General Equilibrium and Welfare

Transcription

1 General Equilibrium and Welfare

2 Contributions to Economics Peter MichaelislFrank SHihler (Eds.) Recent Policy Issues in Environmental and Resource Economics ISBN Jessica de Wolff The Political Economy of Fiscal Decisions ISBN Georg BolfGholamreza Nakhaeizadehl Karl-Heinz Vollmer (Eds.) Risk Measurements, Econometrics and Neural Networks ISBN Joachim Winter Investment and Exit Decisions at the Plant Level ISBN Bernd Meyer Intertemporal Asset Pricing ISBN Uwe WaIz Dynamics of Regional Integration ISBN Michael Carlberg European Monetary Union ISBN Giovanni Galizzil Luciano Venturini (Eds.) Vertical Relationships and Coordination in the Food System ISBN Gustav A. HornlWolfgang Scheremetl Rudolf Zwiener Wages and the Euro ISBN Dirk Willer The Development of Equity Capital Markets in Transition Economies ISBN X Karl Matthias Weber Innovation Diffusion and Political Control of Energy Technologies ISBN Heike Link et al. The Costs of Road Infrastructure and Congestion in Europe ISBN Simon Duindam Military Conscription ISBN X Bruno Jeitziner Political Economy of the Swiss National Bank ISBN Irene Ring et al. (Eds.) Regional Sustainability ISBN Katharina Miiller/Andreas Rylll Hans-Jiirgen Wagener (Eds.) Transformation of Social Security: Pensions in Central-Eastern Europe ISBN Stefan Traub Framing Effects in Taxation ISBN Pablo Coto-Millan Utility and Production ISBN X Frank Riedel Imperfect Information and Investor Heterogeneity in the Bond Market ISBN Kirsten Ralf Business Cycles ISBN Michele BageUa/ Leonardo Becchetti (Eds.) The Competitive Advantage of Industrial Districts ISBN Frank Bohn Monetary Union and Fiscal Stability ISBN Jaime Behar Cooperation and Competition in a Common Market ISBN Michael Malakellis Integrated Macro-Micro-Modelling Under Rational Expectations ISBN continued on page 177

3 Pablo Coto-Millan General Equilibrium and Welfare With 45 Figures and 42 Tables Springer-Verlag Berlin Heidelberg GmbH

4 Series Editors Werner A. Muller Martina Bihn Author Professor Pablo Coto-Millan University of Cantabria Department of Economics Avda. de los Castros sin Santander Spain ISSN ISBN ISBN (ebook) DOI / Cataloging in Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Coto-Millan, Pablo: General equiliblium and welfare: with 42 tables I Pablo Coto-Millan. - Heidelberg; New York: Physica-Vert., 2002 (Contributions to economics) This work is subject to copylight. All lights are reserved, whether the whole or part of the matelial is concerned, specifically the rights of translation, replinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copylight Law of September 9, 1965, in its current version, and permission for use must always be obtained from Physica-Verlag. Violations are liable for prosecution under the German Copylight Law. Springer-Verlag Berlin Heidelberg 2002 Originally published by Physica-Verlag Heidelberg in The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Softcover Design: Elich Kirchner, Heidelberg SPIN / I 0 - Plinted on acid-free and non-aging paper

5 Contents Introduction 1 General Equilibrium F onnal Interpretations of General Equilibrium (GE) GE Model in Pure Exchange (Robinson Crusoe and Viernes): 2 Consumers GE Model with Production: 2 Consumers 8 and 2 Producers Approach from the Agents as Producers Approach from the Agents as Consumers First Stage ofge: From the Invisible Hand to the WalIasian Notion The Walrasian GE Model with Production Walras'Law Walrasian GE Model with Production and Numerarie Money Walrasian GE Model with Production and Circulating and Fiduciary Money Second Stage ofge: From the Walrasian Notion to the Existence Demonstration The GE Model Extended by Arrow-Debreu Existence Theorem (Canonic Approach) Demonstration (Canonic Approach: Arrow-Debreu) Existence Theorem (Game Theory Approach) Existence Theorems (Topological Approach: Brower and Kakutani) Existence Demonstration The Third Stage of GE: Unicity and Stability The Walrasian GE Model Extended by Arrow-Debreu and Gale-Nikaido The Gale-Nikaido Unicity Theorem (Canonic Approach) Demonstration (Canonic Approach: Gale-Nikaido) The Unicity Theorem (Revealed Preference Approach) Demonstration (Revealed Preference Approach) Proposition of Perfect Static Stability 30

6 VI Contents The Perfect Static Stability Theorem (Canonic Approach: Hicks) Demonstration (Canonic Approach) The Local Dynamic Stability (Canonic Approach) The Local Dynamic Stability Theorem (Canonic Approach) Demonstration (Canonic Approach) The Global Dynamic Stability Theorem (Canonic Approach) Demonstration (Canonic Approach) The Global Dynamic Stability Theorem (Revealed Preference Approach) Demonstration (Revealed Preference Approach) 34 Bibliographic References 35 2 Other Models of General Equilibrium Modell Assumptions Development of the Model The Solution The Li-Yorke Theorem (Baumol and Benhabid's Version) Model Assumptions of the Model Development of the Model Individuals' Behavior: Inter-temporal Maximization Equilibrium Dynamics and State The Solution Final Remarks 47 Bibliographic References 47 3 General Equilibrium and Main Functional Forms of Utility and Production The Pure Exchange Model for Cobb-Douglas Utility Function The Pure Exchange Model for Two Agents with Cobb-Douglas Utility Functions and Constant Returns to Scale in Consumption, Different Initial Assignments of (x, y) and Distinct Parameters in Consumption «x, 13) The Pure Exchange Model with Cobb-Douglas Utility Functions, Returns to Scale and a Price for One Good as Numerarie The Pure Exchange Model for a Specific Utility Function The General Equilibrium Model with a Representative Agent with a Producer-Consumer (or of Robinson Crusoe) The Equilibrium Production Model with Constant Returns to Scale The Equilibrium Production Model with Decreasing Returns to Scale 58 Bibliographic References 59

7 Contents VII 4 Computable General Equilibrium The LeontiefModel Applications. Economic Impact Models: Economic Impact Study Introduction Direct Effects of Port Industry Port Authority Customs Other Port Industry Direct Effects of Port Industry Indirect and Induced Effects of Port Industry Regionalization of the National Input-Output Table Indirect and Induced Impact Vectors Indirect and Induced Effects of Port Industry Total Effects of Port Industry Direct Effects of the Industry Depending on the Port Indirect and Induced Effects of the Industry Depending on the Port Indirect and Induced Impact Vectors Indirect and Induced Effects of the Industry Depending on the Port Total Effects of the Industry Depending on the Port Economic Impact Study Final Remarks 94 Bibliographic References 94 5 Welfare Positive Properties of the GE Model The First Welfare Theorem The Second Welfare Theorem Compensation Criteria The Theory of the "Second Best" Problems of the GE Model Problems of Property Rights Allocation Public Goods Natural Resources Common Property Resources Externalities Negotiation and Election Problems between Agents Non-Convexities in Preferences Non-Convexities and General Equilibrium InfOImation Problems: Universality, Transaction Costs, Asymmetries and Anonymity Universality: The Conventional Theory of the Firm and the Incomplete Contracts The Theory of the Firm: Transaction Approach 151

8 VIII Contents The Theory ofthe Firm: Information Asymmetries Approach Anonymity 163 Bibliographic References Social Choice and Individual Freedom: A Thematic Guide Market Failures and Government Failures The Government's Problems in Property Rights Allocation Information Problems The Govemment's Problems in Negotiation and Choice The Voting Order Paradox Impossibility of Aggregation of Personal Preferences Problems in the Majority, Simple and Proportional Choice Systems The Average Voter Paradox Key Parties and Political Coalitions The Maximizing Bureaucrat Paradox The Non-Representative Democracy Paradox The Taxes Paradox The Theory of Pressure Groups Problems of Collective Action: One of the Commonest Collective Actions is Voting The Voting Paradox Strategic Voting The Revolution Paradox and the Theory of the Coup d'etat The Migration Paradox From the Anarchy and Equilibrium in the "Natural State" to the Constitutional Democracy The Invisible Hand and the Minimal State The State and its Institutions The State Origins Contractual Theories Utility Theories Final Remarks 175 Bibliographic References 176