y lead to the same a l l o c a t i o n of resources (equilibrium point) as the p r i o r r i g h t which allows p o s i t i v e l e v e l s of the e x t e r n a l i t y so that the v i c t i m must pay the generator to decrease the exte r n a l i t y ? The problem i s s t i l l not s p e c i f i e d f u l l y . That i s , to know p r e c i s e l y what would happen to resource a l l o c a t i o n under a l t e r n a t i v e p r i o r r i g h t s , we would need to know how the e x t e r n a l i t y affected both agents, and why the e x t e r n a l i t y e x i s t s . Coase merely asserts the existence of an e x t e r n a l i t y , and so do I i n t h i s section. One method of dealing with theqinyaf i-anee o'ferightsuLs to; u t i l i z e ^ b a r g a i n i n g model that incorporates s p e c i f i c assumptions about p r i o r r i g h t s . Fortunately, a bargaining model e x i s t s that can be adapted to deal with the case of an external diseconomy (e.g., p o l l u t i o n ) under al t e r n a t i v e assignments of p r i o r r i g h t s , zero transaction costs, and perf e c t information. I w i l l use the models developed by Dolbear (1967) and Shibata (1971) to show f o r the case of an external diseconomy that the "Coase theorem" does not hold except by chance."*" Let there be two consumers, A and G-,' with quasi-concave u t i l i t y functions defined over a vector of goods, X^, ( i = 1 , . . . , j , . . . ; n - l ) , and X , such that n •T 1 There i s also a pos s i b l e problem with nonconvexity of preferences i n consumption and nonconvex production sets with production e x t e r n a l i t i e s . SeexStarfett (1972) and my discussion of nonconvexities i n Chapter I I I . 25 U A = U A(x^, x A) (1) U G = U G ( x G , x G) (2) l n A G where x^ and x^ are, re s p e c t i v e l y , A's and G's share of good i , that i s , A G A . • , . x^ + x^ = X^. x^ i s an externalxty generated by G and consumed by A G A, therefore, X = x = x . Consumers are required to reveal t h e i r n n n preferences completely and accurately. I t i s then assumed that there e x i s t s a transformation function (or production p o s s i b i l i t y curve) that i s l i n e a r , e x hibits constant returns to scale, i s continuous, and i s the boundary of a convex production s e t . 1 F(X.,X ,...,X.,...,X ) = 0 (3) ± 2 j n (i — l , 2 , . . . , j , . . . , n ) . Factors are assumed to be supplied i n e l a s t i c a l l y and are owned by the two i n d i v i d u a l s . I t i s G's consumption of good that generates the Q e x t e r n a l i t y to A and the X i n equation (3) i s a c t u a l l y x . That i s , n n only the X that G consumes has a market i n t h i s model, x has no n n market. For completeness, we could d i s t i n g u i s h between good X and the n e x t e r n a l i t y , e.g., A consumes loud noise, X^, when G plays h i s radio W G (good X ); X = g(x ). This s p e c i f i c a t i o n c l a r i f i e s the r o l e of the n z n e x t e r n a l i t y but i t s introduction would not a l t e r the general r e s u l t s of Q the model as g(x^) i s only a l i n e a r or m u l t i p l i c a t i v e transformation Q of (x^). Thus the e x t e r n a l i t y only a f f e c t s the market f o r the exchange 1 Constant returns to scale i s a s i m p l i f y i n g , but not necessary assumption. L i n e a r i l t y i s however necessary, as i t preserves the p a r t i a l equilibrium nature of the Coasian framework by imposing f i x e d product p r i c e s . 26 of commodity X^. A l l other markets are assumed to be pe r f e c t . The production of X^ i s unaffected by the e x t e r n a l i t y . The s p e c i a l assumption of a l i n e a r transformation function eliminates the general equilibrium e f f e c t s i n the product and fac t o r markets. We therefore have a general equilibrium framework that has been r e s t r i c t e d by assumption to analyze the "Coase theorem" i n the s p i r i t of Coase's own e x p l i c i t and i m p l i c i t assumptions. Before the e x p l i c i t introduction of p r i o r r i g h t s , G i s consuming good X^ (e.g., p l a y i n g h i s radio) and maximizing h i s u t i l i t y independent of A. The de facto p r i o r r i g h t i s thus that G has the r i g h t s to noisy radio-playing; the status quo i s a p o s i t i v e amount of noise, p o l l u t i o n . The e f f i c i e n t equilibrium f o r G (ignoring A) i s at the point where G's marginal rate of s u b s t i t u t i o n between goods X_. and X^ i s equal to the marginal rate of transformation between the two goods. When A's pre-ferences are included i n the determination of an equilibrium, the e f f i c i e n t e q u i l i b r i a are defined where the sum of the marginal rates of su b s t i t u t i o n f o r goods X. and X for i n d i v i d u a l s A and G are equal to 3 • n the marginal rate of transformation." 1" This equilibrium condition defines 1 The p r i v a t e equilibrium f o r G i s determined from the constrained maximum problem: maximize U G ( x G , x ) 3 n subject to the l i n e a r transformation function X. = X. + bX . 3 3 n The f i r s t order conditions are u G + u -t3?'. 0 x. D u + yb = 0 x n 27 which y i e l d s u G / u = b, or the marginal rate of s u b s t i t u t i o n X j / X n equals the marginal rate of transformation (where u G represents the j G derivative 3u/8x_. and s i m i l a r l y f o r other p a r t i a l d e r i v a t i v e s ) . I f X was a p r i v a t e good, the e f f i c i e n t equilibrium would be where n u G / u G = u A / u A = f / f . X . / X X. / .'IX X. / X :/ n ] / n ]/ n But i f X i s an e x t e r n a l i t y , the problem becomes: maximize U G ( x G , x ) 3 n subject to U A - U A ( x A , x ) = 0 and 3 n X. = X. + bX . 3 3 n The f i r s t order conditions are:: u G + u = 0 x. 3 u G + Au A +..ub = 0 X X n n u A + u = 0. x. 3 Eliminating the Lagrange m u l t i p l i e r s and s u b s t i t u t i n g y i e l d s : u G /u G + u A /u X / X. X / n/ 3 n/ A = b. X . The e f f i c i e n c y condition i s thus that the sums of the marginal rates of s u b s t i t u t i o n between X.. and X^ must equal the marginal rate of transformation between X. and X . 3 n 28 Pareto optima f o r p u b l i c goods, as was f i r s t recognized by Samuelson (1954). There are two important points to make about the Samuelson condition. F i r s t , there i s no unique Pareto optimum; many e f f i c i e n t e q u i l i b r i a are also Pareto optima. The locus of these Pareto optima comprise a contract curve. Selection of one of these points on the contract curve thus requires a s o c i a l ..welfare function (or dictator) that ranks the welfare of each party. 1 Secondly, i f the contract curve i s not a v e r t i c a l l i n e , d i f f e r e n t amounts of the p u b l i c good w i l l be consumed at each equilibrium point."'' The amount of the p u b l i c good consumed and the r e l a t i v e p r i c e of the p u b l i c and p r i v a t e good are thus not independent of the o r i g i n or s t a r t i n g point: the i n i t i a l endowments of the i n d i v i d u a l s . And we assume that p r i o r r i g h t s determine the i n d i v i d u a l s ' i n i t i a l endowments; the d e l i m i t the o r i g i n i n any negotiation. A geometric representation of a bargaining model with e x t e r n a l i t i e s w i l l i l l u s t r a t e the importance of p r i o r r i g h t s . The Edgeworth-Bowley box diagram i s modified to adapt Shibata's model to the case of external diseconomies. Individual G i s assumed to have convex preferences, 1 I f we were considering two goods which were marketed, nomothetic and i d e n t i c a l preferences f o r each i n d i v i d u a l consuming those goods would guarantee that the same proportion of the goods would be consumed at each point along the contract curve at the same r e l a t i v e p r i c e r a t i o . In t h i s case, the r e l a t i v e p r i c e s of the two commodities i n equilibrium are independent of the i n i t i a l endowments of!the i n d i v i d u a l s . Although we can impose homotheticity on both A and G, i t i s not s u f f i c i e n t to guarantee a v e r t i c a l contract curve. One way i n which a v e r t i c a l contract curve can be obtained i s to assume that, for a f i x e d l e v e l of X , the n marginal rate of s u b s t i t u t i o n between X and X. i s constant for both n : A and G. This assumptionti Wo Uid imply a zero income e l a s t i c i t y f o r good X and i s thus a very strong assumption. n 29 • i l l u s t r a t e d with i n d i f f e r e n c e curves of the usual shape (Figure I) defined over a numeraire, j , (for a l l p r i v a t e goods) and the good generating the e x t e r n a l i t y , X^. Individual A's i n d i f f e r e n c e curves are p o s i t i v e l y sloped, i n d i c a t i n g that the more of good X^ he has (e.g., the more noise), more of the numeraire good i s necessary to maintain a given l e v e l of u t i l i t y (Figure I I ) . Each i n d i v i d u a l i s assumed to have an i n i t i a l endowment of income, measured i n terms of the numeraire, X_. (depicted as a and b i n Figures I and I I ) . A transformation function between the good generating the e x t e r n a l i t y and the numeraire i s assumed to be l i n e a r (Figure III)."'" The X. J intercept of the transformation curve i s the combined income of A and FIGURE I FIGURE II 1 The transformation function could also be nonlinear. As long as i t i s convex, the r e s u l t s w i l l not vary from the l i n e a r case. Nonlinearity provides e x p l i c i t consideration of the pos s i b l e r e d i s t r i b u t i o n of income through f a c t o r shares. This would however take us away from Coase's pr op o si; t i o ns.. x. 3b. 30 0 X FIGURE III n Because of the publicness of X^, the amounts of t h i s good (or bad) consumed by A and G are i d e n t i c a l . The ho r i z o n t a l axes of Figures I, I I , and III therefore have the same scale and i t i s poss i b l e to combine the figures into one diagram. Following Shibata, t h i s i s accomplished by transforming A's in d i f f e r e n c e map. The X^ axis of A i s rotated around the o r i g i n u n t i l i t s slope i s equal i n absolute value to the slope of the transformation function. A l l of A's i n d i f -* ference curves must then be adjusted to t h i s new X axis ( c a l l i t X ), n n to maintain the same l e v e l of u t i l i t y (the dashed curves i n Figure I I ) . This adjustment process means that the slope of A's i n d i f f e r e n c e curves at any point i s now equal to u A /u A + f X . / X V n The reason f o r adjusting A's i n d i f f e r e n c e map i s thus to y i e l d d i r e c t l y the Samuelson e f f i c i e n c y conditions when A's and G's in d i f f e r e n c e curves are tangent. Now we inv e r t A's map and superimpose the section above and incl u d i n g the adjusted o r i g i n on to G's i n d i f f e r e n c e map. The X_. axes now coincide 1 Note also that A's adjusted i n d i f f e r e n c e curves must now be everywhere steeper than the transformed X* axis. . ,n 31 as do points a and b. This procedure produces a diagram (Figure IV) with the same production p o s s i b i l i t y r e l a t i o n s h i p as Figure III and G A has c h a r a c t e r i s t i c s analogous to the Edgeworth-Bowley box. 0 0 shows the t o t a l endowment of both i n d i v i d u a l s and point F indicates the d i s t r i b u t i o n of income (in the form of X_.) between A and G. Any point on the diagram (e.g., point E) shows how much of the numeraire each i n d i v i d u a l has (OJ f o r G and J J ' for A) and t h e i r j o i n t consump-t i o n of the good generating the e x t e r n a l i t y f or G and the e x t e r n a l i t y f o r A (ON). Each i n d i v i d u a l must exhaust h i s income and thus the t o t a l consumption of X_, must add up to a point on the transformation curve.. Line C C i s the locus of tangency points between G's i n d i f -ference curves and A's adjusted i n d i f f e r e n c e curves, showing a possible set of Pareto optimal a l l o c a t i o n s of X. (for A and G) and X . Notice : n that the slope at each tangency point along the contract curve i s d i f f e r e n t . Thus the r e l a t i v e p r i c e of X_, to X^ w i l l vary depending on the l o c a t i o n of the i n d i v i d u a l s within the box. N Figure IV 3 2 Given an i n i t i a l p o s i t i o n , the diagram w i l l i n d i c a t e a locus of possible outcomes: i t cannot p r e d i c t where the f i n a l equilibrium ( i f there i s one) w i l l be reached. As Shibata points out, " i t i s at once cl e a r from our diagram that the s i t u a t i o n at hand i s e s s e n t i a l l y one of indeterminate b i l a t e r a l monopoly ... Economists customarily have have very l i t t l e to say about pure bargaining s i t u a t i o n s i n which the outcome i s dependent upon i n t e r a c t i o n s among only a few p a r t i e s " (1971, p. 9). This i s p r e c i s e l y the s i t u a t i o n which Coase has postulated with h i s cows and corn "model". At t h i s point,wwe need to return to the assumptions about p r i o r r i g h t s . I assume that there are two a l t e r n a t i v e assignments of p r i o r r i g h t s defined over good X^. 1 I f G possesses the p r i o r r i g h t s to X^, i t implies that the o r i g i n f o r bargaining i s a p o s i t i v e amount of X^ (e.g., point E) and that G w i l l decrease h i s consumption of X^ only i f he moves to a higher l e v e l of u t i l i t y (a higher i n d i f f e r e n c e curve). I f A controls the p r i o r r i g h t s f o r X n, the o r i g i n i s zero consumption of X (e.g., point F ) , and A w i l l allow G to consume X only i f A moves n n to a higher i n d i f f e r e n c e curve. This information about p r i o r r i g h t s 1 Intermediate cases are p o s s i b l e , e.g., party G may have the r i g h t s to use a l i m i t e d amount of the good generating the e x t e r n a l i t y and be con-strained beyond some point, where A then has the r i g h t s to prevent further use. The common law of nuisance applies to these cases, i . e . , a party i s allowed to pursue an a c t i v i t y up to the point at which i t Is believed to harm others. The c r u c i a l question with nuisance laws i s what constitutes harm. Coase's extensive discussion of l e g a l cases pro-vide many examples of p o s s i b l e i n t e r p r e t a t i o n s of nuisance by the courts. No one has yet (to my knowledge) investigated the e f f e c t of precise or imprecise nuisance laws on agents' behavior i n an economic model. 33 does not enable us to p r e d i c t the exact outcome of any negotiation between A and G as we have not s p e c i f i e d the transaction costs of bargaining. I f we assume that transaction costs are zero, we can i l l u s t r a t e one possible outcome of bargaining with a l t e r n a t i v e p r i o r r i g h t s that d i f f e r s completely from the conclusions drawn by Coase and h i s i n t e r p r e t e r s . In Figure IV, the two i n i t i a l p oints depicting the a l t e r n a t i v e r i g h t s are E and F. I f we s t a r t a t point E, i n d i v i d u a l G w i l l accept a move only to a point such as E 1 on a higher i n d i f f e r e n c e curve. He w i l l decrease h i s consumption of i n exchange for an increase i n X_,. Individual A w i l l give up some of h i s X. to achieve a decrease i n X , J n as he does not decrease h i s u t i l i t y by doing so. As the two i n d i v i d u a l s ' i n d i f f e r e n c e curves are tangent at point E', they are at a Pareto optimum. S i m i l a r l y , i f we s t a r t at point F, individualGG w i l l give up some of h i s X. to A to consume X . A w i l l accept because he can then move to a higher i n d i f f e r e n c e curve. Both i n d i v i d u a l s w i l l then move to point F'. Pareto optima can be achieved under e i t h e r p r i o r r i g h t assignment, but the e f f i c i e n t points which are reached are d i f f e r e n t . Compare points E' and F'. The r e l a t i v e p r i c e s of X_. to X^ are not i d e n t i c a l at E' and F' and the quantity of the e x t e r n a l i t y consumed by both p a r t i e s i s d i f f e r e n t . 1 In the case i l l u s t r a t e d i n Figure IV, the r e l a t i v e p r i c e of X^ to X^ i s greater at point F' than at E'. I f 1 As noted before, the only way we can obtain i d e n t i c a l r e l a t i v e p r i c e s of X, to X i s i f the contract curve i s a v e r t i c a l l i n e . I can f i n d no general conditions under which t h i s s o l u t i o n w i l l be obtained. See footnote 1, page 28. 34 we dropped the assumption of a l i n e a r transformation function, the e f f e c t s of these d i f f e r e n t r e l a t i v e p r i c e s could be traced through the f a c t o r and output markets. What we can conclude from t h i s model i s that d i f f e r e n t impositions of p r i o r r i g h t s do a f f e c t r e l a t i v e p r i c e s , the amount of the e x t e r n a l i t y consumed at Pareto optimal points, and hence, resource a l l o c a t i o n . 1 Although t h i s bargaining model dealt with consumption e x t e r n a l i t i e s , a s i m i l a r approach to production e x t e r n a l i t i e s should y i e l d analogous r e s u l t s . Presumably there are assumptions under which a v e r t i c a l contract curve could be obtained with t h i s approach, e.g.> through s p e c i f i c r e s t r i c t i o n s on p r i o r r i g h t s or by imposing some form of weak s e p a r a b i l i t y on preferences. The important point i s that the "Coase theorem" i s not a general r e s u l t , but depends on r e s t r i c t i v e assumptions not s p e c i f i e d by Coase or any of h i s followers. The "Coase theorem", properly restated, thus says that a l t e r n a t i v e assignments of p r i o r r i g h t s y i e l d d i f f e r e n t but equally e f f i c i e n t resource a l l o c a t i o n s . This "theorem" i s s t i l l not very i n t e r e s t i n g or useful i n analyzing e x t e r n a l i t i e s as i t says no more than i s implied by Pareto optimality with p u b l i c goods. Given universal markets and r i g h t s , and zero transaction costs, e x t e r n a l i t i e s are i n t e r n a l i z e d . The revised theorem does however imply that the assignment of r i g h t s a_ p r i o r i cannot 1 Mishan (1971) notes that changes i n property r i g h t s leads not only to d i f f e r e n t income d i s t r i b u t i o n s , but also to d i f f e r e n t l e v e l s of the e x t e r n a l i t y e x i s t i n g i n equilibrium. He a r r i v e s at t h i s conclusion, using a comparison of compensating versus equivalent v a r i a t i o n measures of welfare gain. Unfortunately, h i s "model" i s hampered by a lack of s p e c i f i c assumptions. Also see McGuire and Aaron (1969) f o r further v e r i f i c a t i o n of the non-uniqueness of a p u b l i c good equilibrium. 35 be made on grounds of e f f i c i e n c y . Assigning r i g h t s determines whose in t e r e s t s count and which agents gain i n any subsequent exchanges. I t i s therefore a normative problem i n t h i s i d e a l world. A very i n t e r e s t i n g implication of t h i s analysis i s that schemes of auctioning property r i g h t s or licences to engage i n an a c t i v i t y (e.g., e s t a b l i s h i n g markets i n licences to pollute) must take i n t o account the ex ante d i s t r i b u t i o n of property r i g h t s , i m p l i c i t l y or e x p l i c i t l y defined. That i s , does the p o l l u t i o n e x i s t i n the status quo or not? The bids for licences w i l l depend on who has the ex ante ri g h t s because r i g h t s a f f e c t income l e v e l s and d i s t r i b u t i o n (budget c o n s t r a i n t s ) . I f we were i n a world where transaction costs existed, r i g h t s would also a f f e c t the transaction costs of operating markets fo r p o l l u t i o n l i c e n c e s . One would expect that a l t e r n a t i v e ex ante d i s t r i b u t i o n s of r i g h t s w i l l lead to d i f f e r e n t e f f i c i e n t l icence bids and ex post r i g h t s d i s t r i b u t i o n s . Thus licence schemes also involve normative judgment as to whose i n t e r e s t s count. The status quo p o s i t i o n cannot be ignored. The inadequacy of the Coasian type of analysis to deal with s p e c i f i c cases of e x t e r n a l i t i e s defined i n the context of market f a i l u r e and l e g a l i n s t i t u t i o n s brings us back to a consideration of transaction costs and the l e g a l rules that a r i s e when transaction costs e x i s t . The analysis i n t h i s chapter has thus not explained why exter-n a l i t i e s p e r s i s t . I turn now to a discussion of imperfect information and e x t e r n a l i t i e s . 36 III. IMPERFECT INFORMATION: OPERATION OF CONTINGENT MARKETS WITH EXTERNALITIES A. Introduction-' This chapter considers the relationship between information and externalities. Part A examines the importance of information in the operation of markets and develops an information/externality taxonomy. Parts B and C concentrate on an analysis of two externality cases that arise from imperfect information. The basic questions asked in this chapter are whether private markets w i l l operate with externalities and whether the resulting equilibria are efficient. The introduction of imperfect information means however that our traditional notions of equilibrium, efficiency and optimality may have to be modified. We! can no longer expect the same conditions for a competitive equilibrium to hold with imperfect information and exter-nali t i e s . Equilibria in the models presented in parts B and C of this chapter are generally characterized by a single price or set of prices that maximize the expected u t i l i t y of an agent affected by the externality subject to a zero pr o f i t condition for insurers. The problem is that this sort of equilibrium is not too meaningful with imperfect information. F i r s t , the af f l i c t e d party's u t i l i t y i s maximized independent of the generating party's decisions about the externality. We may therefore attain equilibria that are not optima in the traditional sense. Secondly, we may be dealing with equilibria that are efficient only 37 r e l a t i v e to the information the agent possesses. As Rothschild notes (1973, p. 1301), "What equilibrium i s i n a p a r t i c u l a r market depends on what i n d i v i d u a l s i n that market know". What we may want i s equilibrium to be defined as a s o l u t i o n which i s s e l f - r e a l i z i n g , that i s , when expectations are r e a l i z e d . 1 Optima would thus be defined r e l a t i v e to the information possessed versus the information attainable. Optima may then be r e l a t i v e to the set of preferences established with imperfect information. . The problem with e q u i l i b r i a of t h i s sort i s that they tend to be a r b i t r a r y and not unique. Secondly, i t i s d i f f i c u l t to determine what constitutes s o c i a l im-provement. We could, for example, define a s o c i a l improvement to occur whenever one acquires more information. This follows from the assumption that preferences based on le s s information lead to l e s s welfare than preferences established with more information. I cannot attempt to answer the questions of what constitutes equilibrium and optimality with imperfect information, but want to point out that some of the d e f i n i t i o n s contained i n t h i s chapter (and Chapter IV) w i l l not n e c e s s a r i l y be the t r a d i t i o n a l d e f i n i t i o n s made under the assumptions of p e r f e c t competition. The t r a d i t i o n a l e x t e r n a l i t y l i t e r a t u r e argues that e x t e r n a l i t i e s can be i n t e r n a l i z e d by contractual arrangements, thereby eliminating the need for l e g a l i n s t i t u t i o n s to specify contingent r i g h t s (prior r i g h t s are s t i l l required f o r the operation of markets). A l l agents 1 See Spence (1973, 1974) f o r examples of market e q u i l i b r i a under a d e f i n i t i o n s i m i l a r to t h i s . 38 are assumed to negotiate c o s t l e s s l y with each other to achieve Pareto optimal resource a l l o c a t i o n s , given the e x t e r n a l i t y . This argument may be i n v a l i d f o r two reasons. F i r s t , the e x t e r n a l i t y cannot be a p u b l i c good or bad. Private contracts w i l l be i n e f f i c i e n t i f the e x t e r n a l i t y e n t a i l s c o l l e c t i v e harm due to problems of non-appropria-b i l i t y and non-revelation of preferences. Again, I w i l l assume e x t e r n a l i t i e s are not p u b l i c bads i n t h i s chapter. But even i f e x t e r n a l i t i e s are p r i v a t e bads, p r i v a t e contracts may s t i l l lead to i n e f f i c i e n t i n t e r n a l i z a t i o n of e x t e r n a l i t i e s i f information i s not per f e c t . The t r a d i t i o n a l argument must thus r e l y on the assumptions that no p u b l i c goods or bads e x i s t and that information i s p e r f e c t -. i n the sense that a l l agents are i d e n t i c a l l y informed ( i . e . , t h e i r information corresponds p e r f e c t l y to the true state of the world). As Radner (1968) has shown, p e r f e c t information i s necessary to guaran-tee contractual agreement. I f information i s p e r f e c t , contracts can be written to cover a l l possible present and contingent events (assuming no p u b l i c goods) and a l l e x t e r n a l i t i e s w i l l be i n t e r n a l i z e d e f f i c i e n t l y i n a general equilibrium world as shown by Arrow and Debreu (1954, J.959)'.. In my framework however, e x t e r n a l i t i e s do not e x i s t i f transaction costs are zero. I have assumed that the a c q u i s i t i o n of information i s a transaction cost encountered i n the operation of markets, and the presence of imperfect information implies p o s i t i v e transaction costs. Imperfect information i s defined as information that does not corres-* pond completely to the true state of the world, but represents an i n d i v i d u a l ' s p r i o r d i s t r i b u t i o n s over what he perceives the state of the 39 world to be. Zero information thus means that the i n d i v i d u a l has no p r i o r s over the state. Perfect information means that h i s b e l i e f s correspond to the true state. When information i s imperfect, exter-n a l i t i e s may a r i s e and p r i v a t e markets may f a i l . 1 Given imperfect information, we can also no longer r e l y on p r i o r r i g h t s to guarantee the operation of markets (see the d e f i n i t i o n i n Chapter I I , p a r t A). What are the precise r e l a t i o n s h i p s between e x t e r n a l i t i e s and information? Why may imperfect information generate e x t e r n a l i t i e s ? These are not simple questions. F i r s t we must define what i s meant by information. Secondly, e x t e r n a l i t i e s tend to be very case s p e c i f i c . That i s , p a r t i c u l a r types of information may lead to d i f f e r e n t types o f e x t e r n a l i t y cases. There are no general cases or r u l e s . I s h a l l however develop an information taxonomy to d i s t i n g u i s h some classes of 2 externality/information cases. 1 C l e a r l y , there are other causessof market f a i l u r e : non-appropriability (public goods) i s the major example. Because I want to concentrate on information problems with non-collective e x t e r n a l i t i e s , I w i l l assume that the other possible causes of market f a i l u r e do not a f f e c t the events and markets under consideration. See Crocker (1973) f o r an i n t e r e s t i n g discussion of the non-appropriable aspects of e x t e r n a l i t i e s . One could also compound the issue by noting that some people (e.g., Arrow (1969)) argue that information i t s e l f has non-appropriable a t t r i b u t e s . I t i s d i f f i c u l t to r e t a i n exclusive r i g h t s to information and to prevent non-buyers from acquiring the information. This argument i s not t o t a l l y convincing and therefore I w i l l assume that non-appropriability does not compound information problems. 2 The taxonomy developed i n t h i s s ection i s by no means exhaustive. I t merely defines some p l a u s i b l e cases and i d e n t i f i e s the cases discussed i n parts B and C of t h i s chapter. Work on information has become quite extensive and other taxonomies and d e f i n i t i o n s have been developed. See for example, Rothschild (1973) and S t i ' g l i t z (1975) . 40 A necessary condition f o r the existence of e x t e r n a l i t i e s z i s that there e x i s t technological interdependencies (or jointness) between the objective functions of economic agents. I f these interdepen-dencies give r i s e to a divergence between the p r i v a t e and s o c i a l marginal valuations of the commodities a f f e c t e d by the interdepen-dencies, an e x t e r n a l i t y a r i s e s . 1 I am not t r y i n g to explain why e x t e r n a l i t i e s a r i s e , but rather, why they p e r s i s t i f competitive markets e x i s t . A l t e r n a t i v e l y , I could ask why competitive markets f a i l when e x t e r n a l i t i e s e x i s t . Certain types of e x t e r n a l i t i e s may p e r s i s t because of imperfect information. Let us characterize im-p e r f e c t information. Uncertainty i s the term used to depict imperfect information about future or random events. Imperfect information i n t h i s case implies that the i n d i v i d u a l ' s p r o b a b i l i t y d i s t r i b u t i o n over the event does not equal the true d i s t r i b u t i o n . P e r f e c t information would of course imply that the i n d i v i d u a l knows with p r o b a b i l i t y one (zero) that the event w i l l ( w i l l not) occur. Interdependencies between i n d i v i d u a l s can thus be stochastic. E x t e r n a l i t i e s can then enter i n d i v i d u a l s ' objective functions i n three ways. They can a f f e c t (1) the consumption or production p o s s i b i l i t i e s i n a future state; (2) the p r o b a b i l i t y of a future state's occurrence; (3)) both the con-r-sumption or production p o s s i b i l i t i e s and the p r o b a b i l i t y of future states. I f e x t e r n a l i t i e s are stochastic and a f f e c t i n d i v i d u a l s i n any 1 I thus r u l e out cases such as defective products which do not harm i n d i v i d u a l s , but merely do not operate as expected. That i s , ;whe're no divergence between p r i v a t e and s o c i a l marginal cost e x i s t s , no e x t e r n a l i t y a r i s e s . 41 one of these ways, we introduce the need f o r contingent contracts or markets to i n t e r n a l i z e e x t e r n a l i t i e s -Imperfect information can also apply to uncertainty about resource endowments, i n d i v i d u a l s ' preference orderings, and/or productive opportunities. H i r s h l e i f e r (1971) c a l l s t h i s technolo-g i c a l information. Individuals may have imperfect technological information not only about occurrences i n future s t a t e s , but also those i n present states of the world. Imperfect technological i n f o r -mation compounds the uncertainty that a r i s e s when e x t e r n a l i t i e s are s t o c h a s t i c . Let us f i r s t see why technological information i s impor-tant with e x t e r n a l i t i e s , then characterize a set of e x t e r n a l i t y / i n f o r -mation cases. The d i f f e r e n c e between e x t e r n a l i t i e s and "normal" (non-externality) goods i s that consumers may s t i l l be able to maximize t h e i r u t i l i t i e s (or firms, t h e i r p r o f i t s ) and achieve Pareto optimal e q u i l i b r i a without technological information about normal goods. This w i l l not i n general be true f o r e x t e r n a l i t i e s . Consumers, f o r example, need not have information about the technology of the production function f o r a p a r t i c u l a r good nor do they require information about other i n d i v i d u a l s ' preferences f o r that good to be able to purchase the good i n a 1 IE 1 H i r s h l e i f e r (1971) also defined a term, market information, to cover cases where agents d i d not know supply and demand functions i n a given market. Imperfect market information can compound the e x t e r n a l i t y problems associated with imperfect technological i n f o r -mation. I w i l l however ignore the problems introduced by imperfect market information as I wish to concentrate on e x t e r n a l i t y models incorporating only imperfect technological information. 42 competitive market (given no market uncertainty). I f I wish to buy a stereo, I do not require information about e l e c t r o n i c s technology nor my neighbour's preferences f o r stereos. I can compute my marginal rates of s u b s t i t u t i o n between stereos and any other normal good and s a t i s f y the f i r s t order conditions f o r u t i l i t y maximization without knowing how the stereo was produced nor how many my neighbour buys."*" With e x t e r n a l i t i e s , t h i s exercise w i l l simply not work. I f the e x t e r n a l i t y i s botulism from improperly processed food, and I cannot i d e n t i f y which cans of green beans contain the botulism t o x i n , i t i s u n l i k e l y that a Paretoooptimal a l l o c a t i o n of resources can be attained, nor that my own 2 u t i l i t y w i l l be maximized. Compare the f i r s t order conditions f o r an e f f i c i e n t e q uilibrium fo r normal goods with one f o r an e x t e r n a l i t y (see Chapter I I , pages 26-27 for the model). The equilibrium conditions for normal goods are that the marginal rates of s u b s t i t u t i o n f o r a l l consumers between any p a i r of goods (assuming a l l goods can be ranked i n preference orderings) are equal to the p r i c e r a t i o s of these goods. With e x t e r n a l i t i e s , e f f i c i e n c y requires f o r a l l consumers aff e c t e d by the e x t e r n a l i t y , that the sum of the marginal rates of s u b s t i t u t i o n between the e x t e r n a l i t y 1 This i s simply the two theorems of welfare economics. Note that we always assume no e x t e r n a l i t i e s e x i s t i n the proofs of the welfare theorems. 2 David Donaldson suggested t h i s example to me. 43 and any normal good equal the p r i c e r a t i o . Thus any i n d i v i d u a l affected by the e x t e r n a l i t y cannot maximize his u t i l i t y independent of others also a f f e c t e d by the e x t e r n a l i t y . A l l a f f e c t e d p a r t i e s must therefore be able to i d e n t i f y each other and A must know G's pr e f e r -ences (or technology i f A and G are f i r m s ) . T r a d i t i o n a l e x t e r n a l i t y theory of course recognized that e q u i l i b r i a could be attained, but may not be e f f i c i e n t i f e x t e r n a l i t i e s were present. What I want to empha-si z e i s one reason why i n e f f i c i e n c i e s may occur: imperfect technological information. I f agents do not have information about each others' technologies or preferences, competitive e q u i l i b r i a ( i f they exist) w i l l tend to be i n e f f i c i e n t and non-optimal. Technological information-i s thus a necessary condition for the existence of e f f i c i e n t e q u i l i b r i a with e x t e r n a l i t i e s . The point i s that optimal a l l o c a t i o n s with exter-n a l i t i e s require involved agents to possess technological information; optimal a l l o c a t i o n s with normal goods do not. Let us define technological information i n the context of exter-n a l i t i e s more p r e c i s e l y . R e c a l l that technological information pertains to a l l agents involved i n an e x t e r n a l i t y . I s h a l l f i r s t d i s t i n g u i s h between the generator(s) and of the e x t e r n a l i t y (denoted by G) and the agent(s) a f f e c t e d by the e x t e r n a l i t y (denoted by A). Let T be the set S i m i l a r l y , Pareto optimality for normal goods requires (3u./3ii .) = G • ^ (9u /3u . ) = 9 f . /3 f• fo r a l l goods i , j and a l l i n d i v i d u a l s A, G. 1 3 1 3 A G With e x t e r n a l i t i e s , the condition i s that (9u /9u. ) + (9u /9u .) = Z D z J 9f /9 f. for an e x t e r n a l i t y , z , and normal good, j , a f f e c t i n g a l l z : in d i v i d u a l s , A and G. 44 of technological information (not a s i n g l e v a r i a b l e ) , where T shows the e f f e c t of the e x t e r n a l i t y on the a f f l i c t e d agents' consumption (or production) set, and T i s the technology (or preferences) of the generating party that i s responsible f o r the creation of the exter-n a l i t y . Take our botulism case as an example. T^ could represent serious i l l n e s s or death to a f f l i c t e d p a r t i e s , r e s u l t i n g i n a decrease i n consumption of some or a l l goods defined i n the i n d i v i d u a l ' s u t i l i t y function (or decreases the i n d i v i d u a l ' s income). 1 T could G be a f a u l t y cooking procedure or can-sealing process that allows botulism t o x i n to grow. We can now s p e c i f y the p o s s i b l e set of inform mation cases, d i s t i n g u i s h between symmetric and asymmetric information, and i d e n t i f y the cases which give r i s e to e x t e r n a l i t i e s . There are eight sensible cases that are i l l u s t r a t e d i n the following table (Table I ) . A + means that the i n d i v i d u a l has p e r f e c t technological information, while a 0 means that the i n d i v i d u a l has imperfect or no technological information. The information i s ex ante, i . e . , i t depicts the technological information each group has p r i o r to the operation of any market. 1 A l t e r n a t i v e l y , the e f f e c t could lead to an increase i n the consumption of goods l i k e medical care and decreased consumption of a l l other goods. The importantbpoint i s that the consumption set of the a f f l i c t e d party i s a l t e r e d by the e x t e r n a l i t y . T^ i s the technological information about these e f f e c t s (e.g., A's marginal rate of s u b s t i t u t i o n between the e x t e r n a l t i t y and normal goods). 45 TECHNOLOGICAL INFORMATION CASE INDIVIDUAL '^ A T G (1) A + + G + + (2) A 0 0 G 0 0 (3) A + 0 G 0 + (4) A 0 0 G 0 + (5) A + 0 G 0 0 (6) A 0 0 G + + (7) A + 0 G + + (8) A + + G 0 + Table I: TECHNOLOGICAL INFORMATION CASES I c a l l cases (1), (2), and (3) symmetrical technological!informal t i o n . That i s , both groups know everything about each other's "technologies", they know nothing, or they each know only t h e i r own technologies: Case (1) depicts the p e r f e c t information assumption made i n most economic models. I f we i n t e r p r e t the zeros i n case C2) 46 to mean no information (not even imperfect), then Radner (1968) has shown that no pri v a t e market w i l l e x i s t f or the exchange of the commodities to which the information pertains. No exchange i s p o s s i -ble unless one introduces other agents (or a government) that provides information to A and G. 1 Exchange may also be possible i f we introduce technological change (disembodied) that both p a r t i e s can acquire. Case (2) with zero information i s thus not very i n t e r e s t i n g f o r the purposes of my analysis. I f we i n t e r p r e t case (2) as implying imperfect information,. market exchange may be possible and s e l f - r e a l i z i n g e q u i l i -b r i a may be obtained. Case (3) simply indicates that i n d i v i d u a l s i n group A only know how the e x t e r n a l i t y a f f e c t s them, but do not know how i t i s generated, i . e . , they do not know G's productive technology or preferences. And conversely, G's know only t h e i r own technologies or preferences, but not how the e x t e r n a l i t y they generate a f f e c t s the Cases (4), (5), (6), (7), and (8) depict asymmetric information. I r u l e out seven other possible asymmetric combinations with the 1 See H i r s h l e i f e r (1971) f o r a discussion of the " s o c i a l value" of p u b l i c l y provided technological information i n a pure exchange model. Unfortunately, H i r s h l e i f e r ' s discussion does not c l e a r l y define s o c i a l value nor d i s t i n g u i s h between ex ante and ex_ post valuations of information. Also see Marshall (1974). 2 We could make cases (2) and (3) asymmetric i f we i n t e r p r e t the zeros to mean imperfect information and assume that A's and G's p r i o r d i s t r i b u t i o n s are unequally correlated with the true state. That i s , A's information may be more (or less) representative of the true state than B's information. 4? assumption that an i n d i v i d u a l cannot have more technological information about the other group's functions than he has about h i s own functions. One combination remains: A + + G O O This s i t u a t i o n seems u n r e a l i s t i c . I t i s u n l i k e l y that a f f l i c t e d p a r t i e s can ever know more about the e x t e r n a l i t y than the p a r t i e s responsible f o r generating the e x t e r n a l i t y . E x t e r n a l i t i e s can emerge with any of the cases except ( 1 ) . I f p e r f e c t information e x i s t s (and a l l other assumptions of p e r f e c t compe-t i t i o n are met) then no e x t e r n a l i t i e s can e x i s t . A l l w i l l be i n t e r n a l i z e d e f f i c i e n t l y through bargaining or the operation of p e r f e c t markets. Once we introduce imperfect information, i t i s no longer c e r t a i n that e i t h e r bargaining or markets ( i f they exist) can lead to e f f i c i e n t competitive e q u i l i b r i a . Just how imperfect information a f f e c t s the competitive solu-t i o n i s examined i n parts B and C o f t h i s chapter. I have already explained why case (2) i s not very i n t e r e s t i n g i n an analysis of p r i v a t e markets. By an analogous argument, (4) and (6) are also rather uninteresting. I f A does not know about the existence of an external diseconomy generated by G, G i s u n l i k e l y to engage i n any transaction with A that reveals the pjresence of the e x t e r n a l i t y . In case (5), A has an incentive to exchange with G, but if: G cannot t e l l how he's generating the e x t e r n a l i t y , he i s u n l i k e l y to trade. (3), (7), and (8) are s i m i l a r i n that each group has at l e a s t 48 technological information about t h e i r own functions. Our information taxonomy can now be complicated by adding uncertainty to the technological information t a b l e . This would increase to fourteen the number of possible cases i f we assume only two possible s i t u a t i o n s f o r A and G. E i t h e r both p a r t i e s are uncertain about the e x t e r n a l i t y ' s occurrence (and t h e i r p r o b a b i l i t y d i s t r i b u t i o n s need not be i d e n t i c a l ) , or G knows when the e x t e r n a l i t y occurs with ce r t a i n t y , but A does not. These cases follow from the assumption that the G's have more information about the p r o b a b i l i t y d i s t r i b u t i o n for the e x t e r n a l i t y than the A's. Therefore, i f G i s uncertain about the occurrence of the e x t e r n a l i t y , A i s also. G may have pe r f e c t information about the event, A may not. We could also combine the technological information cases with the three ways i n which e x t e r n a l i t i e s as stochastic events a f f e c t agents' objective functions. Rather than pursue t h i s exhaustive taxonomy, I w i l l define the two cases which are examined i n parts B and C of t h i s chapter. I c a l l the two cases stochastic e x t e r n a l i t i e s and information e x t e r n a l i t i e s . In a stochastic e x t e r n a l i t y , the e x t e r n a l i t y (or the commodity which generates the e x t e r n a l i t y ) i s assumed to enter the ob-j e c t i v e function of the a f f l i c t e d agent as an argument of h i s u t i l i t y function. I f , for example, the a f f l i c t e d agent i s a consumer, the e x t e r n a l i t y , z, i s assumed to enter h i s u t i l i t y function i n a p a r t i c u l a r state. Let there be two states, i n which the e x t e r n a l i t y e x i s t s i n one state, but not the other. We then have a s t o c h a s t i c e x t e r n a l i t y when * U = T T U ( C . , Z ) + (1 - ir)u(c„). 49 That i s , expected u t i l i t y i s contingent upon the i n d i v i d u a l ' s s t a t e -dependent u t i l i t y , where u t i l i t y i n state one i s defined over the commodities the i n d i v i d u a l would consume i n state one (c^) and the e x t e r n a l i t y . The e x t e r n a l i t y does not a f f e c t consumption i f state two occurs. I assume that technological information i s p e r f e c t . An information e x t e r n a l i t y occurs when the e x t e r n a l i t y enters the i n d i v i d u a l ' s expected u t i l i t y c a l c u l a t i o n as an argument of the p r o b a b i l i t y of a given state's occurrence. That i s , U* = ir ( z ) u ( c ) + [1 - i ' ( z ) ] u ( c 2 ) . The e x t e r n a l i t y i s s t i l l a random event i n that the i n d i v i d u a l does not know whether state one or state two w i l l occur, but the e x t e r n a l i t y now influences h i s expected u t i l i t y by a f f e c t i n g the p r o b a b i l i t y of the occurrence of the states. We therefore must multiply h i s u t i l i t y i n both states by a p r o b a b i l i t y function, ir ( Z ) , where the a f f l i c t e d i n d i v i d u a l cannot c o n t r o l z. Expected, u t i l i t y i s again dependent on which state occurs. Technological information i s assumed to be imperfect and i s represented by case ( 3 ) . The a f f l i c t e d agent knows h i s own technology, but not the generating party's technology, and the generating party knows h i s own technology, but not that of the a f f l i c t e d party. Examples can be derived from our botulism case. In a stochastic e x t e r n a l i t y , cans containing botulism toxin enter the a f f l i c t e d agent's u t i l i t y function i f state one occurs. In an information e x t e r n a l i t y , i t i s the a c t i v i t i e s of the generating party that may lead to the creation of cans containing botulism t o x i n . These a c t i v i t i e s (e.g., monitoring the can-sealing process) thus a f f e c t the p r o b a b i l i t y of 50 f i n d i n g botulism i n cans. The u t i l i t y function f o r each state must therefore by m u l t i p l i e d by a p r o b a b i l i t y function, dependent on these a c t i v i t i e s , rather than merely the a f f l i c t e d i n d i v i d u a l ' s own proba-b i l i t y d i s t r i b u t i o n f o r the state., we.could also include the exter-n a l i t y i n the a f f l i c t e d agent's u t i l i t y function f o r an information e x t e r n a l i t y , but r e f r a i n from doing so f o r simplicity."'' The e x t e r n a l i -t i e s are thus stoch a s t i c i n both cases i n that i n d i v i d u a l s have a p r o b a b i l i t y d i s t r i b u t i o n over the occurrence of the e x t e r n a l i t y , but the technological information and the manner i n which the e x t e r n a l i t y a f f e c t s i n d i v i d u a l ' s objective function v a r i e s . In parts B and C, I also introduce f i n a n c i a l intermediaries (insurance companies). With stochastic e x t e r n a l i t i e s , I assume that the insurance companies also have pe r f e c t technological information about A and G. In the information e x t e r n a l i t y case, I assume that insurance companies do not have technological information about e i t h e r A or G. Given imperfect information, p r i o r r i g h t s may not be defined over a l l commodities, that i s , they are not comprehensive and may also be non-exclusive. The question i s , who has the r i g h t s over the e x t e r n a l i t y ? Both agents are affected by the e x t e r n a l i t y (in opposite d i r e c t i o n s ) , yet. '~.h4-yet the agent producing i t possesses the p r i o r r i g h t s de facto i f the e x t e r n a l i t y e x i s t s (see Chapter I I ) . The problem i s that e x t e r n a l i t i e s 1 We would then have to d i s t i n g u i s h between the z that occurs i n the p r o b a b i l i t y function and the z which enters the u t i l i t y function. I do not d i s t i n g u i s h the zs, again f o r s i m p l i c i t y of notation. 51 a r i s i n g from imperfect information may v i o l a t e some or a l l of the conditions f o r p r i o r r i g h t s . E x t e r n a l i t i e s can a r i s e from imperfect information, and given the imperfect information, p r i o r r i g h t s may no longer e x i s t . The question i s now what i n s t i t u t i o n s w i l l a r i s e ( i f any) to a l l o c a t e resources given imperfect information and e x t e r n a l i t i e s ? Three po s s i b l e a l t e r n a t i v e i n s t i t u t i o n s may a r i s e : (1) the emergence of contingent claims (insurance) markets; (2) l e g a l i n s t i t u t i o n s which assign contingent r i g h t s ; and (3) v e r t i c a l i n t e g r a t i o n (for e x t e r n a l i t i e s that only a f f e c t f i r m s ) . I s h a l l examine and compare p o s s i b i l i t i e s (1) i n t h i s chapter and (2) i n Chapter IV with respect to t h e i r a b i l i t y to i n t e r n a l i z e e x t e r n a l i t i e s e f f i c i e n t l y . 1 Each a l t e r n a t i v e w i l l be discussed generally, then formulated more p r e c i s e l y . B. The Operation of Contingent Markets with Stochastic  E x t e r n a l i t i e s In section A of t h i s chapter, I argued that e x t e r n a l i t i e s may p e r s i s t i f information i s imperfect. In t h i s s e c t i o n , I s h a l l examine stochas t i c e x t e r n a l i t i e s , that i s , e x t e r n a l i t i e s that enter an i n d i v i d u a l ' s expected u t i l i t y c a l c u l a t i o n as an argument of h i s u t i l i t y function i n a p a r t i c u l a r state. Uncertainty describes c e r t a i n types of e x t e r n a l i t i e s 1 See the a r t i c l e s i n the B e l l Journal of Economics and Management Science 6 (Spring 1975) , and Green CL974b) f o r a discussion of information as a stimulus to v e r t i c a l i n t e g r a t i o n . I w i l l not deal with t h i s t o p i c i n t h i s t h e s i s . 52 and, even i n t h i s r e l a t i v e l y simple framework, e x t e r n a l i t i e s may prevent the operation of a contingent claims market. In general however, I f i n d that the stochastic e x t e r n a l i t i e s examined i n t h i s section do not lead to market f a i l u r e . Let us consider the stochastic case where the e x t e r n a l i t y i s a random event and a l l agents have pe r f e c t technological information. The event occurs when one agent inadvertently produces an output that may a f f e c t the production or consumption p o s s i b i l i t i e s of another agent, and hence the event becomes an e x t e r n a l i t y . I t i s assumed that: (1) the e x t e r n a l i t y i s a random occurrence, (2) the generator knows h i s technology, but has no control over the occurrence of the e x t e r n a l i t y , (3) the a f f l i c t e d party knows p r e c i s e l y the e f f e c t of the e x t e r n a l i t y on h i s own production or consumption p o s s i b i l i t i e s and therefore on h i s expected income. The uncertainty only pertains to the occurrence of the e x t e r n a l i t y . I w i l l model t h i s s t o c h a s t i c e x t e r n a l i t y with the state preference approach to uncertainty and confine my example to a s i t u a t i o n where an i n d i v i d u a l (as opposed to a firm) i s a f f e c t e d by the e x t e r n a l i t y Given two possible a l t e r n a t i v e and mutually exclusive states, and S^, and e x t e r n a l i t y can be s a i d to occur i f , f o r example, occurs. There i s no e x t e r n a l i t y i n S 2- The a f f l i c t e d party knows how a f f e c t s h i s u t i l i t y function and i s also assumed to have a p r o b a b i l i t y d i s t r i -bution defined over a l l possible states. As long as the a f f l i c t e d party 1 See Arrow (1964) and H i r s h l e i f e r (1965) f o r the development of the state preference model. 53 cannot a f f e c t the p r o b a b i l i t y of any state's occurrence, the nature of the d i s t r i b u t i o n i s unimportant i n that i t does not a f f e c t the ind i v i d u a l ' s expected u t i l i t y maximizing s o l u t i o n . Possible examples of stochastic e x t e r n a l i t i e s include the botulism case i n part A and other product defects that injure consumers of these goods, and sporadic emission of t o x i c wastes i n t o r i v e r s that a f f e c t downstream firms. I w i l l not consider cases of stocha s t i c e x t e r n a l i t y that involve c o l l e c t i v e harm. The question i s , w i l l contingent markets e x i s t to i n t e r n a l i z e the s t o c h a s t i c e x t e r n a l i t i e s ? The formal equivalence i n theory between cer t a i n t y and uncertainty" depends on the assumption that contingent contracts can be written to cover a l l p o s s i b l e uncertain events. That i s , i n d i v i d u a l s can guarantee (by purchasing p o s i t i v e or s e l l i n g negative contingent claims) a s p e c i f i e d l e v e l of income i n a l l possible states of the world given c e r t a i n know-ledge of a l l present and future p r i c e s ( i . e . , there e x i s t s no market uncertainty). With stoch a s t i c e x t e r n a l i t i e s , we are thus i n an Arrow-Debreu world, where information i s not considered e x p l i c i t l y ; technological information i s assumed to be pe r f e c t . The uncertainty pertains to which of S future states w i l l occur.- Expected u t i l i t y i s dependent upon which state occurs, but i t i s assumed that an i n d i v i d u a l knows what h i s income and consumption w i l l be i n the a l t e r n a t i v e s t a t e s , because i n time zero, the i n d i v i d u a l purchases (or s e l l s ) claims to commodities i n a l l future states. We know from Arrow (1964) that i f there exists a competitive ecolibmy with N i n d i v i d u a l s , X commodities, and S state s , then SX contingent claims must have markets (SX markets) to achieve an optimal 54 a l l o c a t i o n of risk-bearing. This section e n t a i l s an examination of insurance markets as a s p e c i f i c example of a contingent market and set of contingent contracts. I employ insurance markets as a p a r t i c u l a r example of an i n s t i t u t i o n a l response to uncertainty rather than work i n the more abstract.framework 2 of contingent claims models f o r several reasons. F i r s t , we generally make the assumption that any two i n d i v i d u a l s w i l l not exchange contingent 3 contracts unless both are made better o f f by the exchange. I f the two i n d i v i d u a l s are A and G, we would not expect them to engage i n any contingent contracts unless p r i o r r i g h t s were delimited. I f no p r i o r r i g h t s e x i s t , no exchange between the two p a r t i e s i s l i k e l y . This 1 AArrow (1964) also attempted to show that only (S + X) markets would be needed i f there are X spot markets which open when a p a r t i c u l a r state occurs and there are S independent money claims to commodities. See Nagatani (1975) f o r a r e f u t a t i o n of t h i s theorem. 2 Other markets and i n s t i t u t i o n s have developed to deal with uncertainty (and some'information problems), e.g., the stock market and cost-plus contracts. I: s h a l l not deal with these markets as they are not a p p l i -cable to e x t e r n a l i t i e s . I t also should be noted that insurance markets r e a l l y are not necessary f o r the analysis i n t h i s section. I employ them now because they are necessary f o r the analysis i n part C of t h i s chapter and I wish to create a b a s i s f o r comparison. 3 Imperfect information can s e r i o u s l y i n t e r f e r e with t h i s r a t i o n a l i t y assumption. I f agents have imperfect information, they may enter contracts i n which they perceive ex ante that t h e i r welfare increases, but are disappointed ex post. Again, we can get around t h i s problem by r e - d e f i n i n g e q u i l i b r i a and welfare improvements under imperfect information. The market w i l l be s a i d to be i n equilibrium when one's expectations are r e a l i z e d . And, t h i s w i l l constitute an improvement i n welfare r e l a t i v e to the information each agent has. 55 argument of course holds f o r any commodity, not j u s t contingent commodities. But, as argued i n section A of t h i s chapter, we would expect that fewer p r i o r r i g h t s e x i s t f o r contingent commodities (e.g., s t o c h a s t i c e x t e r n a l i t i e s ) than f o r ordinary goods. I f p r i o r r i g h t s e x i s t and are assigned to e i t h e r A or G, pr i v a t e contingent contracts between them are pos s i b l e (given p e r f e c t technological information). Note however that there i s no reason to expect that i d e n t i c a l e f f i c i e n t outcomes would be obtained with d i f f e r e n t assign-ments of p r i o r r i g h t s . The introduction of uncertainty should not a l t e r the r e s u l t obtained i n Chapter I I . I f no p r i o r r i g h t s e x i s t , a f f l i c t e d p a r t i e s may s t i l l seek some sort of contingent contract. We might then expect that a f i n a n c i a l intermediary (e.g., insurance company) may emerge to s e l l contingent claims. Insurance companies may also a r i s e to economize on the transaction costs of operating a market. I f there are scale e f f e c t s (increasing returns) i n d i v i d u a l s may be too small to engage i n e f f i c i e n t b i l a t e r a l contracts'? . There may also be asymmetries i n the risk-b e a r i n g a b i l i t y of the A's and G's. This p o s s i b i l i t y i s e s p e c i a l l y relevant i n cases where the As are i n d i v i d u a l consumers and the Gs large corporations. In the botulism case, f o r example, one could argue that the corporation which produces the leaky cans would, because of the s i z e of i t s assets, be able to insure an i n d i v i d u a l consumer at lower cost than could the i n d i v i d u a l insure the corporation. I f both A and G are small, then e i t h e r may seek to d i v e r s i f y h i s r i s k by purchasing insurance- from a f i n a n c i a l intermediary which can spread i t s r i s k s over many contingent 56 commodities. I argue therefore that because of the possible lack of p r i o r r i g h t s and the presence of transaction costs, we should consider insurance markets rather than b i l a t e r a l contracts between A's and G's as the probable i n s t i t u t i o n a l response to stochastic e x t e r n a l i t i e s . Let us now ask the question: w i l l insurance markets a r i s e to deal with stochastic e x t e r n a l i t i e s ? I f so, w i l l competitive e q u i l i b r i a be attained? From Arrow (1964, 1974) and others (Smith (1968), E h r l i c h and Becker (1972)) we know that i f there i s pe r f e c t technological and market information, an optimal insurance contract can be written over random events as long as the insurance industry i s p e r f e c t l y competitive, the insurer can determine the a c t u a r i a l value of the uncertain event (risks can be reduced to a s t a t i s t i c a l b a s i s ) , and i n d i v i d u a l s maximize t h e i r expected u t i l i t y . 1 I s h a l l use the r e s u l t s of the optimal i n s u r -ance models of Arrow (1974) and E h r l i c h and Becker (1972) to develop a model f or stochastic e x t e r n a l i t i e s . The structure of the analysis i s as follows. I f i r s t model stochastic e x t e r n a l i t i e s i n the optimal insurance framework. I then explain the l i m i t a t i o n s of the model; why ce r t a i n assumptions are implausible. Insurance models are generally based on the principal-agent r e l a t i o n s h i p ; the agent (insurance s e l l e r ) maximizes h i s p r o f i t s by _ I t might seem p e c u l i a r to assume that the insurance industry i s p e r f e c t l y competitive when transaction costs e x i s t . We s h a l l ignore t h i s inconsistency f o r the moment as our.transaction costs are merely no p r i o r x-ights and marketing costs. I show however i n part C of t h i s chapter that perfect competition i s inconsistent with transaction costs when those transactions costs are imperfect i n f o r -mation . 57 maximizing the u t i l i t y of the p r i n c i p a l (insurance buyer). I t i s generally assumed that the r i s k insured against i s l o s s of income or loss of u t i l i t y measured by an income equivalent (or consumption set) i n a l t e r n a t i v e states of the world. The insurance p o l i c y s p e c i f i e s a cash or kind reimbursement (payment) f o r each state of the world. Insurance p o l i c i e s are constrained by two assumptions: (1) the insurer i s assumed to be r i s k neutral and premiums therefore only depend on the expected insurance payment to the p r i n c i p a l ; (2) insurance payments are non-negative. 1 I t i s then assumed that the insured knows the objective p r o b a b i l i t i e s of a l l s t a t e s , h i s pre-insurance income i n a l l states, £?and possesses a u t i l i t y function defined over consumption i n each state. With stoc h a s t i c e x t e r n a l i t i e s , u t i l i t y w i l l vary with the state, i . e . , u t i l i t y i s state-dependent. I s h a l l assume i n i t i a l l y that p r i o r r i g h t s e x i s t and are assigned to the generating p a r t i e s . They w i l l thus demand no contingent contracts. A f f l i c t e d p a r t i e s , on the other hand, w i l l want to insure against the occurrence of the e x t e r n a l i t y to equalize t h e i r expected u t i l i t i e s i n a l l s tates. A f f l i c t e d p a r t i e s are assumed to be r i s k averse. Let us consider a s i n g l e a f f l i c t e d party, A, and how the introduction of a stoc h a s t i c e x t e r n a l i t y a f f e c t s hisddemarid'vf ©reinsurance. I assume that 1 Arrow (1974) r a t i o n a l i z e s non-negative insurance payments on moral hazard grounds and argues that i t may be d i f f i c u l t to c o l l e c t a payment from an i n d i v i d u a l i n states with favourable outcomes. This argument i s not e n t i r e l y convincing as the information requirements of t h i s model would not be inconsistent with p o s i t i v e and negative insurance payments. 58 A i s a representative i n d i v i d u a l i n that the e x t e r n a l i t y a f f e c t s a l l A's i d e n t i c a l l y . This allows us to c a l c u l a t e one equilibrium p r i c e that i s common to a l l a f f l i c t e d p a r t i e s . Consider a simple case where i n d i v i d u a l A i s faced with the problem of maximizing h i s expected u t i l i t y given two uncertain states, 1 and 2. His u t i l i t y function i n each state i s assumed to be s t r i c t l y concave. U t i l i t y i n state 1 i s a function of h i s own expected consumption, c^, and the consumption of another i n d i v i d u a l , c . . U t i l i t y . i n state.2 i s G a function only of i n d i v i d u a l A's consumption i n that state, c . : c 2 G i s the stochastic e x t e r n a l i t y . Both states are of course weighted by the p r o b a b i l i t i e s of t h e i r occurrence, ir and (1. - ir) . . Thus the * expected u t i l i t y of A?/ (U ), i s state-dependent and i n one state, A's u t i l i t y i s dependent upon the consumption of G, the generating party. Individual A (in period zero) then maximizes.his expected u t i l i t y over states one and two (in period one). That i s , he maximizes U* = T T U 1 ( C 1 , C g ) + (1 - T T ) U 2 ( C 2 ) (1) subject to h i s budget constraint P 1 C 1 + P 2 C 2 = k ( 2 ) where k i s a parameter equal to i n i t i a l wealth minus consumption i n period zero, p^ and p^ are contingency p r i c e s that p r e v a i l i n period zero, and may not be the p r i c e s which p r e v a i l , i . e . , those p r i c e s which a c t u a l l y occur when the i n d i v i d u a l i s i n state one or state two i n period one (see Arrow (1964)). 59 The e x t e r n a l i t y does not enter into the budget constraint as i n d i v i d u a l A has no control over i t s e f f e c t on h i s consumption. The f i r s t order conditions f o r a maximum are TTU1 = Xp 1 (3a) (1 -TT)U2 = Ap 2 (3b) P-,^ + P 2 c 2 = k (3c) 1 2 1 where u = 9u(c ,c )/9c and u = 9u(c )/9c . J. J. G J. J. 2 2 We must now examine the e f f e c t of the e x t e r n a l i t y on c^ to see how i t a f f e c t s i n d i v i d u a l A's insurance purchases. T o t a l l y d i f f e r e n t i -ating (3a-c) and s o l v i n g the r e s u l t i n g equations simultaneously y i e l d s 1 Ar. "P,™„ d c l = 2 ' 1 2 . (4) dc G P± §2 iTu + f _ l (1 - TT)U P l P 2 The sign of the denominator w i l l be negative as i t i s assumed that i n d i v i d u a l A i s r i s k averse. Thus his u t i l i t y function i s s t r i c t l y 1 2 concave < 0, u < 0). The sign therefore depends on the cross p a r t i a l , the e f f e c t of the e x t e r n a l i t y on consumption i n state one. c i s a negative e x t e r n a l i t y (diseconomy) and i n most cases we may assume G u ^ < 0 a n <3 the whole expression i s thus negative. 1 A's i n d i f f e r e n c e curves are assumed to be convex^throughout. Thus the second order conditions are s a t i s f i e d . This assumption may not be v a l i d , f or the introduction of the s t o c h a s t i c e x t e r n a l i t y may lead to nonconvex preferences and i n d i f f e r e n c e curves between states one and two. See my discussion of nonconvexities i n part C of t h i s chapter and S t a r r e t t (1972). 2 This,'assumption may not be v a l i d i n some e x t e r n a l i t y cases. 60 The introduction of the e x t e r n a l i t y decreases state one consump-t i o n and we would expect the i n d i v i d u a l to attempt to equalize h i s expected u t i l i t y i n the two states by purchasing insurance against state one's occurrence. Individual A may thus wish to exchange claims to h i s consumption i n state two f o r consumption i n state one, that i s , buy insurance against the stochastic e x t e r n a l i t y i f state one occurs. The a f f l i c t e d party has to know the value of u ^ 2 to determine i f the expected benefits of insurance f o r state one are equal to (or greater than) the p r i c e of the insurance. The p r i c e of insurance w i l l depend (as i n the case of an ordinary uncertain event) on the a c t u a r i a l c a l c u l a t i o n of the r i s k . I f consumption between states can be exchanged at a constant rate, then the p r i c e of insurance, a, w i l l equal dc 2/dc^. Individual A w i l l buy insurance i f TFU., p, 1 /(-•> a = IT 11 = r l . (5) (1-TT)U2 P2 I f the p r i c e of insurance i s a c t u a r i a l l y f a i r , then the r a t i o of the p r o b a b i l i t i e s w i l l equal the p r i c e of insurance (d = i r / l - i r ) and (5) 1 2 becomes 1 = u^/u^. I f A's marginal rate of s u b s t i t u t i o n between states one and two i s decreasing, h i s consumption bundle w i l l be equal-ized i n both states and he w i l l have f u l l insurance against the 1 This r e s u l t i s analogous to conventional u t i l i t y theory, i . e . , i n equilibrium, the r e l a t i v e p r i c e between the two commodities (here the p r i c e of insurance i n terms of the consumption i n the two states) must equal the individual's,margaihal rate of s u b s t i t u t i o n between the two goods. We only add the r a t i o of the p r o b a b i l i t i e s which drop out i f the p r i c e of insurance i s a c t u a r i a l l y f a i r . 61 stochastic e x t e r n a l i t y . A i s thus i n d i f f e r e n t to which state occurs. I f the p r i c e of insurance i s a c t u a r i a l l y f a i r , then the incentive to insure i s independent of the p r o b a b i l i t i e s of the events. That i s , a = 1 i n t h i s case and TT/1-TT drops-out of equation (5). In part C of t h i s chapter, we can no longer u t i l i z e t h i s r e s u l t , asithe p r i c e of insurance w i l l no longer be independent of the p r o b a b i l i t i e s of the events. As might be expected, the introduction of an e x t e r n a l i t y into one's expected u t i l i t y function w i l l not•fundamentally a l t e r the pro-v i s i o n of insurance. The e x t e r n a l i t y merely complicates the expression i f technological information i s p e r f e c t . In general, i f there was f u l l insurance coverage p r i o r to the e x t e r n a l i t y ( i . e . , premiums are actu-a r i a l l y f a i r ) , there w i l l be f u l l coverage a f t e r the introduction of the stochastic e x t e r n a l i t y , given that the e x t e r n a l i t y does not a f f e c t the p r o b a b i l i t i e s of the events. I f the buyers and s e l l e r s of insurance have the information necessary to c a l c u l a t e r i s k and the e f f e c t of the e x t e r n a l i t y on one's consumption p o s s i b i l i t i e s i n a l t e r n a t i v e states, contingent markets w i l l tend to operate. 1 See E h r l i c h and Becker ('1972) f o r further discussion of these points and Arrow (1974) f o r proofs. 2 Note that the conclusion that A i s i n d i f f e r e n t to the outcome assumes that A has a preference ordering over the s t o c h a s t i c e x t e r n a l i t y . This assumption may be u n r e a l i s t i c i f the e x t e r n a l i t y involves the p o s s i b i l i t y of serious i l l n e s s or death. But perhaps we should not worry about t h i s problem. People do buy f u l l l i f e insurance and presumably would also purchase f o r example, botulism insurance. 6 2 There are some d i f f i c u l t i e s with the a p p l i c a t i o n of t h i s insurance model to stochastic e x t e r n a l i t i e s . F i r s t , we must look at the behavioral assumptions i m p l i c i t i n the principal-agent approach. Only the demand side of insurance markets i s modelled i n the principal-agent r e l a t i o n -ship. No s p e c i f i c behavioral hypotheses are postulated f o r the suppliers of insurance except to assume that the agent maximizes his p r o f i t s by maximizing the expected u t i l i t y of the p r i n c i p a l . Given the i d e n t i f i c a -t i o n and a c t u a r i a l determination of a r i s k y event, agents w i l l instan-taneously emerge to maximize the p r i n c i p a l ' s expected u t i l i t y . But who finds whom? How do agents i d e n t i f y the i n d i v i d u a l s p o t e n t i a l l y a f f e c t e d by the event? We must assume that the insurer has p e r f e c t technological information f o r the a f f l i c t e d and generating p a r t i e s . We should also consider who w i l l buy the insurance i n the case of a stochastic e x t e r n a l i t y . C l e a r l y , t h i s depends on the s p e c i f i c a t i o n of p r i o r r i g h t s , i f they e x i s t . One could ask the "Coase" question: i s a l l o c a t i v e e f f i c i e n c y dependent on which party buys insurance? Conceiv-ably, we could have a s i t u a t i o n analogous to the c e r t a i n t y case i n which the a f f l i c t e d party s e l l s insurance to the generator or the reverse, depending on the r i g h t s d e l i m i t a t i o n . Or one could introduce a t h i r d party (the insurance company or a government) which c o l l e c t s premiums from one party and d i s t r i b u t e s them to the other when the event occurs. The payments would cover d i f f e r e n t events. Under one arrangement, the generator would receive an insurance payment i f the e x t e r n a l i t y d i d not occur, whereas under the a l t e r n a t i v e , the a f f l i c t e d party would receive a payment i f the e x t e r n a l i t y d i d occur. This s i t u a t i o n i s the uncertainty 63 analog o f the tax-subsidy case, and one would expect that the e f f i c i e n t s o l u t i o n reached does depend on who buys insurance. Thus f a r , there i s nothing i n the formulation of a stochastic e x t e r n a l i t y that e f f e c t i v e l y d i f f e r e n t i a t e s i t from other s t o c h a s t i c events cove reel Ky optimal insurance contracts. As long as a p r i n c i p a l emerges to s e l l insurance and can determine the a c t u a r i a l value of the e x t e r n a l i t y , an optimal contract can be w r i t t e n , i f r i g h t s are delimited. Determining a c t u a r i a l values requires a s u f f i c i e n t number of observations so that the law of large numbers i s e f f e c t i v e and r i s k s are then s t a t i s -t i c a l l y independent. In general, the numbers affe c t e d by any given stochastic e x t e r n a l i t y w i l l be r e l a t i v e l y small, thus complicating the a c t u a r i a l computations. But we do observe companies such as Lloyds which write insurance f o r j u s t about any event. Risk independence i s preserved f o r s t o c h a s t i c e x t e r n a l i t i e s as long as they are assumed to be non-collective e x t e r n a l i t i e s , i . e . , they are not p u b l i c bads. C l e a r l y , there are many cases where an e x t e r n a l i t y i s stochastic and p u b l i c ; f o r example, core melt-downs of nuclear power plants and o i l s p i l l s from supertankers. In these cases, r i s k s to a l l a f f l i c t e d p a r t i e s are not only interdependent, but the events a f f e c t a large number of people simultaneously. That i s , the r i s k s are too s o c i a l to write p r i v a t e insurance. A core melt-down of a power plant i n a metropolitan area may a f f e c t hundreds of thousands of people. No p r i v a t e , market i s l i k e l y to e x i s t i n these circumstances. The usual argument at t h i s point i s to consider s o c i a l or government insurance. Whether or not government insurance can lead to e f f i c i e n t and optimal solutions 64 i s a topic of considerable debate which I s h a l l not enter. The point i s that the optimal insurance framework may be inappropriate f o r analyzing many e x t e r n a l i t y cases. Could i n d i v i d u a l s reach optimal outcomes given a stochastic e x t e r n a l i t y without purchasing market insurance? One p o s s i b i l i t y i s that i n d i v i d u a l s engage i n self-insurance. E h r l i c h and Becker (1972) define self-insurance as actions taken by i n d i v i d u a l s to reduce the s i z e of the l o s s , f o r example, purchasing rubber bumpers f o r one's auto-mobile to decrease damage when struck by another v e h i c l e . S e l f - i n s u r -ance and market insurance tend to be substitutes and thus the i n d i v i d u a l ' s choice of which insurance a l t e r n a t i v e to take depends on the r e l a t i v e 1 p r i c e s . I f G and A have d i f f e r e n t methods of self-insurance, then there i s no guarantee that the e f f i c i e n c y f r o n t i e r reached by each party with self-insurance (or a combination of market and self-insurance) i s 2 i d e n t i c a l . The differences i n self-insurance a b i l i t y can therefore have ah impact on the choice of p r i o r r i g h t s and s o c i a l outcomes. In the botulism case f o r example, the food f i r m may be able to employ one i n d i v i d u a l to prevent a l l leaky cans from being sold. S i m i l a r l y , each consumer can avoid the purchase of leaky cans ( i f he has p e r f e c t 1 E h r l i c h and Becker solve f o r an e f f i c i e n t l e v e l of self^insurance and combinations of market and self-insurance. 2 This point i s analogous to that made by Archibald and Wright (1974) with regard to abatement techniques under ordinary e x t e r n a l i t i e s . 65 technological information i n that he knows a l l leaky cans contain botulism t o x i n ) . The abatement techniques are s i m i l a r , yet society may be better o f f (in the sense that i t can reach a higher f r o n t i e r ) by employing one i n d i v i d u a l rather than having a l l consumers check f o r leaky cans. In add i t i o n , the s i m i l a r i t i e s i n abatement technique depend on the assumption that technological information i s pe r f e c t . I f information i s imperfect, abatement techniques are not i d e n t i c a l . Consumers may not know how to d i s t i n g u i s h cans which contain botulism from cans which do not. Thus we have the p o s s i b i l i t y that d i f f e r e n t d i s t r i b u t i o n s of p r i o r r i g h t s w i l l lead to d i f f e r e n t s o c i a l outcomes depending on self-insurance techniques, although both may be techni--c a l l y e f f i c i e n t i n the sense that the insureds' marginal rates of su b s t i t u t i o n over states equal the s e l f - or market insurance p r i c e . This suggests that the party which can abate at lower cost or achieve the highest f r o n t i e r should bear the l i a b i l i t y f o r the stocha s t i c e x t e r n a l i t y . 1 I have shown that s t o c h a s t i c e x t e r n a l i t i e s do not prevent the operation of contingent markets as long as technological information i s p e r f e c t . Aside from the d i f f i c u l t i e s of def i n i n g r i s k , p r i v a t e markets could e x i s t f o r the stochastic e x t e r n a l i t y cases considered. Market f a i l u r e i s thus u n l i k e l y to stem from stoc h a s t i c e x t e r n a l i t i e s . This means that we have s t i l l not explained the persistence of exter-n a l i t i e s i n the economy and why c e r t a i n insurance markets do not e x i s t . I turn now to an examination of information e x t e r n a l i t i e s . 1 See Chapter IV, part C f o r an elaboration of t h i s point i n the context of l i a b i l i t y r u l e s . 66 C. The Operation of Contingent Markets with Information  E x t e r n a l i t i e s This section e n t a i l s an examination of market f a i l u r e that arises from information e x t e r n a l i t i e s . R e c a l l from section A of t h i s chapter that an information e x t e r n a l i t y may a r i s e whenever the e x t e r n a l i t y (derived from the production or consumption a c t i v i t i e s of one agent) enters another agent's expected u t i l i t y function as an argument of the p r o b a b i l i t y of the occurrence of a stochastic exter-n a l i t y . Technological information i s also assumed to be imperfect i n that the a f f l i c t e d party does not know the "technology" of the generating party that creates the e x t e r n a l i t y . As i n section B, I assume that p r i v a t e negotiation between A and G to i n t e r n a l i z e the e x t e r n a l i t y i s u n l i k e l y due to the absence of p r i o r r i g h t s , and A thus seeks market insurance. 1 Another assumption, appropriate f o r the cases considered i n t h i s section, i s that any p o t e n t i a l insurer e i t h e r possesses the same or l e s s technological information than the a f f l i c t e d party, never more information. Before presenting my model of an information e x t e r n a l i t y , I would l i k e to note that some of the insurance l i t e r a t u r e , namely, Arrow (1963, 1968), Pauly (1968, 1974), Akerlof (1970), E h r l i c h and Becker (1972), and Helpman and Laffont (1975), have considered the e f f e c t of imperfect information on the attainment of competitive insurance e q u i l i b r i a . 1 I t i s a matter f o r the l e g a l system whether bargaining made without an assignment of r i g h t s i s recognized as an enforceable contract. I w i l l not discuss t h i s issue. 67 I s h a l l incorporate and apply some of the r e s u l t s of t h e i r analyses to my' discussion of e x t e r n a l i t i e s . The insurance l i t e r a t u r e i d e n t i -f i e s two types of e f f e c t s on insurance markets from imperfect techno-l o g i c a l information: moral hazard and adverse s e l e c t i o n . I s h a l l define these terms then show how information e x t e r n a l i t i e s can give r i s e to market f a i l u r e from moral hazard and adverse s e l e c t i o n . Moral hazard and adverse s e l e c t i o n may a r i s e when the insurers have les s technological information (or t h e i r information i s more imperfect) than the insured. Adverse s e l e c t i o n i s s a i d to e x i s t when the s e l l e r cannot determine or evaluate some of the c h a r a c t e r i s t i c s of the buyer that a f f e c t the p r o b a b i l i t y of the occurrence of states (Pauly, 1974, p. 45). The usual example given i s that insurers cannot d i s t i n g u i s h between good and bad r i s k i n d i v i d u a l s i n the present state and thus cannot charge an e f f i c i e n t insurance p r i c e r e l a t e d to the s p e c i f i c r i s k s of each group. Moral hazard e x i s t s when the insured can engage i n a c t i v i t i e s that a l t e r the p r o b a b i l i t i e s of the uncertain events i n response to insurance. Insurance s e l l e r s are assumed to be unable to monitor these a c t i v i t i e s and thus cannot charge premium pr i c e s that are f u n c t i o n a l l y r e l a t e d to the insured's a c t i v i t i e s . I f the insurer can determine the r e l a t i o n s h i p between the insured's a c t i v i t i e s and the p r o b a b i l i t i e s of uncertain events, optimal insurance contracts can be written. An example of moral hazard i n insurance markets i s negligence that leads to f i r e when property i s insured. In both cases, insurers lack technological information, but i n the case of moral hazard, an ad d i t i o n a l problem emerges i n that the p r o b a b i l i t y 6 8 of an uncertain event i s now dependent on i n d i v i d u a l s ' actions (e.g., t h e i r abatement technology). 1 Moral hazard thus involves a s i t u a t i o n analogous to my information e x t e r n a l i t y . I s h a l l now formalize an information e x t e r n a l i t y , then derive some propositions about the operation of markets from the model. I w i l l f i r s t assume that both generating and a f f l i c t e d p a r t i e s can engage i n a c t i v i t i e s that a f f e c t the p r o b a b i l i t y of the occurrence 2 A A A G of the stochastic e x t e r n a l i t y . For example, l e t i r = TT (z ,z ) s s where A and G are again the a f f l i c t e d and generating p a r t i e s , TT^ i s the p r o b a b i l i t y of state s (a stochastic e x t e r n a l i t y to A) occurring, A G and z , z are a c t i v i t i e s which both A and G can engage i n , which A . G a f f e c t the occurrence of the event. In general, we assume z f z . A G An e x t e r n a l i t y i s present when S T T ^ . S Z ^ 0 . I also assume that 2 A G A 9 TT /9z 9z ^ 0 , although t h i s assumption i s not necessary f o r the s existence of an e x t e r n a l i t y . I f state s e n t a i l s losses f o r A, then 1 Another way i n which moral hazard can i n t e r f e r e with insurance markets i s due to improper or incomplete s p e c i f i c a t i o n of the a c t i v i t i e s which give r i s e to the stochastic event. Divorce insurance i s not l i k e l y to e x i s t f o r example, because insurers cannot specify the variables that prevent or lead to divorce. Insurance payment f o r divorces would have to be made contingent on something other thahto"trying hard" to make, marriage work. This i s not a question of information per se, but rather of d e f i n i n g a v a r i a b l e that can be measured. 2 I can complicate the analysis further by assuming that both the p r o b a b i l i t i e s and the u t i l i t y function are a f f e c t e d by the generating party's a c t i v i t i e s . See part A of t h i s chapter. This exercise would complicate already unmanageable expressions without adding much i n content. 69 G A G 2 A A G z i s an external diseconomy i f 9TT /9z > 0 and 9 IT /9Z 9Z < 0. s s A c l a s s i c example of an information e x t e r n a l i t y i s immunization against epidemic disease. State s i s the disease (e.g., the f l u ) which i s a random event to a given population. The occurrence of s to any i n d i v i d u a l A depends both upon h i s own immunization against A G A A the f l u and the immunizations of others. 9TT /9z and Sir /9z are s s both assumed to be negative i n t h i s case, but the t o t a l e f f e c t depends A G on the cross p a r t i a l s between z and z . Note that r i s k s may no longer be s t a t i s t i c a l l y independent i n th i s case. Risk independence i s c l e a r l y l o s t when the TT 1 f o r a l l i in d i v i d u a l s depends on everyone's l e v e l or extent of immunization. In a sense, I have slipped p u b l i c goods into t h i s a n a l y s i s , but t h i s A A G i s not necessary. As soon as TT^ (Z , Z ) occurs f o r any A, G, s t a t i s t i c a l independence i s l o s t , whethertthe e x t e r n a l i t y i s c o l l e c t i v e or not. I f r i s k s are not independent, whether or not any insurance p o l i c i e s are offered by insurers depends on the information they have about the T T 1 (Z 1 ) functions. I f insurers have p e r f e c t information, a c t u a r i a l values can be calcul a t e d , taking into account the interdependencies. I f insurers have imperfect information about T r 1 ( z 1 ) , there e x i s t two (at least) p o s s i b i l i t i e s . F i r s t , insurers may perceive the existence of r i s k dependencies, but do not know how the z 1 a f f e c t i r 1 . In t h i s case, one would not expect p r o f i t maximizing insurers to o f f e r any premiums f o r sa l e . Insurers may not however be aware that p r o b a b i l i t y i s dependent upon z 1 . They w i l l estimate r i s k s and charge premium pr i c e s that do not, except by chance, correspond to the optimum. There 7 0 i s also the p o s s i b i l i t y that insurers w i l l "learn" of the r i s k a f t e r insurance payments to a number of i n d i v i d u a l s are made. Non-existence of an equilibrium i s thus l i k e l y . A zero p r o f i t condition f o r insurers can be simply that E T ^ X 1 = E P 1 , where X 1 i i i s the insurance payment made i n state s to i n d i v i d u a l i (for a l l i and s ) , and P 1 i s the premium charged (both i n terms of income). I f insurers assume that a l l i n d i v i d u a l s are i d e n t i c a l , a l l TT 1 are affe c t e d by z 1 , and insurers charge a premium that i s less than the expected value of losses, then i n d i v i d u a l s w i l l buy excessive amounts of insur-ance. The p r o b a b i l i t i e s of a l l states w i l l be aff e c t e d and insurers w i l l make losses, or E n ^ X 1 > E P 1 . I f insurers charge a premium p r i c e i i i n excess of expected values, and the marginal cost of the i n d i v i d u a l s 1 z 1 a c t i v i t i e s are less than the premium, no insurance w i l l be purchased and thus no equilibrium w i l l e x i s t . I f z 1 "costs" more than the pre-mium, some insurance may be purchased, but then E T T 1 X 1 < E P 1 , excess i i p r o f i t s w i l l be made and the premium p r i c e must decrease. I f p r o b a b i l i t i e s are dependent on a c t i v i t i e s i n some, but not a l l states, equilibrium may continue to be non-existent. I f i n d i v i d u a l s are i d e n t i c a l , and the states which correspond to activity-dependent proba-b i l i t i e s are distinguishable from other states, insurers may be able to write premiums such that E T r 1 X 1 = E P 1 . This may e n t a i l some loading i i i n those states where p r o b a b i l i t i e s are independent and i n d i v i d u a l s have no options of using z 1 (e.g., no abatement techniques). I f i n d i v i -duals are not i d e n t i c a l , adverse s e l e c t i o n may a r i s e and e q u i l i b r i a may not e x i s t . One other p o s s i b i l i t y with non-identical i n d i v i d u a l s i s that 71 only a few i n d i v i d u a l s are capable of i n f l u e n c i n g p r o b a b i l i t y . I f the event a f f e c t s large numbers of i n d i v i d u a l s , the a c t i v i t i e s may cancel out or become i n s i g n i f i c a n t with aggregation. That i s , the impact of the a c t i v i t i e s that generate e x t e r n a l i t i e s i s too small to a f f e c t the p r o b a b i l i t i e s . Let us now assume that insurers can.determine r i s k s .and see what happens to expected u t i l i t y maximization and insurance with an information e x t e r n a l i t y . The information e x t e r n a l i t y can be i n t r o -duced i n several ways. I w i l l i l l u s t r a t e what I think i s the simplest case. There are two states?? 1 and 2, with p r o b a b i l i t i e s TT and (1 - TT) . We w i l l maximize the expected u t i l i t y of a party a f f l i c t e d by the e x t e r n a l i t y . A l l A's are therefore i d e n t i c a l . A's u t i l i t y functions f o r each state are assumed to be concave. Let us f i r s t define the conditions f o r A to maximize h i s expected u t i l i t y , then we s h a l l introduce an insurer. Using notation s i m i l a r to the.case of a stochastic e x t e r n a l i t y , the problem i s to maximize U = TT(C ,z)u(c ) + [ l - TT(C ,z)]u(c ) (6) subject to P 1 C 1 + P 2 C 2 = k ' ( 7 ) where P-^ 'P2 a r e a9a-*-n contingency p r i c e s , and k i s wealth minus consumption i n period zero, z i s the e x t e r n a l i t y and i s a function of the generating party's consumption i n state one; z = .z(c ')."'" A cannot co n t r o l z. 1 z could also be an output of a firm which only occurs i n state one. 72 I assume that the p r o b a b i l i t i e s of states one and two are dependent on the a c t i v i t i e s of both the a f f l i c t e d and generating p a r t i e s , and that A's a c t i v i t i e s are what he could consume i n state one. 3 i r / 8 c ^ i s assumed to be negative and 3TT/3Z p o s i t i v e . That i s , c^ decreases the p r o b a b i l i t y of state one occurring, while z increases the proba-b i l i t y . State one a f f e c t s i n d i v i d u a l A adversely, and z i s therefore an external diseconomy. An example ( i f z i s an output i n state one) •' i s asbestos-inducing cancer. In state one, A contracts cancer, i n state two he does not. He can engage i n a c t i v i t i e s i n state one (e.g., wearing a r e s p i r a t o r , i n s t a l l i n g a i r f i l t e r s i n h i s home and staying indoors) that decrease the p r o b a b i l i t y of state one. Simul-taneously, G can engage i n a c t i v i t i e s that increase the p r o b a b i l i t y and thus generate an e x t e r n a l i t y (e.g., not having emission controls on asbestos f i b r e s ) . A stochastic e x t e r n a l i t y also e x i s t s i n t h i s example, but f o r s i m p l i c i t y , we w i l l not add z (or c ) to A's u t i l i t y G function for state one. The f i r s t order conditions f o r a maximum are T r 1 ^ u ( c 1 ) - T iU(("c 2 . )J + T r ( c i , z ) u 1 + Xp 1 = 0 (8a) [.1 - TT (c 1,z)J:u 2 + Xp 2 = 0 (8b) P 1 C 1 + P2°2 ~ k = 0 ( 8 c ) where TT = 3TT(C ,z)/3c , u = 3u/3c , and u = 3u/3c . X X X ]_ X 2. 2 In equilibrium I T 1 . Q i t c ^ - u ( c 2 ) ] + T T ( C ] L , Z ) U 1 = p ( 9 ) (1 - TT) ( C 1 , Z ) U 2 P 2 73 Equation (9) can be interpreted as requiring the equality of the marginal gain from decreasing the p r o b a b i l i t y and the marginal cost of the purchase of c (given z) i n terms of decreased consumption i n state two. Individual A w i l l be i n equilibrium, but t h i s w i l l not be optimal because he has no control over z. Equation (9) thus i n -dicates A's best attainable point independent of G. But note that A cannot even evaluate t h i s point unless he has technological i n f o r -mation about G's a c t i v i t y , z. I f we assume he has t h i s information for the moment, l e t us consider how the dependency of the p r o b a b i l i t y of state one on A's and G's a c t i v i t i e s a f f e c t s the expected u t i l i t y maximum. Consider a s u f f i c i e n t condition f o r a maximum, 7 T l l d C l ' - U l ~ u ^ c 2 ^ + 7 r i z d c i d Z ' - U l ~ U ^ C 2 ^ + ^ l ^ l ^ l ~ U 2 d ° 2 * + T r ( c 1 , z ) u 1 1 d c 1 + (1 - 7 T ) u 2 2 d c 2 < 0 ( 1 0 ) The expression i s somewhat complex and signing i t i s not an easy task. A number of assumptions are necessary and even with these, no guarantee e x i s t s that the condition w i l l be met. Even i f we assume TT < 0, TT < 0 , TT < 0, and TT, < 0, we cannot t e l l i f (10) i s negative, 22 l z 1 as the terms -TT, ,dc,u(c„) , '-TT, dc.dz[u(c„) ] and -TT u dc,dc„ w i l l be 11 1 2 l z l 2 1 2 1 2 p o s i t i v e . If:!iT < 0, the same problem occurs. In addition, we cannot be sure of the sign of TT . I f TT > 0-over some ranges, then again, l z l z (10) may not be negative. * Also note that we do not even know i f A's expected u t i l i t y (U ) w i l l be quasi-concave. A's concave u t i l i t y function i n state one must be 74 mu l t i p l i e d by the p r o b a b i l i t y function T T ( C ^ , Z ) . Quasi-concavity of U requires { x | U (x) - c } i s convex f o r a l l c > 0. whether or not t h i s condition i s s a t i s f i e d when we multiply A's u t i l i t y functions by p r o b a b i l i t y functions i s not c l e a r . 1 In addition, we may have some reason to expect that the p r o b a b i l i t y functions are nonconcave. As the generating party increases z, c^ becomes l e s s and l e s s e f f e c t i v e i n decreasing TT. Individual A cannot co n t r o l z, but he can a l t e r c^. In p a r t i c u l a r , he may be able to increase h i s purchase of market insurance ( i f available) and simply stop consuming c^ at some l e v e l of z. The question i s , should we worry about the possible non-quasi-concavity of equation (6)? Is quasi-concavity of the expected u t i l i t y function necessary f o r the existence of an equilibrium? We have now introduced the p o s s i b i l i t y that i n d i v i d u a l A's demand curves f o r con-tingent commodities w i l l be discontinuous. Arrow (1964) argues that 1 Even i f we assume that the p r o b a b i l i t y functions are s t r i c t l y concave i n c and z, we cannot quarantee that U* i s concave (but i t may s t i l l be quasi-concave). For s i m p l i c i t y , l e t U (c) = T T ( C ) U ( C ) . Let us ignore the e x t e r n a l i t y and state two. Can we then sign the second d i f f e r e n t i a l of U*? * dU = IT (c)u(c)dc + TT (c)u 1(c)dc = 0 2 * < d U = T r 1 1 (c)u (c)dc + 2ir ( c j u ^ c ) dc + TT ( C ) U ^ (c)dc ^ 0 . The f i r s t and t h i r d terms are negative from our s t r i c t concavity assumptions f o r the p r o b a b i l i t y and u t i l i t y functions. The second term i s p o s i t i v e . Thus U*^ cannot be signed without a d d i t i o n a l information about the r e l a t i v e s i z e of the terms. 75 quasi-concavity of expected u t i l i t y functions i s not necessary f o r the existence of competitive e q u i l i b r i a i f there are a large number of i n d i v i d u a l s , each with small incomes. 1 Helpman and Laffont (1975) show, on the other hand, with an example of an expected u t i l i t y function that i s not quasi-concave, that no competitive e q u i l i b r i a can be attained even i f they aggregate over large numbers of consumers. In t h e i r model, i n -di v i d u a l s e i t h e r choose f u l l insurance (and the l e v e l of a c t i v i t y c^ goes to zero), or they purchase negative insurance. In both cases, the insurance companies incur losses because the p r o b a b i l i t y of the event has changed and t h e i r premium p r i c e has not adjusted to the new r i s k s i t u a t i o n . I cannot reconcile these two c o n f l i c t i n g arguments at t h i s point, but want to merely point out the p o s s i b i l i t y of non-existence of e q u i l i b r i a i f expected u t i l i t y functions are not quasi-concave. We now ask i f i n d i v i d u a l A can purchase market insurance. Assuming i n d i v i d u a l A knows the e f f e c t of z on TT, he w i l l choose a u t i l i t y maxi-mizing premium given (9) and the dependence of the premium and c on 2 the amount of insurance purchased. Expected u t i l i t y i s now defined over consumption and insurance, or 1 Arrow's argument i s based on Rothenberg (1960). He suggests that, with aggregation, a l l the "holes" or d i s c o n t i n u i t i e s i n demand functions are f i l l e d i f i n d i v i d u a l s are d i f f e r e n t . I f i n d i v i d u a l s are i d e n t i c a l , equilibrium i s s t i l l attained over a l l p r i c e s , because i n d i v i d u a l s are i n d i f f e r e n t between the boundaries of the d i s c o n t i n u i t y and the market c l e a r s . Also see Rothschild and S t i g l i t z (1975). 2 See Pauly (1974) for an elaboration of t h i s model (without e x t e r n a l i t i e s ) . This i s the second part of a two-stage maximization. Individual A f i r s t chooses the c^ that s a t i s f i e s equation (9), then determines the amount of insurance he w i l l buy (X) by maximizing h i s expected u t i l i t y given c^ and the value of the premium. 76 * U T r ( c 1 , z ) u ( c 1 - P - L - X) + [ l - TT ( c 1 , z j u ( c 2 - P) (11) where P i s the t o t a l premium paid for X d o l l a r ' s worth of insurance, L i s the loss which occurs only i n state one, and c and P are depen-dent on X. The f i r s t order condition for a maximum of (11) i s 3P (£.;,_,z)u' (1) + [ l - TrMc^zjju' (2)J = - T r ( C l , z ) u ' (1) *_1 Prr (c ,z)u' (1)"] - 9TT_3C_ f u ( l ) - u(2)~l . 1 (12) i L J 9 C,9X L J _9c a i Dropping the p r i c e r a t i o i n (9) and s u b s t i t u t i n g f o r dir/dc^ y i e l d s the optimal premium-to-benefit r a t i o , or insurance p r i c e . 9P 3 c V ™ = - * ( c i / z ) u ' ( 1 ) ~ a j - d - T D ( C 1 , Z ) U ' ( 2 ) ^ ( 1 3 ) r-n'ic^, zju'-\ij + \l - TT j '(c ,z)u' (2) I assume that the insurance market i s p e r f e c t l y competitive and insurers thus s a t i s f y the zero p r o f i t condition given by Z TT 1 X 1 = P 1 (14) i 2 where i i s a l l i n d i v i d u a l s a f f e c t e d by the e x t e r n a l i t y . I f insurers could observe c^ and z, f o r a l l A i n d i v i d u a l s , the premium would vary with TT and an "optimal" amount of insurance could be sold. That i s , each insurer would set h i s premium p r i c e equal to the s o l u t i o n to (13). Again, t h i s i s not a s t r i c t optimum because u(l) = u(c - P - L - X) and u(2) = u(c - P) . 1 2 2 S t r i c t l y , (14) should also be summed over a l l states. 77 neither A nor the insurer can a f f e c t z. I t i s j u s t an equilibrium, given z. Notice however the informational requirements on the i n -surer. He must be able to solve (13), which requires technological information not only about the a c t i v i t i e s of A, but also those of G as w e l l . Insurers must therefore be able to i d e n t i f y the Gs and ascertain the way i n which z enters the p r o b a b i l i t y functions of A. We can then ask i f the Gs w i l l have any incentive to reveal information to insurers. This i s doubtful unless they are required to provide information by an assignment of r i g h t s and l i a b i l i t y . 1 Notice also that even i f insurers can evaluate TT (C ^ , Z ) , acquiring t h i s information i s c o s t l y . I have not e x p l i c i t l y introduced these transaction costs into the model, but I could assume that t h i s r e s u l t s i n loading of insurance premium p r i c e s . We know from Arrow (1974) that loading may decrease the extent of insurance coverage i n any state. I f an insurer cannot observe TT (C ^ , Z ) and therefore cannot base insurance p r i c e s on the a c t i v i t i e s ' e f f e c t s on p r o b a b i l i t y , moral hazard e x i s t s . That i s , i f the insurer does not vary the premium p r i c e with changes i n the l e v e l of c^ and z, he w i l l not charge a pr i c e equal to the s o l u t i o n to (13). Pauly (1974) shows how the competitive equilibrium w i l l vary from the "optimal" outcome expressed by (13). The argument i s that any one insurer w i l l be unable to deter-mine the t o t a l amount of insurance each i n d i v i d u a l a f f e c t e d by the ex t e r n a l i t y purchases. Insurers w i l l only know the amount of insurance 1 See Chapter IV f o r discussion of t h i s incentives problem. 78 bought from t h e i r own firm and not the coverage purchased from other insurers by the A's. Therefore, each insurer cannot adjust the premium p r i c e to the amount of insurance purchased by each i n d i v i d u a l . Expected losses increase with the amount of insurance purchased, i . e . , the greater the amount of insurance A purchases, the smaller w i l l be h i s l e v e l of preventive a c t i v i t y , c , and thus, the larger the p r o b a b i l i t y of the stochastic e x t e r n a l i t y . z w i l l probably not change i n response to insurance on A, as G's are assumed to be maximizing t h e i r u t i l i t y (or p r o f i t s ) independent of A. Insurers w i l l thus be under-pricing t h e i r premiums. I f insurance buyers have perfect market information about insurance p r i c e s , they w i l l perceive that they face a h o r i z o n t a l supply curve and insurers must therefore charge one p r i c e f o r a l l units of insurance. 3P/9X then becomes p, one p r i c e f o r a l l units of insur-ance, f or a l l i n d i v i d u a l s . The equilibrium p must s a t i s f y the zero p r o f i t condition (14), or p = E t 1 X1/*1. The X 1 cancel as they are i the same for a l l i n d i v i d u a l s for any given p. The condition then becomes p = TT. TT i s c l e a r l y less than the premium schedule given by (13). Thus, there tends to be an overproduction of insurance r e l a t i v e to the "optimum", and an underuse of a c t i v i t y c . I f insurers cannot determine T T ( C ^ , Z ) , but can observe A's t o t a l purchase of insurance, Pauly (1974) showed that the "optimal" schedule of premiums could be found by maximizing the expected u t i l i t y of A subject to the insurer's zero p r o f i t condition. I f a l l i n d i v i d u a l s are i d e n t i c a l , they w i l l a l l purchase the same amounts of insurance 79 given a p r i c e schedule. But the introduction of z may imply that a l l i n d i v i d u a l s are not i d e n t i c a l . F i r s t , although state one..may-be defined f o r a l l i n d i v i d u a l s , z may only enter the u t i l i t y functions of some of these i n d i v i d u a l s . For "optimality", insurers should be able to d i s t i n g u i s h these i n d i v i d u a l s from those whom z does not a f f e c t . The t o t a l amount of insurance purchased by a f f l i c t e d p a r t i e s w i l l be d i f f e r e n t for a given premium schedule, P(X), then the insurance purchased by those unaffected by z. In p a r t i c u l a r , we would expect more insurance purchased by a f f l i c t e d p a r t i e s , as dc^/dz, the e f f e c t of the e x t e r n a l i t y on A's a c t i v i t y , i s negative. TT i s therefore higher f o r As than the TT f o r a l l unaffected p a r t i e s . We now have an adverse s e l e c t i o n problem. That i s , insurers must not only be able to observe t o t a l insurance purchases, they must also be able to d i s -t i n g u i s h between r i s k classes of i n d i v i d u a l s . Insurers may t r y to compete for the low r i s k group, but w i l l not be able to do so unless they have the information to d i s t i n g u i s h between r i s k classes. I f they have t h i s information, i t i s possible that the z e r o c p r o f i t condition on a l l contracts w i l l be v i o l a t e d . I f insurers pool t h e i r r i s k s and charge one p r i c e (when i n d i v i d u a l s vary), an i n e f f i c i e n t outcome i s obtained. I f i n d i v i d u a l s are d i f f e r e n t , whether insurance ( i f s o l d at a l l ) i s under or over-provided r e l a t i v e to the "optimum" i s d i f f i c u l t to determine. The moral hazard aspect of the problem would lead to over-insurance, whereas the adverse s e l e c t i o n would lead to under-insurance. One suspects that no equilibrium w i l l e x i s t . I f an equilibrium e x i s t s , 80 i t i s not l i k e l y to be e f f i c i e n t . Unless a l l insurers have i d e n t i c a l information about the TT - T T ( C ^ , Z ) f o r a l l i n d i v i d u a l s and can p e r f e c t l y discriminate i n premium p r i c i n g with respect to r i s k (of the a f f l i c t e d versus the n o n - a f f l i c t e d p a r t i e s ) , e i t h e r excessive amounts of insurance w i l l be sold with the n o n - a f f l i c t e d i n e f f e c t s u b s i d i z i n g the a f f l i c t e d (as a l l pay the same premium), or no insurance w i l l be sold as a l l firms would make losses. One could then ask the question: i f the government wanted to achieve a Pareto optimal l e v e l of e x t e r n a l i t y by imposing f o r example, l i a b i l i t y laws or through taxation and subsidy, what would t h i s s o l u t i o n look l i k e i n the case of an information e x t e r n a l i t y ? 1 I s h a l l show that t h i s Pareto optimal s o l u t i o n i s rather p e c u l i a r . I f we maximize the a f f l i c t e d party's expected u t i l i t y subject to keeping the generating party's expected u t i l i t y constant, a Pareto 2 optimal a l l o c a t i o n between the two p a r t i e s can be determined. For s i m p l i c i t y , I assume that only A's p r o b a b i l i t i e s are dependent on h i s and G's a c t i v i t i e s and there are only two s t a t e s . The problem i s thus to maximize the Lagrangian 1 A l t e r n a t i v e l y , we could view t h i s as an exercise i n determining the optimal bargaining s o l u t i o n between A and G. But I f i n d the govern-ment question much more r e a l i s t i c . Private bargaining requires that both p a r t i e s know the e f f e c t s of A's and G's a c t i v i t i e s on TT. While i t i s l i k e l y that they may know t h e i r own a c t i v i t y ' s e f f e c t , there i s no way they w i l l a p r i o r i be able to determine the e f f e c t s of the other party's a c t i v i t i e s . Given the p o s s i b l e mendacity of each party (as both can gain by revealing f a l s e information), bargaining i s a remote p o s s i b i l i t y , or i f c a r r i e d out, l i k e l y to be i n e f f i c i e n t . 2 Again, t h i s i s subject to the d i f f i c u l t i e s imposed by possible non-convexities . 81 V* = TT[C A,Z(C G)] U A ( C A ) +• [ l - TT [C A,Z(C G)]J U A ( c A) + X [ Y u G ( c G ) + (1 - Y ) u G ( c G ) - U G] + y 1 ( c 1 + c r - c±) + y 2 ( c A + c G - c 2 ) . (15) Q Note that i n t h i s case, z = z ( c ^ ) . F i r s t order conditions are that TT r u A ( c A ) - u A ( c A ) ] + TT[C A z ( c G ) ] u A + p. = 0 (16a) 1 1 Z 1 1 1 [ l - TT) [ c A , z ( c G ) ] ] u A + u 2 = 0 (16b) Z'TT [ u A ( c A ) - u A ( c A ) ] + X ( y u G ) + y, = 0 (16c) Z 1 Z C^ 1 X[ (1 - Y )U G ] + y o = 0 (16d) C2 2 A A where u = 9u /9c, and so on. Eliminating the m u l t i p l i e r s y i e l d s C l 1 the unwieldy expression A G , r A A A A , r A G, ,u_ yu TT - Z It [U (C ) - U (C ) ] TT[C Y,Z C )] G . ' C. 1 z 1 2 + 1, . c i ; -1 = ] (17) (1 - TT) [ c A z ( c G ) ] u A (1TTT)[C A Z (C G ) ]U C ( 1 - Y ) U G 1 1 c 2 1 1 c2. c 2 Note that t h i s s o l u t i o n i s very d i f f e r e n t from the Pareto pptimality conditions with ordinary commodities. The so l u t i o n i s "Pareto optimal" not with respect to i n d i v i d u a l ' s revealed p r e f e r -ences, but with respect to the technological information about each 82 party's functions. As noted i n section A, technological information i s necessary f o r optimality when we have e x t e r n a l i t i e s . The informa-t i o n demand on the government would thus be enormous, and Pareto optimal outcomes thus u n l i k e l y . Is there any r o l e f o r government with information e x t e r n a l i t i e s ? There are two basic options f o r government: providing s o c i a l insurance or imposing laws or regulations on the operation of p r i v a t e insurance markets. 1 Government can provide compulsory insurance i n an attempt to reduce the possible over-insurance r e s u l t i n g from im-p e r f e c t information. Individuals would only be allowed to purchase f i x e d amounts of insurance. Whether the amount of insurance sold and premium p r i c e charged correspond to the "optimum" depends on the government's information. I f the government can c a l c u l a t e a premium schedule that s a t i s f i e s the condition 8c . . , — l ( l - T f ) (c. ,z)u' (2) |P = „ + x _ i l = - T r ( c 1 , z ) u ' ( l ) - 3X 1 ( 1 8 ) oX oX — — — — -TT(C ,Z)U' (1) + (1-TT) ( C ; L ,Z)U' (2) * 2 the optimal number of premiums, X , can be sold. I f the government * can also regulate the p r i v a t e insurance industry to s e l l X and charge 1 There i s a t h i r d option: the imposition of a l e g a l l i a b i l i t y system that assigns r i g h t s (contingent) a f t e r the event occurs. This i s the subject of Chapter IV. 2 This expression i s derived from the assumption that the government can observe an i n d i v i d u a l ' s response to an increment i n insurance. See Pauly (1974, p. 49). I t i s also assumed that i n d i v i d u a l s are i d e n t i c a l . The notation i s the same as i n equation (12). 83 9P/9X that s a t i s f i e s (18). The government could also require by law that i n d i v i d u a l s reveal to insurers the t o t a l amount of insurance purchased. A l l firms would then charge the same premium for any incremental cover-age i n d i v i d u a l s may seek over, the optimum (due to a decrease i n t h e i r c^ a c t i v i t i e s ) . How t h i s law would be enforced i s an i n t e r e s t i n g question that cannot be answered i n t h i s t h e s i s . I f i n d i v i d u a l s are not i d e n t i c a l and thus the information exter-n a l i t y does not a f f e c t a l l people equally, government insurance can lead to some improvement over no insurance (possibly). Because governments can pool r i s k s , insurance may be o f f e r e d f o r events that would remain uninsured i n p r i v a t e markets due to small numbers or interdependent r i s k . Adverse selection- w i l l be eliminated by t h i s p o l i c y , but i t w i l l be replaced by a t r a n s f e r of income from good r i s k to bad r i s k i n d i v i -duals. Whether or not s o c i a l improvements r e s u l t depends upon the r e l a t i v e numbers of a f f l i c t e d versus n o n - a f f l i c t e d p a r t i e s . That i s , with compulsory insurance, a f f l i c t e d p a r t i e s ( i f s u f f i c i e n t l y large i n number), may be imposing a burden on n o n - a f f l i c t e d p a r t i e s i n the form of higher premiums. I t i s not then c l e a r whether any s o c i a l improvement takes place, as n o n - a f f l i c t e d p a r t i e s ' welfare decreases and the e x t e r n a l i t y may s t i l l be non-optimally insured. I w i l l b r i e f l y summarize the points derived from the model of information e x t e r n a l i t i e s . (1) P e r f e c t l y competitive insurance markets may not a r i s e because r i s k s are no longer s t a t i s t i c a l l y independent with information e x t e r n a l i t i e s . (2) I f i n d i v i d u a l ' s expected u t i l i t y functions are not quasi-concave, insurance e q u i l i b r i a 84 may not e x i s t . (3) Even i f competitive insurance markets and e q u i l i b r i a e x i s t , the competitive market so l u t i o n may lead to non-optimal (in the revised context) premium pr i c e s f o r insurance i f insurers cannot monitor a f f l i c t e d and generating p a r t i e s ' a c t i v i t i e s . (4) Technological information over a l l A and G p a r t i e s i s necessary for "Pareto optimal" a l l o c a t i o n s with information e x t e r n a l i t i e s . I r e i t e r a t e that one must be very p e s s i m i s t i c about the p o s s i -b i l i t y of reaching an optimal a l l o c a t i o n of resources through p r i v a t e markets when e x t e r n a l i t i e s a r i s e from imperfect information. The amount of information required to obtain an optimum i n any e x t e r n a l i t y s i t u a t i o n i s sub s t a n t i a l and complex. Given costs of acquiring information, few, i f any, insurance markets w i l l operate. Government insurance or regulated monopolies w i l l not ne c e s s a r i l y achieve f i r s t best optima, but may lead to some s o c i a l improvement. There i s an argument f or government co n t r o l when information i s imperfect. I f priv a t e markets do not have perfect information, perfect competition i s incompatible with e f f i c i e n t e q u i l i b r i a (and may lead to non-existence) . I f pe r f e c t information e x i s t s , the type of e x t e r n a l i t i e s described i n t h i s chapter w i l l not p e r s i s t . Therefore, i f one i s concerned about i n t e r n a l i z i n g e x t e r n a l i t i e s , a l b e i t imperfectly, government regulation or government p r o v i s i o n of information i s necessary. We turn now to a s p e c i f i c nonmarket means of dealing with e x t e r n a l i t i e s a r i s i n g from imperfect information: l i a b i l i t y laws and l e g a l r u l e s . 85 IV. INSTITUTIONAL RESPONSE TO IMPERFECT INFORMATION: LIABILITY LAWS AND LEGAL RULES A. Introduction We have seen from the analysis i n Chapter III that p r i v a t e insur-ance markets may f a i l , or operate i n e f f i c i e n t l y when stocha s t i c and information e x t e r n a l i t i e s are present. Government may regulate i n d i -v i d u a l s ' a c t i v i t i e s or operate s o c i a l insurance markets, but there i s no guarantee that e f f i c i e n c y or o p t i m a l i t y r e s u l t s from government con t r o l . One problem with e i t h e r s o c i a l or p r i v a t e insurance was the determination ex ante of the r i s k of any event i n v o l v i n g an e x t e r n a l i t y due to the small numbers of agents involved and interdependency of p r o b a b i l i t i e s . A second problem was that p r i o r r i g h t s may not be assigned to s p e c i f i c agents i n the case of a stochastic or information e x t e r n a l i t y . In t h i s chapter, I w i l l evaluate an a l t e r n a t i v e i n s t i t u -t i o n a l response to e x t e r n a l i t i e s a r i s i n g from imperfect information: the r o l e of the l e g a l system i n the assignment of r i g h t s and the e f f e c t of r i g h t s on resource a l l o c a t i o n given s t o c h a s t i c and information e x t e r n a l i t i e s . I assume that the government has created a l e g a l system comprised of law-making bodies (a parliament, l e g i s l a t u r e , or regulatory agencies), a set of common and statutory laws, a court system (judges, j u r i e s , and lawyers), and methods of enforcing a l l laws and regulations. The l e g a l system has the task of d e l i m i t i n g p r i o r and contingent r i g h t s and enforcing compliance with the powers these r i g h t s e n t a i l . 86 I f p r i o r r i g h t s are defined over stoch a s t i c e x t e r n a l i t i e s , we have a s i t u a t i o n as depicted by the model i n Chapter I I I , part B. That i s , i f i t i s known which party i s l i a b l e i n any s i t u a t i o n , the p r i v a t e market's problem i s simply the determination of the a c t u a r i a l value of the stochastic e x t e r n a l i t y . Insurance markets could function e f f i c i e n t l y i n t h i s case. R e c a l l however that the " e f f i c i e n t " solutions obtained i n part B (and part C as well) are r e l a t i v e to the assignment of r i g h t s . E f f i c i e n c y f r o n t i e r s f o r d i f f e r e n t assignments of r i g h t s w i l l not i n general be i d e n t i c a l . Also note that the e f f i c i e n t solu-tions were not optimal as neither the insurer nor the a f f l i c t e d party could a f f e c t the generating party's behavior. One would expect i n cases where l e g a l j u r i s d i c t i o n was c l e a r l y defined, that p r i o r r i g h t s would cover stochastic e x t e r n a l i t i e s , as the information requirements are small',relative to other e x t e r n a l i t y cases. Given the assignment of p r i o r r i g h t s f o r s t o c h a s t i c e x t e r n a l i t i e s , the l e g a l system then has a choice over the powers these r i g h t s convey. P r i o r r i g h t s w i l l not only i d e n t i f y the l i a b l e party but also set f o r t h the rules and l i m i t s of compensation under the l e g a l system i f the event occurs. Both l e g a l rules f o r compensation and p r i v a t e insurance can thus provide st a t e -dependent payments. whether or not i n d i v i d u a l s buy p r i v a t e insurance depends upon the r e l a t i v e costs of insurance (premium/benefit r a t i o ) and enforcement of one's r i g h t s ( l i t i g a t i o n fees, i f necessary). P r i v a t e insurance markets may s t i l l a r i s e (and be necessary) i f the p r i o r r i g h t s favour the generating party and the a f f l i c t e d party has no l e g a l recourse to compensation. 87 Legal rules which specify the l e v e l and a l l o c a t i o n of compensation given a stochastic or information e x t e r n a l i t y w i l l be c a l l e d l i a b i l i t y r u l e s . An example of a l i a b i l i t y r u l e applicable to p r i o r r i g h t s is-s t r i c t l i a b i l i t y . The party with the r i g h t s w i l l be compensated f o r a l l l o s t income by the party without the r i g h t s when the e x t e r n a l i t y occurs. This i s therefore an i m p l i c i t insurance p o l i c y . 1 The compen-sation i s generally awarded a f t e r the l e g a l system (through the courts) has established that the event has occurred and the l i a b l e party (the defendent) was indeed responsible f o r the event. The l e g a l system w i l l also specify which party has the burden of proof f o r showing that damage has occurred. I t i s generally assumed that the l i a b l e party (the one without the p r i o r rights) has the burden of proof; i . e . , he-must show that he was not responsible f o r the event and damage to avoid paying compensation. Courts may also specify who pays the l e g a l and 2 court fees i n the l i t i g a t i o n procedure. One important question which cannot be f u l l y answered i n t h i s t h e s i s , i s , what c r i t e r i a should the l e g a l system use to determine the assignation of p r i o r r i g h t s ? In Chapter I I , I argued that the assign-ment of p r i o r r i g h t s affected not only the d i s t r i b u t i o n of income 1 There may also be some taxpayer subsidy to the party with the r i g h t s to the extent that l e g a l costs are not covered by the l i a b l e party's compensation. 2 This l i a b i l i t y r u l e may c l e a r l y be non-optimal, as the party without the r i g h t s now bears a l l the r i s k and a d d i t i o n a l insurance may thus be necessary. See part C of t h i s chapter for an analysis of the r e l a t i v e e f f i c i e n c y of a l t e r n a t i v e l i a b i l i t y r u l e s . 88 between generating and a f f l i c t e d p a r t i e s , but also the r e l a t i v e p r i c e s of commodities. The l e g a l system thus cannot assign r i g h t s without a f f e c t i n g resource a l l o c a t i o n . I t i s somewhat u n r e a l i s t i c to assume that the l e g a l system can compute general equilibrium solutions under a l t e r n a t i v e r i g h t s assignments. But, c l e a r l y , any decision made with respect to r i g h t s assignments w i l l have e f f e c t s that should i n theory be evaluated. 1" Equity may also be an important consideration i n r i g h t s determination. I d e a l l y , l e g a l decision-makers would have a ranking of i n d i v i d u a l s ( s o c i a l welfare function) to evaluate a l t e r n a t i v e schemes of r i g h t s . Arguments which imply that the i n i t i a l determination of r i g h t s does not a f f e c t the equilibrium p o s i t i o n attained under s o c i a l decision-, making are untenable. Buchanan and Tullock (1962) pp. 46,48) argue for example, that r i g h t s must be delimited before they consider problems of i n d i v i d u a l c o n s t i t u t i o n a l choice, but "the ' e f f i c i e n c y ' or ' i n e f f i c i e n c y ' i n the manner of d e f i n i n g human and property r i g h t s a f f e c t s only the costs of organizing .joint a c t i v i t y ( e x t e r n a l i t i e s ) , not the p o s s i b i l i t y of a t t a i n i n g a p o s i t i o n of f i n a l equilibrium". What Buchanan and Tullock never make clear i s that choice of r i g h t s and the f i n a l outcome are interdependent."' One cannot assume r i g h t s e x i s t , then ignore t h e i r e f f e c t s . I t i s v a l i d 1 to argue that r i g h t s a f f e c t costs of d e c i s i o n -making, but one should then go on to say that d i f f e r e n t sets of r i g h t s 1 When I consider a l t e r n a t i v e l i a b i l i t y rules i n section B of t h i s chapter, a l l general equilibrium e f f e c t s w i l l be ignored. As w i l l be seen, p a r t i a l e quilibrium cases are themselves quite complex. 89 lead to d i f f e r e n t costs, which i n turn imply the p o s s i b i l i t y of a t t a i n i n g d i f f e r e n t e q u i l i b r i a or of not a t t a i n i n g an equilibrium at a l l . I w i l l very b r i e f l y sketch some of the methods which might be used by the l e g a l system to determine r i g h t s and the problems ass o c i -ated with these approaches. There are two basic methods of determining p r i o r rights.^" The f i r s t i s by government l e g i s l a t i o n , e i t h e r through a parliamentary body or by a regulatory agency. I f a parliament determines r i g h t s , i t s decision-making should i n theory r e f l e c t some e x p l i c i t or i m p l i c i t s o c i a l welfare function consistent with the preferences of a majority of voters. Rights assignment would then take into account to some extent both equity and general equilibrium e f f e c t s . We would not however expect that government decisions w i l l represent a s o c i a l optimum f o r the following reasons. F i r s t , although we can impose Bergson-Samuelson s o c i a l welfare functions on decision-makers, we cannot generate an Arrow s o c i a l welfare function from a minimum set of assumptions about i n d i v i d u a l preferences. Secondly, we have no p r e d i c t i v e model of government decision-making, whether by a parliament or regulatory agency. T h i r d l y , even i f a s o c i a l wel-fare function e x i s t s , we must assume that l e g i s l a t o r s or c i v i l servants are knowledgeable about a l l aspects of the s t o c h a s t i c e x t e r n a l i t y and i t s e f f e c t s . Those i n d i v i d u a l s a f f e c t e d by the e x t e r n a l i t y w i l l of course have the most information. The r i g h t s assignment made i s 1 These methods also apply to the determination of contingent r i g h t s . But with contingent r i g h t s , the issues are even more complex as we s h a l l see i n part C of t h i s chapter. 90 therefore l i k e l y to depend on the a f f l i c t e d and generating p a r t i e s ' r e l a t i v e bargaining (lobbying) power.:?with the government. These r e l a t i v e lobbying strengths, one suspects, w i l l be heavily influenced by the p a r t i e s ' income l e v e l . F i n a l l y , l e g i s l a t i v e bodies tend to enact l e g i s l a t i o n slowly (due to both government i n e r t i a and the time needed to c o l l e c t information). Lags between the recognition of a stochastic e x t e r n a l i t y and determination of r i g h t s w i l l thus e x i s t . 1 The second and most prevalent method of determining p r i o r rights. i s through the common law and j u d i c i a l system. In the determination of p r i o r r i g h t s by the courts, the s t o c h a s t i c e x t e r n a l i t y must f i r s t a f f e c t at l e a s t one party who Brings a case against the generating 2 party. I f no p r i o r r i g h t s existed previously f o r the p a r t i c u l a r event, the court must then determine l i a b i l i t y f o r the e x t e r n a l i t y . 1 An example of l e g i s l a t i v e assignment of r i g h t s i s discussed by. Samuels (1971). Owners of cedar trees are held l i a b l e f o r a f u s t that p e r i o d i c a l l y damages apple trees. The rust s t a r t s on the red cedars but does not damage them. The e x t e r n a l i t y a r i s e s because the r u s t o c c a s i o n a l l y spreads to apple trees i n the v i c i n i t y . Apple tree owners thus have been awarded the r i g h t s i n the event of a rust epidemic. I t i s i n t e r e s t i n g to note that apple tree owners were not awarded the r i g h t to receive compensation f o r t h e i r losses. In l i e u of compensation, cedar tree owners were required to destroy a l l t h e i r trees whenever the disease appeared i n one tree (even unaffected trees) and thus forego the p o t e n t i a l logging revenues from the trees. The e f f e c t - of t h i s d i s t r i b u t i o n of r i g h t s c e r t a i n l y has questionable e f f i c i e n c y p r o p e r t i e s . 2 Notice that the determination of r i g h t s by the j u d i c i a l system places the burden of l i t i g a t i o n on the a f f l i c t e d party because the generating party has the de facto r i g h t s . 91 Henceforth, a l l i d e n t i c a l stochastic e x t e r n a l i t i e s are covered by that p r i o r r i g h t . Again, we can ask what c r i t e r i a govern the deter-mination of r i g h t s . In c i v i l cases, the law of t o r t s covers l i a b i l i t y (and hence, rights) determination. I t i s c l e a r that i n many cases, t o r t law advocates assignments t o t a l l y unrelated to economic e f f i c i e n c y . 1 One c r i t e r i o n used to determine l i a b i l i t y i n the United States i s the Hand formula (see Posner (1972), pp. 69-70). In terms of a s t o c h a s t i c and information e x t e r n a l i t y , t h i s formula would hold the generator l i a b l e f o r the damage caused by the e x t e r n a l i t y i f the damage, m u l t i p l i e d by the p r o b a b i l i t y of the e x t e r n a l i t y occurring, exceeds the cost of the precautionS-'the generator might have taken to avoid the event. In other words, the expected value of the event i s compared to the cost of pre-ventive a c t i v i t y . The Hand formula w i l l not lead to e f f i c i e n t l e v e l s of the e x t e r n a l i t y i f a f f l i c t e d p a r t i e s can also engage i n a c t i v i t i e s that reduce the p r o b a b i l i t y of the event. The formula thus acts as a d i s i n c e n t i v e f o r a f f l i c t e d p a r t i e s to engage i n preventive a c t i v i t y . Other examples of l e g a l c r i t e r i a are the doctrines of contributory and comparative negligence. These doctrines cover cases where both p a r t i e s can a f f e c t the occurrence of an e x t e r n a l i t y . Contributory negligence states that the a f f l i c t e d party w i l l not be awarded the r i g h t s (and a b i l i t y to recover h i s damages) i f he could have prevented the event at a cost lower than the generating party's preventive costs. Note that t h i s r u l e acts as a negative incentive on generating p a r t i e s ' 1 See Posner (1972) f o r more extensive discussion of the r e l a t i o n s h i p between c i v i l law and prodedure and economic e f f i c i e n c y . 92 preventive a c t i v i t i e s . Comparative negligence reduces the a f f l i c t e d party's claims to damages by the percentage that h i s own a c t i v i t i e s (or lack of a c t i v i t i e s ) contributed to the event. This r u l e may also lead to i n e f f i c i e n c y i n that i t may lead to excessive t o t a l preventive a c t i v i t i e s (both p a r t i e s overinvest i n prevention). Rights decisions can be made i n two ways i n the j u d i c i a l system: by judges or j u r i e s . In eit h e r case, the evidence and arguments pre-sented by the p l a i n t i f f ' s and defendent's lawyers w i l l have an impor-tant e f f e c t on the decision reached. The l e g a l market a f f e c t s both the l i t i g a t i o n of e x t e r n a l i t y cases and the court's decision on the assignment of r i g h t s . We therefore would l i k e a model of the supply of and demand f o r lawyers and l e g a l s e r v i c e s . I w i l l now b r i e f l y examine some of the issues associated with the market f o r l e g a l 2 services. One's demand f o r l e g a l services i s a derived demand. What an i n d i v i d u a l involved i n any stocha s t i c or information e x t e r n a l i t y wants i s an assignment of r i g h t s and l i a b i l i t y through the l e g a l system. The demand f o r r i g h t s i s b a s i c a l l y a demand f o r a nonmarket a l l o c a t i o n due to the f a i l u r e of p r i v a t e insurance markets. But what we now have 1 See sections B and C of t h i s chapter .for discussion of po s s i b l e l e g a l rules (due care standards) that may reduce these negative incentives. 2 One should note the s i m i l a r i t y between the markets f o r l e g a l services and f o r medical care. See Arrow (1963) f o r an analysis of medical care markets. 93 i s a nonmarket a l l o c a t i o n system (rights and l i a b i l i t y determination) that i s s t i l l dependent to some extent on the operation of a p r i v a t e risk-bearing market (legal s e r v i c e s ) . The e f f i c a c y of the nonmarket system i s thus dependent upon the operation of l e g a l markets. In other that small claims cases, lawyers and l e g a l services are necessary f o r adjudication, whether one i s successful i n obtaining r i g h t s and l i a b i l i t y favourable to himself i s i n part a function of the s k i l l and q u a l i t y of the l e g a l services. The i n d i v i d u a l also faces uncertainty i n the adjudication process. F i r s t , he i s uncertain i f he w i l l win h i s case. Secondly, he i s uncertain about the q u a l i t y of the l e g a l services which cannot be evaluated p r i o r to the t r i a l or l e g a l negotiations. T h i r d l y , he i s uncertain, even i f he wins the case, what the extent of the award w i l l be. The demand for l e g a l service w i l l be i r r e g u l a r and unpredictable as i t depends upon the occurrence of a stochastic e x t e r n a l i t y (or other random event). Thus the demand f o r l e g a l services derives from the lack of insurance markets when e x t e r n a l i t i e s e x i s t , and the l e g a l market becomes a market f o r bearing r i s k . Due to i t s supply c h a r a c t e r i s t i c s , the fee structure, and pro-scribed types of c i v i l s u i t s , the l e g a l services market tends to f a i l i n i t s risk-bearing function. Entry i s r e s t r i c t e d i n the l e g a l services market by l i c e n s i n g , which i s i n turn r e s t r i c t e d by educational require-ments. Licensing and education act to a c e r t a i n extent as signals f o r the p r o d u c t i v i t y and q u a l i t y of the service, but the signals are not p e r f e c t . Because the productive a c t i v i t y comprises the good sold on the market, the buyer cannot f u l l y determine the value of the output 94 p r i o r to the completion of the service and f i n a l outcome i n court. The value of the l e g a l service would thus be an expected value; the amount of compensation awarded times the p r o b a b i l i t y of winning the case. To maximize h i s u t i l i t y , the i n d i v i d u a l would then set the expected value of l i t i g a t i o n equal to the cost of l e g a l services (at the margin). This strategy would lead to the e f f i c i e n t operation of l e g a l markets given a zero t o t a l p r o f i t s condition f o r suppliers of l e g a l services. The l e g a l market does not however operate e f f i c i e n t l y . F i r s t , even i f i n d i v i d u a l s d i d have enough information to compute expected values, a maximum may not be achieved due to the lumpiness of l e g a l fee schedules."*" Legal fees are based on the d e f i n i t i o n of the service provided (e.g., $X per l e t t e r ) , the time involved i n case preparation, and the s e n i o r i t y of the lawyer (a s i g n a l f o r h i s q u a l i t y ) . The c l i e n t w i l l not face a marginal schedule of payments, but discontinuous amounts of service. Fees are also not set competitively, but determined by the l i c e n s i n g body (bar a s s o c i a t i o n s ) . As the l i c e n s i n g body also controls entry of suppliers into the market, the fees are l i k e l y to include monopoly rents to the lawyers (analogous to medical service f e e s ) . Like medical care, l e g a l services are more r e a l i s t i c a l l y defined 1 The assumption that i n d i v i d u a l s can compute expected values i s ques-tionable. Not only are p r o b a b i l i t i e s d i f f i c u l t to compute because they are so case s p e c i f i c , the compensation payments themselves, .are subject to (somewhat random) v a r i a t i o n . That i s , the i n d i v i d u a l may seek $X i n damages, but only be awarded $(X — Y). 95 i n terms of t o t a l episodes (the l i t i g a t i o n process). One could a l t e r n a t i v e l y handle the optimal p r o v i s i o n of l e g a l service i n a manner analogous to the principal-agent r e l a t i o n s h i p i n insurance markets. The l e g a l f i r m would determine the optimal fee schedule by maximizing the expected u t i l i t y o f i t s c l i e n t s subject to a zero p r o f i t constraint. The l e g a l system would thus bear the r i s k of the uncertain l i t i g a t i o n and charge premium p r i c e s f o r t h i s s ervice. Again, the l e g a l system does not operate i n t h i s manner. Fees are not only unrelated to the p r o b a b i l i t y of the outcome of the case, but lawyers are p r o h i b i t e d from seeking c l i e n t s on the basis of t h e i r a b i l i t y to win c a s e s . 1 The buyer must seek a lawyer and bear the r i s k s of the l i t i g a t i o n himself. Retaining a lawyer thus becomes analogous to taking ai gamble and one would expect d i f f e r e n t i n d i v i -duals to vary i n t h e i r demand f o r l e g a l services according to t h e i r 2 a t t i t u d e toward r i s k . 1 Lawyers acting as entrepreneurs (termed fomenting) i s proscribed be-cause the l e g a l profession believes t h i s would lead to excessive amounts of petty l i t i g a t i o n which would overburden the court system and thus increase costs the taxpayer must bear (increased judges' s a l a r i e s , new c a p i t a l expenditures on courtrooms, e t c . ) . 2 Casual empiricism suggests that i n d i v i d u a l s d i s p l a y decreasing r e l a t i v e r i s k aversion over some range of t h e i r expected u t i l i t y function i n t h e i r demand f o r l e g a l services i n cases of stoc h a s t i c and information exter-n a l i t i e s . This observation (or assumption) combined with the lumpiness and monopolistic elements of l e g a l fees suggests that one would tend to see more l i t i g a t i o n i n events a f f e c t i n g r e l a t i v e l y higher income i n d i ~ v i d u a l s . I f i n d i v i d u a l s are r i s k averse i n general, one would expect that few stochastic ,an& information e x t e r n a l i t y cases would be l i t i -gated and the de facto r i g h t s assignment w i l l r e f l e c t the status quo. 96 Many l e g a l decisions are made however i n out-of-court s e t t l e -ments. Posner (1972, p. 337) notes f o r example i n the automobile accident f i e l d , 95% of a l l l e g a l cases are s e t t l e d by the a f f e c t e d p a r t i e s before they reach the courts. These settlements do not e s t a b l i s h r i g h t s . This means that each time the s t o c h a s t i c exter-n a l i t y occurs a new round of l i t i g a t i o n begins. For example, the thalidomide cases i n Europe and the United States were a l l s e t t l e d out of court. The r i g h t s were not assigned e x p l i c i t l y to the deformed children and thus no nniform standard of compensation was established. This system not only tends to be inequitable, but i s also c o s t l y i n terms o f l e g a l services required. Thus, i n d i v i d u a l s may not obtain an assignment of r i g h t s with l i t i g a t i o n . One l e g a l mechanism ex i s t s i n the United States which enables i n d i v i d u a l s to decrease t h e i r r i s k through pooling i s the c l a s s action s u i t . In cases where the damages to any one i n d i v i d u a l are quite small, yet many people are a f f e c t e d by the event and t o t a l damage i s thus large, one i n d i v i d u a l can bring s u i t on behalf of a l l a f f l i c t e d p a r t i e s . In class a c t i o n s u i t s , l e g a l fees can be based on the t o t a l award. Thus there are no negative incentives against l i t i g a t i o n and the fee structure combined with r i s k pooling would tend to lead to an improvement i n resource a l l o c a t i o n with class action s u i t s . 1 " There may also be a tendency i n a l l cases which are l i t i g a t e d to preserve the status quo d i s t r i b u t i o n of r i g h t s . This occurs because 1 Class a c t i o n s u i t s are currently rare - i n Canada. 97 of the nature of l e g a l decision-making; established common and sta -tutory laws set the precedent f o r many new decisions. The problem with t h i s approach i s that events (or technologies) have changed and i t i s no longer c l e a r that the p r i n c i p l e s established by e x i s t i n g laws are applicable to the determination of new sets of p r i o r and contingent r i g h t s . Note also that the argument that status quo rig h t s represent the preferences of i n d i v i d u a l s i s not v a l i d unless we assume that decision-makers have p e r f e c t f o r e s i g h t about techno-l o g i c a l change and new goods (new r i g h t s ) . I f we do not know what technological interdependencies w i l l occur tomorrow, or when e x i s t i n g interdependencies lead to divergences between p r i v a t e and s o c i a l valuations, or we have imperfect information about e x i s t i n g i n t e r -dependencies , r i g h t s formulated today (the status quo) may be inap-p l i c a b l e tomorrow and thus not represent anyone's preferences. I have not e x p l i c i t l y considered the costs of reaching l e g a l decisions and assigning r i g h t s . This i s c l e a r l y an empirical issue, but some points can be made. Assigning the t o t a l court costs involved i n l i t i g a t i o n to the party l o s i n g the case w i l l of course act as a deterrent to r i s k averse p l a i n t i f f s . The government could consider providing p u b l i c l e g a l a i d to, f o r example, low income p l a i n t i f f s or o f f e r s o c i a l l e g a l insurance to o f f s e t the cost deterrents. In evaluating the operation of the l e g a l system, one should also consider the costs of enforcement, plus the costs of a l t e r i n g l e g a l decisions. Legal i n s t i t u t i o n s (as nonmarket a l l o c a t i o n mechanisms) have the 98 drawback ( r e l a t i v e to p r i v a t e markets) that they are i n f l e x i b l e with slow adjustment made to changes i n eventssand technology. B. A l t e r n a t i v e L i a b i l i t y Rules In.this chapter, I have discussed some examples of l e g a l rules.-fo r e s t a b l i s h i n g r i g h t s and assigning l i a b i l i t y i n cases of stoc h a s t i c and information e x t e r n a l i t i e s . I s h a l l now consider the formation of contingent r i g h t s and t h e i r possible e f f e c t s on incentives and i n d i v i d u a l behavior i n more d e t a i l . The assignment of contingent r i g h t s and l i a b i l i t y i s more complex than the case of p r i o r r i g h t s . In general, I w i l l assume that the assignment of p r i o r r i g h t s only applies to stochastic e x t e r n a l i t i e s . Contingent r i g h t s apply to information e x t e r n a l i t i e s . That i s , r i g h t s and l i a b i l i t y w i l l be assigned by the l e g a l system based on the l e v e l and nature of a c t i v i t i e s undertaken by the a f f l i c t e d and generating p a r t i e s p r i o r to the occurrence of the uncertain event. 1 We have already mentioned some examples of t o r t laws sp e c i f y i n g contingent r i g h t s : s t r i c t l i a b i l i t y , the Hand r u l e , contributory and comparative negligence. 1 Diamond (1974a) distinguishes between care and a c t i v i t y as separate v a r i a b l e s , and between a c t i v i t i e s and events. An a c t i v i t y i s what an i n d i v i d u a l was doing at the time of the p a r t i c u l a r event. Care per-tains to the l e v e l and nature of the a c t i v i t y . For example, i f the event i s an accident, one i n d i v i d u a l ' s a c t i v i t y i s crossing a s t r e e t , care i s whether he looked before crossing, wore brig h t c l o t h i n g , etc. I see-no need to d i s t i n g u i s h between care and a c t i v i t i e s . We. can--simply define an a c t i v i t y j o i n t l y with care and assume that the courts-monitor the i n d i v i d u a l ' s a c t i v i t y l e v e l and composition. 99 As we saw i n Chapter I I I , p r i v a t e insurance markets may not operate i n cases of information e x t e r n a l i t i e s due to nonconvexities and the d i f f i c u l t y of monitoring a c t i v i t i e s . The basic diff e r e n c e between insurance markets and l i a b i l i t y systems i s that the l a t t e r a l l o c a t e s resources ex post. Legal systems thus have the b e n e f i t of obtaining and u t i l i z i n g more information that do insurance markets. Id e a l l y both market and nonmarket systems would monitor a c t i v i t i e s p r i o r to the occurrence of the event, but i t i s generally assumed that the costs of monitoring would be p r o h i b i t i v e . Insurance would also approzimate the l e g a l system i f insurers required the insured p a r t i e s to show proof that t h e i r a c t i v i t i e s d i d not contribute to the event. Unfortunately, p r i v a t e insurance would tend to be asymmetric; that i s , insurance w i l l only be sought by a f f l i c t e d p a r t i e s . Generators w i l l never have any incentive to a l t e r t h e i r a c t i v i t i e s . Legal systems have the a b i l i t y to a f f e c t the a c t i v i t i e s of both generators and a f f l i c t e d p a r t i e s . I s h a l l now enumerate and explain possible sets of l i a b i l i t y laws, then show how d i f f e r e n t laws can a f f e c t agents' behavior and resource a l l o c a t i o n with information e x t e r n a l i t i e s . The possible laws w i l l not i n general achieve an optimal a l l o c a t i o n of resources (in the t r a d i t i o n a l sense), but some s o c i a l improvement i s possi b l e . Again, we may wish to redefine the concepts of optimality and s o c i a l welfare i n the context of l e g a l rules rather than i n the framework of competitive markets. In section C of t h i s chapter, optimality w i l l be defined r e l a t i v e to an 100 i n d i v i d u a l ' s l e v e l of care (preventive a c t i v i t i e s ) . Given that a l l i n d i v i d u a l s are below t h e i r optimal l e v e l o f care, a s o c i a l improve-ment occurs i f a l e g a l r u l e induces one party to increase h i s care l e v e l without decreasing the care l e v e l s of any other i n d i v i d u a l s . Note also that e f f i c i e n c y i s always r e l a t i v e to the assignment of r i g h t s . Again, I am not e x p l i c i t l y considering the costs of formu-l a t i n g and implementing l e g a l r u l e s . One should note, however'',that the l e g a l system tends to have high f i x e d costs. I am only considering one aspect of the l e g a l system, laws and l e g a l r u l e s . One would suspect that the average variable cost schedule f o r l e g a l rules i s r e l a t i v e l y f l a t . ( o r L-shaped). I t i s assumed that l e g a l systems cannot monitor the p r o b a b i l i t y -dependent a c t i v i t i e s of agents p r i o r to the occurrence of the event f o r two reasons. F i r s t , monitoring i s l i k e l y to be c o s t l y i n many cases and techniques f o r detecting c e r t a i n a c t i v i t i e s may not e x i s t . Secondly, i t i s often not known p r i o r to the event what a c t i v i t i e s to monitor or which p a r t i e s are involved. Even a f t e r the event occurs, i t may be d i f f i c u l t to i d e n t i f y either the generating party i n an information e x t e r n a l i t y , or the a c t i v i t y he was engaged i n which af-fected the p r o b a b i l i t y o f the event. I w i l l ignore t h i s problem and assume that the l e g a l system can i d e n t i f y the a c t i v i t i e s of both agents involved i n an information e x t e r n a l i t y . The l e g a l decision-makers must al s o be able to discern the v e r a c i t y o f the i n d i v i d u a l s as each type w i l l have an incentive to reveal f a l s e information about 10-1 h i s involvement i n the event. Thus, the l e g a l system (l i k e p r i v a t e markets) faces information problems even though i t s monitoring and ri g h t s assignment i s ex post. A d i s t i n g u i s h i n g c h a r a c t e r i s t i c of l i a b i l i t y laws i s the due care standard. The due care standard i s a threshold l e v e l of the preventive (or causative) a c t i v i t y established by the l e g a l system fo r a l l recognized a c t i v i t i e s and i s used as a ru l e f o r determining negligence. The l e g a l system, i n formulating contingent r i g h t s , examines the event ex post and attempts to determine whether any of the p a r t i e s ' ex ante a c t i v i t i e s contributed to the event. Those a c t i v i t i e s which the system determine to have aff e c t e d the p r o b a b i l i t y of the event are r e f e r r e d to as proximate causes. I t i s against these proximate cause a c t i v i t i e s that care standards are imposed. The l e g a l system thus has two decisions to make even p r i o r to l i a b i l i t y assign-ment; what constitutes a proximate cause a c t i v i t y and at what l e v e l does t h i s a c t i v i t y (or lack of i t ) become negligence. The c r i t e r i a the l e g a l system uses i n t h e i r evaluations may be unrelated to any economic e f f i c i e n c y c r i t e r i a . I w i l l not consider the process of determining proximate causes or what constitutes negligence. I f a preventive (causative) a c t i v i t y i s below (above) the care standard, the agent i s judged negligent and, depending on the l e g a l r u l e i n e f f e c t , may be held l i a b l e f o r any losses s u f f e r e d r i n the event. -" Due care standards thus act as quantity constraints on i n d i v i d u a l s ' actions. With information e x t e r n a l i t i e s , separate care standards are needed f o r the a c t i v i t i e s of the a f f l i c t e d and 102 generating p a r t i e s . Diamond (1974b) c a l l s t h i s a two-activity i n -cident as opposed to a s i n g l e - a c t i v i t y event where both p a r t i e s are engaged i n the same a c t i v i t y . L i a b i l i t y i n the two-activity case i s much more complex because negligence i s dependent on the care l e v e l of each party r e l a t i v e to the care l e v e l of the other p a r t y . 1 Care standards thus can provide incentives f o r both p a r t i e s to con-sume or produce more preventive a c t i v i t y (less causative a c t i v i t y ) . Agents may a l t e r t h e i r behavior such that they no longer ignore the e f f e c t of t h e i r actions on the u t i l i t y or^output of others, i . e . , l i a b i l i t y r u l e s may i n t e r n a l i z e e x t e r n a l i t i e s . Standards can, f o r example, induce a f f l i c t e d p a r t i e s to increase t h e i r preventive a c t i -v i t i e s and generating p a r t i e s to reduce t h e i r exacerbating a c t i v i t i e s from what they would be i n an unregulated, uninsured s i t u a t i o n (or even from an insured point as w e l l ) . The change i n a c t i v i t y l e v e l would thus decrease the p r o b a b i l i t y of the event and i n turn decrease 2 the need f o r l i t i g a t i o n to determine l i a b i l i t y . 1 L i a b i l i t y does not necessarily imply that compensation must be made. I f the a f f l i c t e d party i s held l i a b l e f o r an event because-, his care l e v e l f e l l short of the standard, he would not have to compensate the generating party. He merely would not have the ri g h t s to receive compensation f o r h i s losses. See Diamond (1974a, 1974b) and Green C1974a) f o r t h e i r discussion of due care standards. 2 R e c a l l from Chapter III that i n an unregulated (and perhaps i n -sured) s i t u a t i o n , any increase i n the generating a c t i v i t y was accompanied by a decrease i n the a f f l i c t e d party's a c t i v i t y (in the convex region of p r o b a b i l i t i e s and preferences), thereby increasing the p r o b a b i l i t y of the event. 103 One other c h a r a c t e r i s t i c of l i a b i l i t y laws i s that they generally assign the t o t a l costs incurred i n the event (and subsequent l i t i g a t i o n ) to one party o r the other. Costs are never shared. Whether or not cost-sharing makes sense depends upon the d i s t r i b u t i o n of costs p r i o r to l i a b i l i t y assignment. The appropriate sharing r u l e could lead to an "optimal" l e v e l of e x t e r n a l i t y i n t e r n a l i z a t i o n by making each party take into account both h i s own costs and those of others i n decreasing the p r o b a b i l i t y of the event. There are thus two possible ways i n which l i a b i l i t y laws can v generate e f f i c i e n t a l l o c a t i o n s . F i r s t , the optimal preventive care l e v e l can be sought with due care standards. Secondly, i f care l e v e l s cannot change i n response to standards (due for example to f i x e d c o e f f i c i e n t s i n production or consumption;3 no abatement technology), the optimal compensation and l i a b i l i t y assignment could be determined a f t e r the event. The taxonomy of l i a b i l i t y laws i s derived as follows. A care standard i s set f o r the proximate cause a c t i v i t i e s of a f f l i c t e d and generating p a r t i e s . A d i f f e r e n t standard must be established f o r each party. Let S^ be A's care standard and S^ be the standard f o r G. Each party has three options: He can e i t h e r meet or exceed the care standard, or he can choose not to meet the standard. As I have assumed (in Chapter III) that a f f l i c t e d parties'" a c t i v i t i e s diminish the p r o b a b i l i t y of the event, while generating p a r t i e s ' a c t i v i t i e s increase p r o b a b i l i t y , the standards w i l l be asymmetric. That i s , A's 104 standard w i l l impose a lower l i m i t to the a c t i v i t y , while G's w i l l impose an upper l i m i t . Given the i n d i v i d u a l s ' decisions to meet or not meet the standard, possible l i a b i l i t y laws then depend on the p a r t i e s ' r e l a t i v e p o s i t i o n s . I w i l l use the following schematic matrices to show the meaningful combinations of i n d i v i d u a l behavior and l i a b i l i t y law. A f t e r enumer-ating a l t e r n a t i v e l i a b i l i t y laws, I w i l l then show t h e i r possible e f f e c t s on i n d i v i d u a l s ' care l e v e l decisions. That i s , the care standards spec i f y negligence and the l e g a l rules determine l i a b i l i t y . The question i s then what e f f e c t s the a l t e r n a t i v e l e g a l rules have on a f f l i c t e d and generating p a r t i e s ' interdependent choice of a c t i v i t y (care l e v e l ) , and the r e s u l t i n g equilibrium l e v e l s of the a c t i v i t y . We may then compare the equilibrium l e v e l s of both p a r t i e s ' a c t i v i t i e s with and without l e g a l r u l e s , and the r e s u l t i n g imposition of l i a b i l i t y . In the following table (Table I I ) , a + w i l l s i g n i f y l i a b i l i t y assigned to the generator (rights to the a f f l i c t e d p a r t y ) , while a 0 represents no l i a b i l i t y to the generator (generator's r i g h t s ) , that i s , the a f f l i c t e d party bears the l i a b i l i t y . I n d ividual A (the a f f l i c t e d p a r t y ) , i s defined as negligent whenever h i s a c t i v i t y i s les s than h i s standard (denoted < S ), and non-negligent when his a c t i v i t i e s exceed h i s standard (denoted |= s ). G (the generating p a r t y ) , w i l l be negligent when h i s a c t i v i t i e s exceed h i s standard (denoted > S ) and non-negligent when h i s a c t i v i t i e s are le s s than G or equal to h i s standard (denoted = S ). Rule A's A c t i v i t i e s G's A c t i v i t i e s < S„ > S_ (1) > s. < s. 0 0 (2) > s = A < S, A (3) ± SA < S. (4) ^ SA < S. A (5) > S, < S (6) > S. A < S. A (7) > S A < S. (8) > S. < s. A Table I I : Legal L i a b i l i t y Rules 105 106 I can explain the d i s t i n c t i o n s between the cases by assuming that the type of l i a b i l i t y r u l e chosen by the l e g a l system depends on the information (technological) the court has, or can obtain about a f f l i c t e d and generating p a r t i e s ' l e v e l of care or a c t i v i t i e s p r i o r to the occurrence of the event. 1 Cases (1) and (2) impose s t r i c t l i a b i l i t y on one party or the other. The courts may impose s t r i c t l i a b i l i t y when i t i s impossible to determine and monitor the care l e v e l s taken by both p a r t i e s p r i o r to the event. Due care standards are thus inoperative under s t r i c t l i a b i l i t y r u l e s . This type of l i a b i l i t y r u l e w i l l have strong asymmetric incentive e f f e c t s on both p a r t i e s (see sections C . l and C.2). I f the l e g a l system cannot monitor A's a c t i v i t i e s , but can monitor G's, i t may. enact a r u l e that imposes l i a b i l i t y on G whenever hi s care l e v e l i s les s than the standard, independent of A's a c t i v i -t i e s . G i s not l i a b l e when he meets or exceeds h i s standard. This i s r u l e (3) (see s e c t i o n C.3). Due care standards thus e x i s t only fo r G. S i m i l a r l y , i f A's a c t i v i t i e s can be monitored but G's cannot, the courts may enact a rule that imposes l i a b i l i t y on G, independent of h i s l e v e l of care, as long as A's care l e v e l i s greater than or 1 Again, one may wish to consider the r e l a t i v e costs of a l t e r n a t i v e r u l e s , but I wish to concentrate on the e f f e c t s of these rules on behavior, independent of costs. McKean (1970) discusses the r e l a -t i v e transaction costs of some l i a b i l i t y rules i n the context of defective products, but uses i n t u i t i v e arguments rather than a s p e c i f i c model or empirical evidence. McKean also f a i l s to recognize the point that e f f i c i e n c y i s r e l a t i v e to the l e g a l r u l e that i s i n e f f e c t . 107 equal to the standard. This i s ru l e (4) (see section C.4). G i s not l i a b l e whenever A does not meet h i s standard. In ru l e (4) then only A has a due care standard. Rule (5) i s known as negligences-contributory negligence, and i s the most prevalent " r e a l world" 1 l e g a l r u l e . I t must be assumed under t h i s rule that the court can monitor both i n d i v i d u a l s ' care l e v e l s , thus p l a c i n g , r e l a t i v e to the other l e g a l r u l e s , the greatest informational requirements on the l e g a l system. Due care standards w i l l thus be established f o r both p a r t i e s . Under c e r t a i n assumptions, t h i s i s the only rule which w i l l lead to " e f f i c i e n t " equilibrium care l e v e l s (see section C.5). Rules (6), (7), and (8) are not too i n t e r e s t i n g nor are they very r e a l i s t i c a l t e r n a t i v e s f o r the courts, as the l e g a l system must be able to monitor both p a r t i e s " care l e v e l s . And, i f i t can determine these care l e v e l s , rule (5) would be imposed. I f the courts cannot monitor care l e v e l s (or only c e r t a i n p a r t i e s ' care), then rules (1-4) would be chosen. I w i l l therefore not consider cases (6-8). C. The E f f e c t s of L i a b i l i t y Rules on Nonmarket E q u i l i b r i a In t h i s section, I consider the i n t e r a c t i o n between l i a b i l i t y r ules and i n d i v i d u a l s ' choices of care l e v e l s . E s s e n t i a l l y , the model i s the information e x t e r n a l i t y case examined i n Chapter I I I , but s i m p l i f i e d to some extent to focus on the e f f e c t s of l i a b i l i t y r u l e s . 1 This i s the case investigated by Diamond (1974a, 1974b). 108 I am following Diamond's model (1974b) with modifications to make i t applicable to information e x t e r n a l i t i e s , rather than the accident cases he considers. I assume that a given l e g a l rule has already been imposed by the l e g a l system and i s known by A and G. We would then l i k e to know the e f f e c t of the due care standards on i n d i v i d u a l s 1 care l e v e l s . Individuals are uncertain about the occurrence of the e x t e r n a l i t y , but not about how the e x t e r n a l i t y a f f e c t s them. They thus seek to maximize t h e i r expected u t i l i t i e s given the l e g a l r u l e and due care standard by. adjusting t h e i r l e v e l of care. I f i r s t consider possible e q u i l i b r i a under a l t e r n a t i v e r u l e s , then discuss the " e f f i c i e n c y " of the r e s u l t i n g e q u i l i b r i a . Equilibrium consists of a set of decisions about the l e v e l of care taken by each party, given the care of the other party, and correct perception of the expected damages from the e x t e r n a l i t y . Let there be two i n d i v i d u a l s (or groups of i d e n t i c a l i n d i v i d u a l s ) , A and G, who are assumed to be r i s k neutral only with respect to the bearing of accident c o s t s . 1 Both engage i n a c t i v i t i e s which a f f e c t the p r o b a b i l i t y of the event. The l e v e l of t h e i r a c t i v i t i e s i s i n i t i a l l y assumed to be a l t e r a b l e and i t i s assumed that the a c t i v i t i e s of both groups 1 The assumption of r i s k n e u t r a l i t y i n accident costs s i m p l i f i e s the r e s u l t s . The introduction of r i s k averse behavior would not a l t e r the basic analysis as long as i t was assumed that a l l i n d i v i d u a l s within a given c l a s s had i d e n t i c a l r i s k preferences. I f attitudes toward r i s k vary, determination of equilibrium care l e v e l s becomes more d i f f i c u l t and i t may be impossible to obtain d e f i n i t i v e conclusions about care l e v e l s . Risk n e u t r a l i t y i s a r e a l i s t i c assumption i n t h i s model as i n d i v i d u a l s have only one decision v a r i a b l e (their care level) and thus cannot d i v e r s i f y to spread t h e i r r i s k s . Nor are contingent contracts a v a i l a b l e . 109 enter the u t i l i t y functions of each. The a c t i v i t i e s are defined i n quantity space and confined to the u n i t i n t e r v a l . Both A and G are assumed to have p e r f e c t information about the l e v e l of each other's care. This assumption i s rather u n r e a l i s t i c and I w i l l b r i e f l y discuss the possible consequences of asymmetric information about care l e v e l s l a t e r i n sectioncD.'ofothis chapter. U (x,y) i s A's l e v e l of expected u t i l i t y given h i s choice of a c t i v i t y x and G's l e v e l of a c t i v i t y y (where x / y ) . That i s , A and Q G engage i n d i f f e r e n t a c t i v i t i e s by assumption. S i m i l a r l y , U (x,y) describes G's expected u t i l i t y of a c t i v i t y y, given A's l e v e l of A G a c t i v i t y x. U and U are assumed to be s t r i c t l y concave and twice d i f f e r e n t i a b l e i n x and y (I ignore possible nonconvexities). In addition i t i s assumed that TJ^(0,y) > 0 f o r a l l y, Q tMx,0) > 0 f o r a l l x, l i m U ^ X j y ) = -°° for a l l y, x->l Q l i m U (x,y) = -» for a l l x, y-H) A A G where equals 9U /8x and s i m i l a r l y f o r U . These assumptions provide upper and lower bounds f o r a c t i v i t i e s and are s u f f i c i e n t to ensure i n -t e r n a l maximization and to deal with the discreteness of the care standards. 110 Whenever the stochastic event occurs, A s u f f e r s damages. As we are considering ex ante decisions of i n d i v i d u a l s , these damages can be represented by an expected cost function, C(x,y), which i s assumed to be convex i n x and y, twice d i f f e r e n t i a b l e , and where C > 0 , C < 0 , C > 0 , C <0. Although I could cast t h i s model x y xy into a state-preference framework, assuming the e x t e r n a l i t y only occurs i n state one, I w i l l not do so as t h i s would only complicate the analysis without adding any substantive r e s u l t s . We therefore only consider the behavior of A and G i n the state i n which the exter-n a l i t y occurs. 1. S t r i c t L i a b i l i t y on A Given t h i s background, we w i l l .now see how d i f f e r e n t l i a b i l i t y r ules a f f e c t the determination of care l e v e l s and standards. Rule (1), s t r i c t l i a b i l i t y on A (G has the rights) i s of course the s i t u a t i o n that would occur i f no l e g a l system existed. I t i s therefore u s e f u l to consider t h i s case as a benchmark against which to compare the l e g a l r u l e s . Presumably, the l e g a l system could also a r r i v e at a s t r i c t l i a b i l i t y r u l e f or i n d i v i d u a l A. A hypothetical r a t i o n a l e f o r t h i s case i s that A's a c t i v i t i e s have the major impact on the occurrence of the event (or only A has an abatement technology, G does not). With s t r i c t l i a b i l i t y on A, A and G maximize t h e i r expected u t i l i t y independent of a care standard, but given each other's care l e v e l . An equilibrium would be characterized by the simultaneous s o l u t i o n to the I l l f i r s t order conditions of each i n d i v i d u a l . That i s , we maximize A G U (x,y) - C(x,y) with respect to x and U (x,y) with respect to y. A of course bears a l l the damage costs i n t h i s case. Maximization y i e l d s U A(x,y) - C x(x,y) = 0 (1) U G(x,y) = 0 (2) That i s , each i n d i v i d u a l i s maximizing h i s u t i l i t y by choosing a l e v e l of care, given the care l e v e l of the other party (an exogenous variable A G > each cannot c o n t r o l ) . I t i s assumed that 8U /9y < 0 and 9U /3x = 0; that i s , G's a c t i v i t y decreases A's u t i l i t y and A's a c t i v i t y e i t h e r A G has no e f f e c t or increases G's u t i l i t y . Also, we assume U , U < 0, xy yx i . e . , increases i n the a c t i v i t y by one party decrease the l e v e l of the a c t i v i t y taken by the other party. Denote the care l e v e l s which solve equations (1) and (2) for a l l l e v e l s of y and x (respectively) by x^ = x^(y) and y^ = y^(x). Note that t h i s equilibrium w i l l not be optimal (in the t r a d i t i o n a l sense) because we have no assurance t h a t x ^ and y^ are set at l e v e l s which would r e s u l t i f the p a r t i e s maximized t h e i r u t i l i t y j o i n t l y . That i s , i f we maximize A's expected u t i l i t y (including the damage co s t s ) , holding G's expected u t i l i t y constant, the optimum l e v e l s of x and y would be the solu t i o n to the following expressions: 112 T/(X, Y) - C (x,y) - X[U G(x,y)] = 0 (3) uj(x,y) - C (x,y) - A[U G(x,y)] = 0, (4) which, we r e c a l l from Chapter I I , i s the Pareto optimal equilibrium for p u b l i c goods. We now want to see how A's equilibrium l e v e l of care varies as a function of y and how G's equilibrium l e v e l of care varies as a function of x. This can be represented by supply functions or reaction functions (graphed i n x,y space). The reaction functions are the solutions to equations (1) and (2), x^(y) and y^(x). We now want to know the slopes of these functions, so we d i f f e r e n t i a t e (1) and (2) again. This y i e l d s A dx dy -U 2SY_ J 2 L :A (5) U XX XX dx -U 22L u yy (6) G then decreases h i s l e v e l of a c t i v i t y as A increases h i s care, and A decreases h i s l e v e l of a c t i v i t y as G increases h i s a c t i v i t y (decreases his care). 113 Given the negative slopes of (5) and (6), we can then p l o t the reaction functions as i n Figure V. Figure V 114 We denote the equilibrium as (x ,y ). I t i s important to note that nothing i n the formulation of the model allows us to r u l e out the p o s s i b i l i t y of multiple solutions to equations (1) and (2), and thus, multiple e q u i l i b r i a . I therefore assume the existence of a unique equilibrium and also assume that i t i s stable. That i s , each party adjusts sequentially to the other party's care d e c i s i o n . The necessary condition f o r l o c a l s t a b i l i t y i s dx T~ A , ."1 cfe < 1 d? |_Y1(X)J dx" = X-2. S t r i c t L i a b i l i t y on G I now assume that the l e g a l system cannot monitor e i t h e r A's or G's a c t i v i t i e s , but decides to impose s t r i c t l i a b i l i t y on the generating party (gives a f f l i c t e d p a r t i e s the r i g h t s ) . Again, no care standards are imposed. One could argue that t h i s i s the other benchmark case, but d i f f e r s from rule (1) i n that l e g a l costs may be incurred. That i s , a l e g a l system must e x i s t before any kind of l i a b i l i t y on generating p a r t i e s can be imposed. I f my analysis e x p l i c i t l y incorporated the l e g a l system's costs, the equilibrium outcomes under rule (2) would c l e a r l y d i f f e r from those i n r u l e (1). I s h a l l show that even without introducing l e g a l costs e x p l i c i t l y , r u l e (2) generates a d i f f e r e n t equilibrium than r u l e (1). 1 This follows from Diamond (1974b). This s t a b i l i t y condition thus rules out cases where x (y) i s steeper than y (x). 115 With no due care standards, G now bears a l l the costs suffered by A when the e x t e r n a l i t y occurs. The u t i l i t y functions of the two A A G G p a r t i e s are now U = U (x,y) and U = U (x,y) - C(x,y). Simultaneous so l u t i o n of t h e . f i r s t order conditions of these expected u t i l i t y functions w i l l define an equilibrium. Again, we can describe the equilibrium with the reaction functions; solutions to the f i r s t order conditions. Let us denote these solutions as x^ = (y) ^ o r i n d i v i d u a l A and y^ = y 2(x) f o r i n d i v i d u a l G. We assume the e q u i l i -brium i s unique and l o c a l l y stable.. An equilibrium i s then denoted by the point (x ,y ). The imposition of l i a b i l i t y w i l l induce the l i a b l e party to increase his care l e v e l r e l a t i v e to that party's non-liable care l e v e l . From the i n i t i a l assumptions, we know that each i n d i v i d u a l ' s care l e v e l decreases as the other party's care l e v e l increases. I t then follows from the A G concavity of U ' (x,y) and the convexity of C(x,y) that the care l e v e l taken when one i s l i a b l e exceeds the care l e v e l when one i s n o n - l i a b l e . 1 Or, more generally, the greater the costs borne by the i n d i v i d u a l , the more care he takes. An i n t u i t i v e explanation for t h i s argument i s that increases i n care decrease the p r o b a b i l i t y of the accident and thus decrease the expected costs t h e l l i a b l e party must bear i f the accident occurs. We have assumed that the generating party's a c t i v i t i e s are p o s i t i v e l y r e l a t e d to the p r o b a b i l i t y of the e x t e r n a l i t y . Therefore, when 1 See Diamond (1974b) f o r a more formal discussion of t h i s point. The conclusion follows from the assumptions made about the signs of the second d e r i v a t i v e s of each function. 116 G i s l i a b l e , he w i l l decrease the l e v e l of h i s a c t i v i t i e s . A's a c t i v i t i e s decrease the p r o b a b i l i t y , so he too w i l l decrease h i s a c t i v i t i e s under r u l e (2) as he i s non-liable. That i s , f o r any x or y, ^ ( y ) > ± 2 (y) and £ (x) > y2 (*) • Let us then consider the poss i b l e equilibrium s i t u a t i o n s when both p a r t i e s decrease t h e i r a c t i v i t i e s . There are three possible outcomes (six, i f one or both p a r t i e s cannot change t h e i r a c t i v i t y l e v e l ) . The e q u i l i b r i a depend on the r e l a t i v e s h i f t s of the rea c t i o n functions. I f both p a r t i e s respond i d e n t i c a l l y , i . e . , they s h i f t t h e i r reaction functions by the same amount, then the equilibrium , oo oo . . , o oo _ o oo , „ . „ T . (x ,y ) i s characterized by x > x and y > y - (see Figure VI). I f A decreases h i s a c t i v i t y by more than G, then i t i s poss i b l e (but not always true) that x° > x°°, but y° < y°° (Figure V II). And f i n a l l y , i f A decreases h i s a c t i v i t y by les s than G, then i t i s poss i b l e that x° < x°°, and y° > y°° (Figure VTII). I t i s also possible that, i n some cases, x = x or y = y . There i s no way i n which we can pr e d i c t unambiguously where the f i n a l (x° 0,y° 0) equilibrium w i l l l i e r e l a t i v e to (x°,y°)" unless we know the precise s h i f t s of each party's reaction functions, or that one party cannot adjust h i s a c t i v i t y at a l l . This ambiguity i s paradoxically very important, as i t implies that determining the e f f e c t of a s h i f t i n l i a b i l i t y from As to Gs depends on the technological information the l e g a l system has about A's and G's reaction functions. I f the l e g a l system can determine the r e l a t i v e a b i l i t i e s of both p a r t i e s to change the l e v e l of t h e i r a c t i v i t i e s , i t may be able to enact a simple s t r i c t l i a b i l i t y r ule that improves 117 Figure VIII 118 s o c i a l welfare. In r u l e (1) ( s t r i c t l i a b i l i t y on A), G p a r t i e s have no incentive to reduce t h e i r a c t i v i t i e s as they bear none of the damages. Only As s u f f e r . Conversely, i n r u l e (2) ( s t r i c t l i a b i l i t y on G), As have l i t t l e incentive to take care as they are compensated f o r damage. One suspects however that there w i l l be asymmetries i f A has to incur l e g a l fees to show that the G are responsible f o r the e x t e r n a l i t y . G incurs no l e g a l fees as no payments are made. As may thus have a higher l e v e l of care r e l a t i v e to Gs when they are both (alt e r n a t i v e l y ) non-liable. 3. L i a b i l i t y on G,' Independent of A I now turn to consideration of a case i n which the l e g a l system has l i m i t e d a b i l i t y to monitor i n d i v i d u a l ' s a c t i v i t i e s ; r u l e (3). I assume that the l e g a l system i s able to determine G's l e v e l of a c t i v i t y p r i o r to the e x t e r n a l i t y , but cannot monitor A's a c t i v i t i e s . The l e g a l system thus establishes a due care standard f o r G, S^. No standard can fife.'established f o r A (and x a c t i v i t i e s ) . One possible l e g a l r u l e i s then to hold G negligent and hence l i a b l e f o r A's damages whenever he does not meet h i s due care standard, that i s , whenever the l e v e l of h i s a c t i v i t i e s , y, exceed S , independent of A's l e v e l of a c t i v i t y . G's G expected u t i l i t y w i l l then be 1 See part D o f t h i s chapter f o r an elaboration of t h i s argument. 119 U G(x,y) i f y U (7) U (x,y) - C(x,y) i f y > S. Reca l l i n g from rules (1) and ( 2 ) , we denote the l e v e l of care (for a given x) that maximizes G's u t i l i t y when he i s non-liable by y^, where y^ = y^(x) i s the s o l u t i o n to U^(x,y) = 0. Then, y^ i s the l e v e l of care which maximizes G's u t i l i t y when he i s l i a b l e , i . e . , y^ = ^ 2 ^ ^ Q solves U^(x,y) - C^(x,y) = 0. When generating p a r t i e s are l i a b l e , they thus decreasettheir a c t i v i t i e s . We can represent G's expected u t i l i t y Q functions as follows (Figure IX). U (x,y) i s the relevant curve when Q G i s non- l i a b l e , while U (x,y) - C(x,y) i s G's u t i l i t y function when l i a b l e . Note that to i n t e r p r e t Figure IX, one must read from r i g h t to l e f t , r e c a l l y i n g that the standard i s an upper bound on G's a c t i v i t i e s . ;,u U G(x,y) U (x,y) - C(x,y) Figure IX The imposition of a. care standard makes only c e r t a i n portions of these expected u t i l i t y functions relevant. G w i l l choose to be negligent or non-negligent depending on the l e v e l of S . There are three p o s s i -G b i l i t i e s . F i r s t , consider > y^. G's u t i l i t y function becomes the dotted l i n e i n Figure X, with i t s maximum at y^. G w i l l choose to be 120 non-liable at a l l l e v e l s where y < S and maximize h i s u t i l i t y at y . G 1 U U G(x,y) ^«*J U (x,y) - C(x,y) Figure X If y < S < y , G's u t i l i t y function becomes the dotted l i n e i n 2 G J. Figure XI. In t h i s case, G w i l l exactly meet the due care standard, S , as he cannot maximize his u t i l i t y on e i t h e r u t i l i t y function. G 1 1 1 / 1 1 ^ ^ U G ( x , y ) / ^ / / 1 " " ^ j U (x,y) Y 2  S G Figure XI I f S exceeds y , we have to compare the standard which gives the same G 2 G G u t i l i t y on U (x,y) as the maximum l e v e l of U (x,y) - C(x,y) to determine the i n d i v i d u a l ' s care choice. That i s , i t i s the care standard that G G equates y 2 (the maximum of U (x,y) - C(x,y)) with a point on U (x,y). The r a t i o n a l e behind t h i s point i s that an i n d i v i d u a l w i l l never choose 121 a point that gives him less u t i l i t y than the maximum of h i s function when l i a b l e . C a l l t h i s l e v e l of care S . S„ i s i l l u s t r a t e d i n G G Figure XII. I f the due care standard i s between y and S , G w i l l 2 G > -choose to exactly meet the standard. I f S„ = S , the i n d i v i d u a l G G w i l l choose to be negligent and maximize h i s u t i l i t y at y 0 . U G(x,y) U G(x,y) - C(x,y) Figure XII These r e s u l t s can be summarized as follows: Due Care Standard: Choice for G S > y y < S < y S = S G 1 y2 G y l G G Optimal Level of Care: y Table I I I : Optimal Care Levels for G 4. L i a b i l i t y on G, Dependent on A I now assume that the l e g a l system can obtain information aJoout. the l e v e l of A's a c t i v i t i e s p r i o r to the occurrence of the e x t e r n a l i t y and can thus define a due care standard for A, but no information can be 122 obtained about G's a c t i v i t i e s . We now consider l e g a l r u l e (4). The l e g a l system thus cannot determine when G i s negligent, and defines l i a b i l i t y to be dependent on A's a c t i v i t i e s . The l e g a l r u l e s p e c i f i e s that G i s l i a b l e whenever A meets or exceeds h i s due care standard, independent of G's care l e v e l . We must therefore examine A's choice of care as a function of h i s due care standard. The arguments are analogous to the previous case, but reversed because the standard imposes a lower l i m i t on A's a c t i v i t i e s . In t h i s case, A w i l l be held l i a b l e f o r the damages he incurs whenever h i s a c t i v i t i e s f a l l short of h i s due care standard, -S^. He i s not l i a b l e whenever he meets or exceeds the standard. A's expected u t i l i t y w i l l therefore be r u A i f x = S A U (x,y) ^U A(x,y) - C(x,y) i f x < (8) x^ i s the value which maximizes A's u t i l i t y when he i s not l i a b l e , and x^ maximizes h i s u t i l i t y when l i a b l e . We can again i l l u s t r a t e A's u t i l i t y functions when l i a b l e and non-liable (Figure XIII), noting that we now read l e f t to r i g h t . ^ A U TJNX^) - C(x,y) Figure XIII 123 Note that exceeds x^; the i n d i v i d u a l takes more care when l i a b l e . I ndividual A w i l l again choose three d i f f e r e n t l e v e l s of care, depending on the l o c a t i o n of the care standard. Rather than i l l u s t r a t e the cases, I w i l l summarize the r e s u l t s i n Table IV. Choice f o r A Due Care Standard: S = x x > S > x S = S A 2 •- 1 A 2 A A Optimal Level of Care: S S x, 2 A 1 Table IV: Optimal Care Levels f o r A G w i l l then be l i a b l e independent of any care l e v e l he takes whenever A's due care standard i s greater than S^. One would not expect G to take any care i n t h i s case as the l e v e l of G's a c t i v i t i e s do not a f f e c t h i s l i a b i l i t y . That i s , G w i l l choose to be negligent and be at y 2 . This conclusion d i f f e r s from that of ru l e (3) because even though A had no standards imposed i n (3), he may s t i l l take care to decrease the p r o b a b i l i t y of being damaged by the e x t e r n a l i t y . This occurs because G can choose to be non-negligent and A thus bears the l i a b i l i t y ( i . e . , damages) i f the e x t e r n a l i t y occurs. In rule (4), G w i l l take no care because no standard i s imposed on him. Thus cases (3) and (4) are not symmetric. 124 5. Negligence - Contributory Negligence We now turn to the case where the l e g a l system can monitor the a c t i v i t i e s of both A and G. Due care standards are established f o r both p a r t i e s and the l e g a l r u l e s p e c i f i e s that G i s l i a b l e only when he does not meet his care standard and A meets or exceeds his care standard. The analysis i n t h i s case becomes more complex as we must determine i f and when an equilibrium e x i s t s f o r any p a i r of due care standards ( s A ' S Q ) * This i s an important l e g a l rule as i t requires both p a r t i e s to take care and allows f o r the p o s s i b l e attainment of " e f f i c i e n t " e q u i l i b r i a . Following Diamond (1974b) and using the r e s u l t s of rules (1) through (4), we can define f i v e p o s s i b l e e q u i l i b r i a that are attainable with the negligence- contributory negligence rule} Each i n d i v i d u a l has three choices: (1) to be negligent and maximize h i s u t i l i t y , U(x,y) - C(x,y); (2) to be non-negligent and maximize his u t i l i t y , U(x,y); or (3) to exactly meet his due care standard. The e q u i l i b r i a follow from the assumptions that the l e g a l system imposes l i a b i l i t y only on one party. Thus, only one party bears the damage costs i n any equilibrium. This rules out cases where both meet t h e i r standards or both are non-negligent. An i n d i v i d u a l w i l l exactly meet h i s due 1 Diamond di d not seem to recognize that f i v e e q u i l i b r i a are p o s s i b l e with r u l e (5). He d i d not consider that both p a r t i e s could be n e g l i -gent simultaneously. In t h i s s i t u a t i o n , A i s l i a b l e . This resultJ can be v e r i f i e d by r e f e r r i n g back to the negligence-contributory negligence r u l e on page 105. Diamond (1974b) also considered the p o s s i -b i l i t i e s of multiple e q u i l i b r i a and non-existence. I w i l l not deal with these problems. 125 care standard only when he can thereby avoid l i a b i l i t y , i.e.,•when the other party bears the costs. The following two tables define the pos s i b l e e q u i l i b r i a and show the due care standards necessary to a t t a i n the e q u i l i b r i a . Choice f o r A f f l i c t e d Party Choice f o r Generating Party Table V: E q u i l i b r i a under Negligence-Contributory Negligence Rule Combinations of (S ,S ), (S ,y ) , and (St, ,S ) are ru l e d out by the r i \j r i - L assumption that only one party bears the damage costs. For example, i f G i s at h i s due care standard and thus not l i a b l e , A would never choose to remain at h i s due care standard or be non-negligent because he bears the costs i n t h i s s i t u a t i o n . A s i m i l a r argument applies i f A i s at h i s due care standard and G i s l i a b l e . 126 Due Care Standards for G  S > y, G *1 y < S < y y2 G y l - < G G < G G - < G G Table IV: Due Care Standards for Negligence-Contributory  Negligence Why should we be concerned about the type of equilibrium that occurs? In general, e q u i l i b r i a of types I and IV w i l l not be " e f f i c i e n t " . That i s , they w i l l not lead to an equilibrium that i n t e r n a l i z e s the damages that r e s u l t from the e x t e r n a l i t y . E q u i l i b r i a of types II and III may be " e f f i c i e n t " ( i f they can be attained). E f f i c i e n c y i n the context of l e g a l r u l es i s however somewhat p e c u l i a r ( r e l a t i v e to the t r a d i t i o n a l concept of e f f i c i e n t a l l o c a t i o n with e x t e r n a l i t i e s ) . 1 F u l l e f f i c i e n c y would require both p a r t i e s to base t h e i r care decisions on the t o t a l costs involved i n the event, as we showed i n part C . l of 1 The nature of the e f f i c i e n t a l l o c a t i o n was noticed by Diamond (1974b). Possible E q u i l i b r i a A I: x and y i = s, 1 1 A A I I : x and S^ S = S 1 G A A I I I : S A and y 2 k± > SA > *2 IV: x 2 and ^ 2 SR = ^ V: x and y s, = S 1 2 A A 127 t h i s chapter (equations (3) and (4)). That i s , A incurs the damage costs i f the e x t e r n a l i t y occurs and both p a r t i e s incur costs of taking care. I d e a l l y , the l e g a l system would a l l o c a t e the t o t a l costs of the event, but i n t h i s model, i t only deals with the recognized damages r e s u l t i n g from the e x t e r n a l i t y . That i s , i t does not attempt to j o i n t l y maximize the two i n d i v i d u a l s ' u t i l i t y functions with the e x t e r n a l i t y . A modified d e f i n i t i o n of e f f i c i e n c y i s thus that each party makes h i s care decision dependent on h i s own costs and on the 'legally recognized costs. (Diamond, 1974b). This " e f f i c i e n t " p o s i t i o n can be described by the equations A U - C = 0 (9) u G - C = 0 y y A G The l e g a l system thus ignores U and U , and , i f these d e r i v a t i v e s y x are non-negative i n equilibrium (for a l l values of x and y ) , f u l l e f f i c i e n c y cannot be attained. This does not mean however that no soeiail'-improvement occurs. As we noted before (part A of t h i s chapter), s o c i a l improvment can be s a i d to occur whenever one party's care l e v e l increases and no other i n d i v i d u a l s ' care decreases (assuming no one i s at t h e i r optimal care l e v e l ) . The modified e f f i c i e n t e q uilibrium can be attained with c e r t a i n due care standards and l e g a l r u l e s . * * Denote the s o l u t i o n to (9) as (x ,y ). Now l e t use see which types of e q u i l i b r i a w i l l a t t a i n t h i s s o l u t i o n . The e f f i c i e n t point w i l l s a t i s f y the equations 128 * * x = x (y ) d o Y = y 2 U ) That i s , both p a r t i e s act as i f they were l i a b l e f o r the damages. Figure XIV shows the r e s u l t i n g " e f f i c i e n t " equilibrium compared to the e q u i l i b r i a attained under l e g a l rules (1) and (2). We assume a p a r a l l e l s h i f t of both reaction functions, although t h i s i s not a " necessary assumption as the r e s u l t s are the same for any r e l a t i v e s h i f t of the functions (assuming neither function i s f i x e d ) . Figure XIV 129 Notice that the " e f f i c i e n t " equilibrium leads both p a r t i e s to take more care than with e i t h e r of the s t r i c t l i a b i l i t y e q u i l i b r i a . That i s , A "increases h i s a c t i v i t i e s , G decreases h i s a c t i v i t i e s , as both act as i f l i a b l e . (x ,y ) thus shows the maximum attainable care l e v e l s p ossible under any l e g a l r u l e and care standard combina-t i o n . I t i s i n t h i s sense that i t can be s a i d to be "optimal". * * Equilibrium of types I and IV w i l l not lead to an (x ,y ) s o l u t i o n as they do not induce both p a r t i e s to act as i f they were l i a b l e . * * Only e q u i l i b r i a of types I I , I I I , and V can a t t a i n (x ,y ). II and III imply that one party i s l i a b l e , and the other threatened with l i a b i l i t y i f he drops below h i s due care standard. In V, both p a r t i e s act as i f l i a b l e . None of the other l e g a l rules considered i n t h i s s e c t i o n w i l l achieve type I I , I I I , or V e q u i l i b r i a and thus cannot a t t a i n the " e f f i c i e n t " s o l u t i o n . 1 I f the l e g a l system has s u f f i c i e n t information to be able to e s t a b l i s h due care standards and evaluate i n d i v i d u a l s 1 a c t i v i t i e s , and i t wishes to a t t a i n " e f f i c i e n t " e q u i l i b r i a , l e g a l r u l e (5) (negligence--contributory negligence) and care standards as s p e c i f i e d by Table VI for e q u i l i b r i a of types I I , I I I , or V could be implemented. Before advocating what the l e g a l system should do, we need to know the costs of implementing and operating due care standards. These costs would also include the repercussions of s e t t i n g the due care standard at a 1 Other types of l e g a l rules (for example, (6), (7), and (8)) may achieve type I I , I I I , or V e q u i l i b r i a . I have not considered these rules as they tend to require as much information as negligence-contributory negligence and would thus not have any advantage over t h i s r u l e . 130 l e v e l that prevents the attainment of a type I I , I I I , or V e q u i l i -brium. If the l e g a l system has imperfect technological-information, i t cannot determine p r i o r to the event, the e f f e c t of i t s standards on the care taken by i n d i v i d u a l s . The l e g a l system w i l l not know i f i t s standards are too high (for A) or too low (for G) unless i t knows the u t i l i t y functions of both A and G when they are held l i a b l e and non-l i a b l e . What we have i s a s i t u a t i o n analogous to moral hazard i n insurance markets; the choice of the due care standard plus l e g a l r u l e a f f e c t s i n d i v i d u a l s ' behavior and hence the p r o b a b i l i t y of the ex t e r n a l i t y ' s occurrence. The l e g a l system has an advantage over pr i v a t e insurance markets with respect to t h i s moral hazard problem i n that i t has the a b i l i t y to a l t e r the care standards and l e g a l rules (hence, contingent r i g h t s ) , i f i t finds that the standards and rules lead to i n e f f i c i e n t e q u i l i b r i a . D. Conclusion We have seen that l e g a l r u l e s can lead to a type of e f f i c i e n t equilibrium where there e x i s t information or stochastic e x t e r n a l i t i e s . There i s the p o s s i b i l i t y under c e r t a i n l e g a l rules that e q u i l i b r i a w i l l be non-existent or i n e f f i c i e n t due to the discreteness of the due care standards. But there e x i s t other combinations of l e g a l rules and care standards that w i l l achieve our modified e f f i c i e n c y c r i t e r i o n . The l e g a l rules which lead to e f f i c i e n t outcomes are however more complex 131 (negligence-contributory negligence) than the rules which w i l l not i n general generate e f f i c i e n t e q u i l i b r i a ( s t r i c t l i a b i l i t y rules) i n that they require more information and more precise s p e c i f i c a t i o n of due care standards. I f the l e g a l system cannot set standards at the l e v e l s which w i l l lead to e f f i c i e n t e q u i l i b r i a , the simpler rules may be preferable. That i s , there i s no guarantee, i f the l e g a l system i s uncertain about the imposition of due care standards, that the r e s u l t i n g e q u i l i b r i a w i l l be d i f f e r e n t from the solutions attainable under the simpler r u l e s . Although the outcome of -legal rules may be uncertain ( i . e . , the l e g a l system may not know i f s p e c i f i c sets of rules and standards w i l l y i e l d e f f i c i e n t e q u i l i b r i a ) , the l e g a l system may have an advantage over p r i v a t e insurance markets ( i f they e x i s t ) . Legal rules may lead to increases i n s o c i a l welfare because they can provide the appropriate incentives to p a r t i e s . Whether the equilibrium i s e f f i c i e n t or not, rules and standards w i l l induce p a r t i e s to increase t h e i r care l e v e l s to avoid l i a b i l i t y . Increased care decreases the p r o b a b i l i t y of the e x t e r n a l i t y ' s occurrence. Without a complete analysis of a l l the transaction costs involved i n an information e x t e r n a l i t y , we cannot say d e f i n i t i v e l y that an outcome i s (or i s not) optimal. The assumptions of the model presented i n t h i s chapter are f a i r l y r e s t r i c t i v e . In p a r t i c u l a r , i t i s assumed that a l l i n d i v i d u a l s of type A or G are i d e n t i c a l i n a l l respects. I t i s also necessary to have A and G groups be the same s i z e , or the t r a n s f e r of l i a b i l i t y through the l e g a l system from one group to the other w i l l be asymmetric. That i s , 132 we would have to a l t e r the cost functions depending on which party-was l i a b l e . The model i s also p e c u l i a r i n that i t requires compensa-t i o n to be one-on-one. We are assuming that no p u b l i c goods' problems ari s e (free r i d e r s , non-revelation of preferences). With l e g a l r u l e (4) f o r example, each member of the G group compensates an A party, or the t o t a l G compensates t o t a l A. We do not worry about the d i s t r i -bution of compensation (or bearing of l i a b i l i t y ) within each group. This assumption may not be too u n r e a l i s t i c i n some cases, e.g., class action s u i t s i n the United States where the l i a b l e p a r t i e s make a t o t a l settlement, d i s t r i b u t e d equally amongst the p a r t i e s awarded the contingent r i g h t s . The model i s appropriate i n t h i s s i t u a t i o n because the a f f l i c t e d p a r t i e s are i d e n t i c a l . W i l l l e g a l rules generate " e f f i c i e n t " e q u i l i b r i a (or any e q u i l i b r i a ) when i n d i v i d u a l s are not i d e n t i c a l ? I w i l l not analyze t h i s question formally, but point out some of the d i f f i c u l t i e s encountered with l e g a l rules and nonuniform i n d i v i d u a l s . 1 Individuals within each group can vary with respect to the e f f e c t s of t h e i r a c t i v i t i e s on the p r o b a b i l i t y of the event, the p r o d u c t i v i t y cost of the a c t i v i t i e s , t h e i r income l e v e l and d i s t r i b u t i o n , and t h e i r s p a t i a l l o c a t i o n or distance from the other group. For example, i f the agents involved are firms which are i d e n t i c a l i n a l l respects except f o r t h e i r distance from each other and from members of the other group, these agents are no longer i d e n t i c a l . I d e a l l y , the l e g a l system should be able to d i s t i n g u i s h between i n d i v i d u a l s 1 Diamond (1974a, 1974b) and Green (1974a) consider formally the problem of nonuniform e q u i l i b r i a i n the context of accidents. 133 and implement nonuniform ( d i f f e r e n t i a l ) due care standards. The l e g a l rules would be unaffected. Implementing d i f f e r e n t i a l care standards requires more information and thus increases the costs of -operating the l e g a l system. There i s also the problem of l e g a l j u s t i c e . The l e g a l system tends to operate on the p r i n c i p l e that a l l i n d i v i d u a l s should be treated equally, and t h i s was the case i n the model presented i n t h i s chapter. I f differences between i n d i v i d u a l s are small, then equal treatment, that i s , one standard f o r each group and no sharing of costs, then due care standards set at t h e i r optimal point f o r the l e g a l rules can achieve " e f f i c i e n t " equilibria."'" In general, as the d i s p a r i t y amongst i n d i v i d u a l s widens, uniform care standards on the nonuniform in d i v i d u a l s w i l l no longer lead to " e f f i c i e n t " e q u i l i b r i a . The l e g a l system must then impose d i f f e r e n t standards on the nonuniform i n d i v i d u a l s i f i t seeks e f f i c i e n t outcomes. I t must also weigh the costs of obtaining the a d d i t i o n a l information necessary to define these standards against the e f f i c i e n c y gains. Again, there may be a preference f o r simpler l e g a l r u l e s and care standards given the uncertainty of the outcome. The model also s t i p u l a t e s that i n d i v i d u a l s i n each group know pre^-c i s e l y the l e v e l of care taken by i n d i v i d u a l s i n the other group. I f t h i s assumption i s dropped, we may again favour the simpler r u l e s p.) through (4) which do not presume that the l i a b l e party has any information 2 about the non-liable party's a c t i v i t i e s . 1 Green (1974a) proves t h i s a s s e r tion f o r the case where i n d i v i d u a l s vary i n the costs of taking care. 2 One could also revise the model by assuming that the a c t i v i t y l e v e l i s 134 I f the l e g a l system cannot obtain enough information to e s t a b l i s h the due care standards necessary to achieve e f f i c i e n t e q u i l i b r i a , can we say anything about the r u l e i t should impose? Under c e r t a i n assump-ti o n s , I think we can. We found i n section C.5 that the " e f f i c i e n t " * * r l e v e l s of care (x ,y ) lead to the..1 lowest y and the highest x of any l e g a l r u l e . This r e s u l t was only attainable (potentially) under n e g l i -gence-contributory negligence. The question i s , can we approximate ft * (x ,y ) with a simpler l i a b i l i t y rule? What would be the r e s u l t f o r example of moving from a s t r i c t l i a b i l i t y r u l e on A to s t r i c t l i a b i l i t y on G? The technological information the l e g a l system has about A's and G's reaction functions i s c r u c i a l to the answer to these questions. We know from our analysis of s t r i c t l i a b i l i t y of G (rule 2), that the response each i n d i v i d u a l makes to the imposition of l i a b i l i t y depends on h i s a b i l i t y to change the l e v e l of h i s a c t i v i t i e s . D i f f e r e n t responses lead to d i f f e r e n t equilibrium s o l u t i o n s . I f the l e g a l system has i n f o r -mation about each party's response to l i a b i l i t y (how i t s reaction functions s h i f t r e l a t i v e to each other), i t may be able to impose a s t r i c t l i a b i l i t y - . r u l e that r e s u l t s i n a s o c i a l improvement. That i s , W^ e-may moye -unambiguously closer to (x ,y ). I f , f o r example, we have a s i t u a t i o n as depicted by Figure VIII (page 117), then Gs s h i f t t h e i r a c t i v i t i e s down i n response to an impo-s i t i o n of l i a b i l i t y r e l a t i v e l y more than As decrease t h e i r a c t i v i t y i n response to n o n - l i a b i l i t y . S t r i c t l i a b i l i t y on G w i l l thus lead to an s t o c h a s t i c . Diamond (1974a) considers t h i s problem for s i n g l e - a c t i v i t y accident cases, and the r e s u l t s are quite messy. 135 0 0 0 0 0 0 ^ 0 0 0 0 . j . j ' (x ,y ) where x > x and y < y , i . e . , we move towards x ,y , and both p a r t i e s are induced to take more care. Figure XV i l l u s t r a t e s t h i s case. x Figure XV Figure XV may be representative of many r e a l world e x t e r n a l i t y cases. Take our botulism example from Chapter I I I . I f food processing firms can i d e n t i f y the cans that contain botulism t o x i n at l i t t l e expense (e.g., employing someone to monitor the cooking temperature), while consumers cannot t e l l which cans contain botulism except at great expense (e.g., running chemical analyses or feeding suspicious cans to t h e i r p e t s ) , imposing s t r i c t l i a b i l i t y on processing firms w i l l lead to a s o l u t i o n as depicted by (x°°,y 0 0) i n Figure XV. The same r e s u l t occurs i f we know that As cannot adjust t h e i r a c t i v i t y at a l l , but G's can. Or a l t e r n a t i v e l y , i f only A'S can modify t h e i r a c t i v i t i e s , s t r i c t l i a b i l i t y on them w i l l lead to an (x°,y°) that * * approaches (x ,y ) without a decrease i n the l e v e l of care taken by one 136 party. Only i f A and G have p a r a l l e l s h i f t s i n t h e i r reaction functions, do we get the r e s u l t that s t r i c t l i a b i l i t y (on e i t h e r party) increases the care l e v e l of one i n d i v i d u a l , while decreasing the care l e v e l of the other (or, i n the context of a c t i v i t i e s , i t increases A's a c t i v i t y and increases G's a c t i v i t y , or decreases both A's and G's a c t i v i t i e s ) . The p a r a l l e l s h i f t case would seem to be a sp e c i a l case. We might expect that Ais^.and G's reactions functions are asymmetric i n many e x t e r n a l i t y cases. The l e g a l system, i n these cases, does not need pe r f e c t techno-l o g i c a l information (unless i t wants to compute e q u i l i b r i a p r e c i s e l y 1 ! ) . A l l i t needs to know i s the r e l a t i v e a b i l i t y of a f f l i c t e d and generating p a r t i e s to engage i n a c t i v i t i e s that reduce the p r o b a b i l i t y of the ex t e r n a l i t y ' s occurrence. This i s a very encouraging r e s u l t i n an analysis that has been overwhelmed with market f a i l u r e s and p o t e n t i a l non-existence of e q u i l i b r i a . The l e g a l system may thus not be superior to market systems i f we evaluate both i n terms of te c h n i c a l economic e f f i c i e n c y , but we have found that r e l a t i v e l y simple l e g a l r u l es may lead to s o c i a l improvements even though the e x t e r n a l i t y i s not f u l l y i n t e r n a l i z e d . 137 V. CONCLUSION Let me conclude by b r i e f l y summarizing the r e s u l t s of t h i s t h e s i s . Chapter II f i r s t defined a l e g a l r i g h t s taxonomy, then showed that resource a l l o c a t i o n i s affected by the assignment of r i g h t s i n a de-c e n t r a l i z e d economy given the existence of general e x t e r n a l i t i e s (both p u b l i c and p r i v a t e ) , even when we assume zero transaction costs. The "Coase theorem" was shown to be i n v a l i d , except under r e s t r i c t i v e assumptions about i n d i v i d u a l s ' preferences. Chapter III designed an information/externality taxonomy, then examined two cases, stochastic e x t e r n a l i t i e s and information e x t e r n a l i -t i e s , to see i f p r i v a t e insurance markets would a r i s e to i n t e r n a l i z e these e x t e r n a l i t i e s . I t was found that stochastic e x t e r n a l i t i e s present no problem for the creation of p r i v a t e insurance markets i f p r i o r r i g h t s e x i s t and i f a c t u a r i a l values of the r i s k s of the e x t e r n a l i t i e s ' occur-rence can be calculated by insurers. Information e x t e r n a l i t i e s on the other hand, introduced the p o s s i b i l i t y that competitive insurance markets and e q u i l i b r i a would not e x i s t . Non-existence may occur because r i s k s are not s t a t i s t i c a l l y independent and because i n d i v i d u a l s ' ex-pected u t i l i t y functions may no longer be quasi-concave with information e x t e r n a l i t i e s . Insurance e q u i l i b r i a may e x i s t , but are not n e c e s s a r i l y e f f i c i e n t or optimal. I t was generally found that the amount of i n f o r -mation necessary to operate p r i v a t e insurance markets i s s u b s t a n t i a l , and that p e r f e c t competition i n insurance markets i s incompatible with e f f i c i e n t e q u i l i b r i a when information i s imperfect. Government insurance 138 or regulation of pri v a t e markets may lead to some s o c i a l improvement, but w i l l not ne c e s s a r i l y achieve f i r s t best optima. Chapter IV considered the e f f e c t of l e g a l l i a b i l i t y r u l e s and due care standards on the attainment of " e f f i c i e n t " e q u i l i b r i a , given an information e x t e r n a l i t y . I t was found that only the negligence-contri-butory negligence rule could achieve e q u i l i b r i a where a l l p a r t i e s to an ex t e r n a l i t y took the maximum care to prevent the e x t e r n a l i t y 1 s occur-rence. The negligence-contributory negligence r u l e does require sub-s t a n t i a l amounts of information i n the s e t t i n g of care standards. I f the l e g a l system cannot obtain engugh precise information to impose a negligence-contributory negligence r u l e , but can obtain information about the r e l a t i v e a b i l i t i e s of the p a r t i e s to take care i n preventing the e x t e r n a l i t y , then i t was shown that imposition of a s t r i c t l i a b i l i t y r u l e on one party may lead to s o c i a l improvement. F i r s t best optima are generally not attainable with l e g a l r u l e s . Given the information necessary to operate p r i v a t e insurance markets and the i n a b i l i t y of insurance to a f f e c t the behavior of a l l p a r t i e s engaged i n an e x t e r n a l i t y , one becomes very p e s s i m i s t i c about the a b i l i t y of p r i v a t e insurance markets to i n t e r n a l i z e private e x t e r n a l i t i e s that a r i s e from imperfect information. Legal rules also f a i l to i n t e r n a l i z e e x t e r n a l i t i e s , but may lead to some s o c i a l improvement using l e s s precise technological information than i s necessary f o r the operation of pri v a t e insurance markets. The formulation of optimal p o l i c i e s f o r i n t e r n a l i -zation of c e r t a i n types of e x t e r n a l i t i e s i s thus quite complex when one incorporates s p e c i f i c assumptions about the transaction costs that give r i s e to market f a i l u r e . 139 VI. BIBLIOGRAPHY Akerlof, G.A. 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