Public goods and decentralization: The duality approach in the theory of value

Abstract

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.