Walrasian
General Equilibrium Theory

Tricolor above the Paris Bourse

Contents

Prologue

Part I - Preliminaries

(1) Introduction
(2) History of Walrasian General Equilibrium Theory
(3) Landmarks in General Equilibrium Theory: A timeline

Part II - The Lausanne School: the Walrasian System

(1) The Walras-Cassel System
(2) The Wald System
(3) Walras's Progressive Theory of Capital
(4) The Encaisse Désirée of Léon Walras
(5) The von Neumann System I: Equilibrium
(6) The von Neumann System II: Consumption
(7) The von Neumann System III: The Turnpike
(8)
Mathematical Appendix: Linear Systems of Equations, Linear Programming and Duality


Part III - The Lausanne School: the Paretian System

(1) The Paretian System I: Equilibrium
(2) The Paretian System II: Efficiency
(3) The Paretian System III: Market Failure
(4) The Paretian System IV: Social Welfare
(5)
Mathematical Appendix: Classical Programming

Part IV - The Neo-Walrasian General Equilibrium System

(1) The Consumer
(2) Production: the Cowles contributions
(3) Existence of Equilibrium: the Arrow-Debreu contribution
(4) The Welfare Theorems
(6) Mathematical Appendix: Convex Structures, Continuity, Fixed Point Theorems

Part V - The Hicksian Programme

(1) The Hicksian "Grand Themes"
(2) Neo-Walrasian Capital Theory
(3) Money in General Equilibrium
(3) Local Multi-Market Stability
(4) Global Stability
(5) Non-Tatonnement Stability
(6) Uniqueness of Equilibrium
(7) Finiteness of Equilibria
(8) Aggregation: the Sonnenschein-Mantel-Debreu bombshell
(9) Mathematical Appendix: Differential Equations, Stable Matrices, Lyapunov's Method

Part VI - The Edgeworthian Revival

(1) After Edgeworth
(2) The Continuum Economy
(3) The Non-Standard Economy
(4) Core Convergence
(5) Adjustment Processes
(6) Some Final Remarks
(7) Mathematical Appendix: Measure Theory, Integration, Non-Standard Analysis

Part VII - Occam's Razor

(1) The McKenzie Proof of Existence
(2) Incomplete and Intransitive Preferences
(3) Equilibrium with Infinite Commodities
(4) Large Square Economies
(5) Non-Convexities
(6) Mathematical Appendix: Vector Spaces, Non-Smooth Derivatives

Part VIII - General Equilibrium under Uncertainty

(1) Equilibrium with State-Contingent Markets
(2) Equilibrium with Asset Markets
(3) Equilibrium with Incomplete Asset Markets
(4) Equilibrium with Production and Finance
(5) Endogenous Uncertainty
(6) General Equilibrium and Information
(7) Rational Expectations Equilibrium


Part IX - Market Failure


PROLOGUE

"The best safeguard against overestimation of the range of applicability of economic propositions is a careful spelling out of the premises on which they rest. Precision and rigor in the statement of premises and proofs can be expected to have a sobering effect on our beliefs about the reach of the propositions we have developed."

(Tjalling C. Koopmans, Three Essays on the State of Economic Science, 1957: 147).

"In attempting to answer the question `Could it be true?', we learn a good deal about why it might not be true."

(Kenneth J. Arrow and Frank H. Hahn, General Competitive Analysis, 1971: p.vii)

"..this negative role of Arrow-Debreu equilibrium I consider to be almost sufficient justification for it, since practical men and ill trained theorists everywhere in the world who do not understand what they are claiming to be the case when they claim a beneficient and coherent role for the invisible hand"

(Frank H. Hahn, On the Notion of Equlibrium in Economics, 1974: 52).

"The benefits of the axiomatization of economic theory have been numerous. Making the assumptions of a theory entirely explicit permits a sounder judgement about the extent to which it applies to a particular situation."

(Gerard Debreu, "Economic Theory in a Mathematical Mode", American Economic Review, 1984)

"Being denied a sufficiently secure experimental base, economic theory has to adhere to the rules of logical discourse and must renounce the facility of internal inconsistency. A deductive structure that tolerates a contradiction does so under the penalty of being useless since any statement can be derived flawlessly and immediately from that contradiction. In its mathematical form, economic theory is open to an efficient scrutiny for logical errors."

(Gerard Debreu, "The Mathematization of Economic Theory", American Economic Review, 1991)

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