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An Essay on Some Aspects of Thŕ Economie Theorv of Public Goods THE EUROPEAN UNIVERSITY INSTITUTE Department of Economics An Essay on Some Aspects of thè Economie Theorv of Public Goods Luciano PAS1 June 1993 Thesis submitted for assessment with a view to obtaining thè Degree of Doctor of thè European University Insdtute. Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 I Florence, June 1993 / An Essay on Some Aspects of thè Economie Theorv of Public Goods Luciano PASI Thesis Committee: Pierre Dehez, Université Catholique de LSìttàin, supervisor Peter Hammond, Stanford University, supervisor Alan Kirman, EUI Michel Le Breton, GREQE, Marseille Ignazio Musu, Università di Venezia Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 ‘p TABLE OF CONTENT INTRODUCTION AND MOTIVATION PART1. ON CORES AND PUBLIC GOOD ECONOMIES Chapter 1.1. Introdnction Chapter 1.2. Some renuurks on thè theory of thè core 1.2.1 Basic defìnition and results 1.2J Examples 1.2^. 1 The core in a replica economy 1.2.2.2 Problems in defining thè core with an esternai diseconomy H J The noo-emptyness of thè core 1.2.4 The core and market faihires 1.23 The core of a coalition production economy Chapter 13. Pnblk goods 13.1 Nash Coornot behaviour with public goods 1JJ! Nash Cournot equillbria 133 Nash eqnilibria versus Pareto allocations Chapter 1.4. A survey of thè literature on core, e sternali ties and public goods 1.4.1 Llndahl’s sohition and thè core of an economy with public goods, 1970 1.4^ Esternai economies and cores, 1971 1.43 The core and thè I Jndahl equilibrhun of an economy with a public good: an example, 1972 1.4.4 Theory of vaine with public goods: a survey article, 1972 1.43 A generalization of thè pure theory of public goods, 1973 1.4.6 The core of a public good economy, 1974 1.4.7 The Undahl solution for economies with public goods, 1974 1.4JI Public goods with exdusion, 1980 1.4.9 Continuum economies with finite coalitkms: core, equilibrili m, and wldespread externallties, 1989 1.4.10 Cast share equillbria: a I indahlian approacfa, 1989 1.4.11 The equivale ncc of core and cost share equilibri» in an economy with a public good, 1991 1,009 1 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 *p TABLE OF CONTENT PART 2. ON THE GAME-THEORETIC APPROACH TO PUBUC GOOD ECONOMIES Chapter 2.1. Introduction Chapter 2.2. Game theory and public goods Chapter 2J. Consideration on games in characteristic form 23.1 On characteristic functions 13.1.1 The Harsanyl modification 2 J .U Games in partition-function form and limite to coalitiou formation 2.3.2 On S-equivalenet and nonnalization 2-3.2.1 Characteristic functions and proba bili ty measnre 1 1 3 On payofT vectors Chapter 2.4. On payofT imputa tions in thè core 2.4.1 On restrictions to thè set of thè outeomes available to coali tions 2.4.2 On a characteristic function that assnmes that outstders do contribute Chapter 2.5. The cooperative approach to esternali ties and pobik goods Chapter 2.6. The Vickrey aoction PA RTÌ ON TAXES AND PUBUC GOODS Chapter 3.1. Taxes and pobik goods 3.1.1 Some basic no tions on tax systems 3.1.2 How much of public goods with different taxes? Chapter 3 1 Tax alloca tion systems Chapter 33. Voting Chapter 3.4. Voting over tax allocation systems PART 4. AGGREGATION OF PREFERENCES AND RESTRICTIONS IN VOTING MODELS Chapter 4.1. Introdoction Chapter 4.2. Aggregation of preferences 4.2.1 Social ftinctions af individuai data 4 1 2 On convenient restrictians on sets of orderings 4 1 3 A "respect thè minori ty’ restrictkn on permissible sets of alternative» 1,009 2 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 Ip TABLE OF CONTENT 4.2.4 Appropriate restri ctions associa ted to public goods, and their effects on Arrow’s impossibilità results Chapter 43. On usuai restri ctions in voting models rART 5. THE MEDIAN VOTER THEOREM Chapter 5.1. Introduction Chapter 5.2. The model PART & HOW MUCH ROOMIS THERE REALLY FOR STRATEGIC VOTING? Chapter 6.1. Introduction Chapter 6 1 An example of strategie voting Chapter 6.3. A combinatoria! model 63.1 Computing thè number of orderings and profiles Chapter 6.4. Tbe Borda Rule as an aggregation rnle 6.4.1 Some d otions and definiti ons 6.4Jt How thè Borda Rule works 6.43 Tbe algorithm used in thè analysis Chapter 6.5. Two exampies and some results Chapter 6.6. Non manipulability from thè set of total scores Chapter 6.7. A modifled Borda Rule PART 7. CONCLUSIONS AND FUTURE RESEARCH PART 8. BIBUOGRAPHY 1,009 3 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 INTROMOT.DOC INTRODUCTION AND MOTTVATTONS Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 Ip Introduction and motivations Sincc my first couise on microcconomic theory -whìch dates back to 1979- I was impressed by tbe rclatively scarct attention dedicated by thè economie thought to two subjects that I consider of primary importance for thè understanding of that part of human activitìes which is thè object of economie and social sciences. Tbese are public goods and coalitional behaviour. There are excellent reasons that support thè fundamental iole of tbe competitive model based on thè analysis of individuai actions: tbe mere fact that most economista agree on tbese reasons explains why thè majority of textbooks, most of tbe li teniture, and in generai tbe standard training in economies are not conce med with public economies and group actions. This description of thè situation is both closer to tbe reality and more unjustifiable in a country like Italy: not only Italian scholars provided in tbe past important contributions to tbe field of public economies, but in Italy thè value of public goods and of publicly produced private goods accounts for tbe largest share of thè annual gross national produci. Moreover, in this country many economie dedsions, both at tbe private and at thè govemmcntal level, are taken in a process that is far away from what we consider thè typical framework of competitive systems: what we could describe as "feudal behaviours in a pre-capitalistic system” is fairly well summarized by "a generai tende ncy towaid agree me nts and collusion". Wben I started working on this tbesis I found that there is indeed an impiessive amount of li teniture in tbe field of public economics: bowever, it must be said that most of thè work on theoretìcal matters dates back to thè seventies and that we stili lack a generai model of a public good economy that has gained thè sanie importance of tbe Airow-Debieu model for tbe private good economy. Qui te immodestly I had detided to provide such a standard ieprcsentation: tbe task tumed out to be well beyond my capaci ty. To undeistaod eamestly this simple fact look me a lot of time during which I wrote tbe background for such a task and much more: what remains after eliminating thè more trivial parts constitutes this tbesis, which is made of 6 main parts. Tbe idea that thè Lindhal equilibrium could represent in public good economies, what thè competitive equilibrium means in private good economies, has becn around for qui te a long time. The study of this subject 1,018 1 Pasi, Luciano (1993), An essay on some aspects of the economic theory of public goods European University Institute DOI: 10.2870/7482 •p is linked to tbe dcvelopment of core-related concepts. The first part of this thesis is a discussion about thè core and public goods, as well as a rcview of tbe relevant literature, which is mainly aimed to show thè progrcssion of tbe field. Part 2 deals with thè game theoretic approach to economie behaviour: it provides -beside other things- a discussion of thè notion of domination that offers a clear explanation of thè relation between thè core and stable sets. I elaborate thè idea that thè usuai characteristic function is not adequate to describe thè process of coalition formation: thè presence of public goods makes this task impossible. Infonnally, it is based on excessively pessimistic assumptions about thè behaviour of thè complementary coalition. Moreover, it seems to pay too much attention to thè simple dialectic between one coalition and its complcmcnt: a more complex structure of coalitions is typically stable in tbe real world and 1 argue that tbe outeome described by a game in characteristic form -or some alternative description- should be ab le to explain it fully.
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