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Economic Evolution and Equilibrium

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theory,whichformalizesa dynamiceconomicsystemasa systemofdi?erence, or di?erential, equations. There equilibria mean ‘equilibrium trajectories’ of the whole evolution that, in a certain sense, are optimal. A particularly un- tisfactory feature of this conceptualization of an equilibrium, however, is the factthattheintertemporaloptimizingapproachcompletelypredeterminesthe whole future of the economic system. This “closed loop” approach gives rise to the common reproach that economic theory is predominantly concerned with the question of ‘how the economic system ought to behave’ rather than with the question of ‘how does it behave actually’. This is the point at which the new branch of evolutionary economics has made its entrance. In contrast to growth or business cycle theory, evolutionary economics perceives the evolution of the economic system as essentially “open” to true novelties that are unforeseeable by their very nature. This view clearly makes obsolete any conception of equilibrium that resorts to the idea of a ?nal state of rest, or to the idea of an intertemporally optimizing trajectory which is prespeci?ed ab initio by a system of di?erential equations and initial con- tions. To be sure, there have been attempts to reconceptualize the notion of equilibrium from the evolutionary viewpoint. However, these proposals also appear, in one way or another, to hinge on the ideas of rest. This parti- larly applies to the branch of nonlinear dynamics and deterministic chaotic motion.
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Contents
1
2
General Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Notations and Mathematical Preliminaries13. . . . . . . . . . . . . . . .
Part I Conceptualization and Definition of Evolutions of Economies in Four General Equilibrium Frameworks
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4
5
6
Introduction to Part I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Evolutions in the Traditional Walrasian Exchange Equilibrium Framework29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Evolutions Based on the Model of an Exchange Economy by Arrow and Hahn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.2 Evolutions Based on Dierker’s Version of the Model of an Exchange Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.3 Evolutions Based on a Model of a Large Exchange Economy . . 37
Evolutions in an Exchange Equilibrium Framework Without Walras Law and Homogeneity41. . . . . . . . . . . . . . . . . . . 5.1 Evolutions Based on a Model of an Exchange Economy Without Walras’ Law and Homogeneity . . . . . . . . . . . . . . . . . . . . 42 5.2 Evolutions Based on a Model With Weakened Boundary Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Evolutions in a General Equilibrium Framework With Production, Taxes, and Subsidies. . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.1 Evolutions Based on a General Equilibrium Model With Production and Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.2 Evolutions Based on a General Equilibrium Model With Production, Taxes, and Subsidies . . . . . . . . . . . . . . . . . . . . . . . . . . 68
VI
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Contents
Evolutions in the Temporary Fixprice Equilibrium Framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Evolutions Based on a Quantity Constrained Micromodel With Effective Demand à la Benassy . . . . . . . . . . . . . . . . . . . . . . . 7.2 Evolutions Based on a Quantity Constrained Multi-Sectoral Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Part II Formal Analysis
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10
11
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13
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Introduction to Part II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
72
77
87
91
NearEquilibrium Paths95. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Existence of Joining Equilibrium Components and of Near-Equilibrium Paths for Each Type of Evolution From Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 10.2 A Criterion for Identifying Points on Joining Equilibrium Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Equilibrium Paths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 11.1 Approximating Evolutions of Exchange Economies With Nice Equilibrium Paths Based on Dierker’s Model from Section 4.2 . 106 11.1.1 Polynomial Approximating Exchange Evolutions . . . . . . 107 11.1.2 Piecewise Linear Approximating Exchange Evolutions . . 115 11.2 Approximating Evolutions With Equilibrium Paths for the Other Basic Models From Part I . . . . . . . . . . . . . . . . . . . . . . . . . . 120 11.3 A Strong Connectedness Result for the Graphs of the Equilibrium Correspondences of the Basic Models From Part I 126
Economic Refinements of the Notion of an Evolution of Economies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 12.1 Course Evolutions and Connection Evolutions . . . . . . . . . . . . . . . 142 12.2 New and Old Commodities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
The Structure of the Equilibrium Price Set of an Evolution of Exchange Economies. . . . . . . . . . . . . . . . . . . . . . . . . 155
Comparison With Related Results in the Literature. . . . . . . 161 14.1 Studies of the Graph of the Walras Correspondence . . . . . . . . . . 161 14.2 The Regular Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Conclusions. . . . . . . . . . . . . . . . . . . . . . . 175. . . . . . . . . . . . . . . . . . . . . . . . .
20
Appendix A. . . . . . . . . . . . . . . . . . . . . . . 231. . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Conclusions and Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . 227
21
Appendix B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Appendix C. . . . . . . . . . . . . . . . . . . . . . . 259. . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
19
The Method of Kinetic Analysis of Evolving Economies in Historical Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Introduction to Part III. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
VII
Contents
Applications of the Analytical Results From Part II in the Economists Laboratory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 17.1 Extending the Path-Following Method to the Computation of Equilibria of Non-Regular Economies . . . . . . . . . . . . . . . . . . . . . . 184 17.2 Generalizing Comparative Statics to Economies With Multiple Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Part IV General Conclusions and Outlook
Conclusions. . . . . . . . . . . . . . . . . . . . . . . 223. . . . . . . . . . . . . . . . . . . . . . . . .
18
Evolving Economies in Historical Time. . . . . . . . . . . . . . . . . . . . 199 19.1 Evolving Economies in Discrete Historical Time . . . . . . . . . . . . . 203 19.2 Alternative Models of Evolving Economies in Continuous Historical Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 19.2.1 Flow Commodity Models of Piecewise Continuously Balanced Evolving Economies . . . . . . . . . . . . . . . . . . . . . . . 204 19.2.2 The Frequency Model of a Piecewise Continuously Balanced Evolving Economy . . . . . . . . . . . . . . . . . . . . . . . . 210 19.3 Time Consuming Equilibrium Adjustment Processes . . . . . . . . . 214 19.4 Frictionless Tuning of Coordination Signals in Evolving Economies in Continuous Historical Time . . . . . . . . . . . . . . . . . . . 217 19.4.1 General Conceptualization . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19.4.2 Frictionless Tuning in the Quantity Constrained Multi-Sectoral Model From Chapter 4 . . . . . . . . . . . . . . . . 221 19.4.3 Frictionless Tuning in the General Equilibrium Framework With Production, Taxes, and Subsidies From Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
17
Part III Economic Analysis
VIII
Contents
References. . . . . . . . . . . . . . . . . . . . . . . 263. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
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