Public Goods and Decentralization: The Duality Approach in the Theory of Value

ISBN-13: 9789401176378 / Angielski / Miękka / 2012 / 246 str.

Pieter H. M. Ruys

Opis

The introduction of public goods into economic theory has recently received substantial attention from economists. Both the increasing significance of public goods and the deficiencies of the private goods-oriented allocation mechanisms call for a re orientation of the classical general equilibrium models such as the one designed by Walras exactly a century ago. Although several approaches to this problem are possible, the duality approach seems to be very fruitful. In this study, Dr. Ruys applies and develops the mathematical theory of polarity to gain a deeper insight into the economic theory of value. He not only uses the duality approach to simplify formal proofs related to public goods, but he also gives an interpretation to the application of polarity operations which goes far, beyond its formal significance. This study is in a way closely related to the publication 'Axiomatic choice models' by Dr. H. N. Weddepohl, which is volume 3 of the Tilburg Studies on Economics.

Spis treści

I. Economics.- 1. Introduction.- 1.1. Economic theory and economic environment.- 1.2. Private and public goods.- 1.3. The duality approach.- 1.4. Decentralized allocation mechanisms.- 2. Equilibrium in a system of economic relations.- 2.1. General equilibrium theory.- 2.2. Optimal allocations.- 2.3. An exchange economy.- 3. Production.- 3.1. Production sets and production multifunctions.- 3.2. Conditions in the production model.- 3.3. The price structure corresponding to a technology.- 3.4. Conditions in the price space.- 3.5. Preference orderings of inputs.- 3.6. Satiation for and dispensability of inputs.- 3.7. The demand- and the price-multifunction.- 4. Consumption and production of public goods.- 4.1. The consumption model.- 4.2. Private goods, public goods and externalities.- 4.3. Private goods, public goods and transaction costs.- 4.4. Social consumption and production.- 4.5. An economy with local public goods.- 5. Equilibrium in economies with private and public goods.- 5.1. The valuation representation of an economy.- 5.2. Equilibrium in an economy with public goods only.- 5.3. Equilibrium in an economy with private and public goods.- 5.4. The two-level price equilibrium.- 5.5. Financing the public sector.- 6. The organization of economic decisions.- 6.1. Allocation mechanisms.- 6.2. Centralization and decentralization.- 6.3. Procedures with a social preference ordering.- 6.4. Procedures with individual preference orderings.- 6.5. Multi-level organization.- 7. Extensions.- 7.1. Between values and resources.- 7.2. Theory of motion.- II. Mathematics.- 8. Basic mathematical notions and notations.- 8.1. Sets, relations and multifunctions.- 8.2. Continuity of multifunctions.- 8.3. Sets and algebraic operations in Rn.- 9. Sets and duality.- 9.1. Supporting hyperplanes and separating hyperplanes.- 9.2. Polar sets.- 9.3. Reflexive sets.- 9.4. Separation and intersection of sets.- 10. Multifunction and duality.- 10.1. Operations on multifunctions.- 10.2. Properties of multifunctions.- 10.3. Convex processes.- 10.4. Convex cone-interior processes.- 10.5. Convex star and convex aureole processes.- Summary.- References.