A Static Microeconomic Model of Pure Competition

ISBN-13: 9783540193586 / Angielski / Miękka / 1988 / 139 str.

Christoph Klein

Opis

This book studies a large economy. It deals with a static microeconomic model of an exchange market with pure competition. Instead of the sigma-additive theory, the finitely additive theory, the general Jordan content and the general Riemann integration are used respectively. By a specialized probability model, the author obtains a precise interpretation strictly based on microeconomic methods of measurement. In particular, the meaning of an agent and of a coalition is explained and the Core-Walras equivalence is deduced. The author elaborates an elementary representation by broken continuous functions and the classical Riemann integral. A conjecture concerning the reduction of the dynamical case onto generalized differential equations is added.

Spis treści

I. The Deterministic Grounding of the Model.- 1. The Observation of a Set of Agents.- 1.1 Observability Principles.- 1.2 Stone Spaces and Compactifications.- 1.3 The Extension of a Finitely Additive Measure.- 1.4 Conclusion.- 2. The Observation of a Market.- 2.1 The Observation of Endowment Mappings.- 2.2 The Observation of Properties.- 2.3 The Observation of Measures.- 2.4 Conclusion.- II. The Replica Model.- 3. The Deterministic Replica Model.- 3.1 Finite Markets.- 3.2 The Boolean Algebra of Periodic Sets.- 3.3 The Unique Natural Influence Measure.- 3.4 Deterministic Markets.- 3.5 Conclusion.- 4. The Probabilistic Replica Model.- 4.1 Markets with Pure Competition.- 4.2 The Elementary Representation.- 4.3 Conclusion.- III. Core and Walras Allocations.- 5. The Definition of the Core.- 5.1 Attainable Allocations.- 5.2 Preferred Allocations.- 5.3 Unacceptable Allocations.- 5.4 The Core.- 5.5 Conclusion.- 6. Walras Allocations.- 6.1 Price Systems.- 6.2 p-Attainable Allocations.- 6.3 p-Unacceptable Allocations.- 6.4 p-Walras Allocations.- 6.5 Conclusion.- 7. Core Versus Walras Allocations.- Al Boolean Algebras and Stone Spaces.- A.1.1 Boolean Algebras.- A.1.2 Stone Spaces.- A.1.3 Measure Theoretic Tools.- A2 The Riemann Darboux Integration.- A.2.1 The Generalized Jordan Content.- A.2.2 The Generalized Riemann Integral.- A3 Some Proofs.- A.3.1 Proofs Concerning Chapter I.- A.3.2 A Proof Concerning Chapter III.- A4 The Elementary Model.- A.4.1 The Elementary Representation.- A.4.2 A Final Comment.- References.