The present monograph is a synthesis of what has been contributed during the last decade to the analysis of market demand in large econ- omies where consumers may have non-convex preference relations. Al- though research in this field has not yet come to an end there exists a variety of interesting results, established in different frameworks by means of different conceptual and formal tools. a It is my aim to give comprehensive treatment of the existing lit- erature including my own contributions. In working out differences and interrelations of the various ap- proaches I adopted and modified several of the original results. My desire to present the problem and the methods by which it has been treated in such a way, that also non-specialists can follow, con- flicted sometimes with the inevitable complexity of tools to be used. Therefore, I decided to give enough room to the introductory and prepa- ratory part of this work. This part consists of the introduction and of the first four chapters. The main part of the present analysis consists of chapters 5 to 7.
1 Demand and Equilibria.- 1.1 Introduction.- 1.2 Individual demand.- 1.3 Market demand.- 1.4 Equilibria.- 1.5 Concluding remarks.- 2 Smoothing Demand by Aggregation.- 2.1 Many different consumers.- 2.2 Convexifying by averaging.- 2.3 Concluding remarks on diversification.- 3 Spaces of Preferences and Large Economies.- 3.1 Introduction.- 3.2 Preference relations.- 3.3 Spaces of preference relations.- 3.4 Large economies.- 4 Heuristic Remarks on Some Basic Concepts.- 4.1 Genericity.- 4.2 Stability.- 4.3 Equal distribution.- 4.4 The law of large numbers.- 5 The Parametric Approach.- 5.1 Introduction.- 5.2 Dispersion of tastes.- 5.3 Continuous mean demand.- 5.4 Differentiable mean demand.- 5.5 Concluding remarks.- 6 The Ergodic Approach.- 6.1 Introduction.- 6.2 G-dispersion.- 6.3 Continuous mean demand.- 6.4 Differentiable mean demand.- 6.5 Concluding remarks.- 7 Other Approaches.- 7.1 Dispersion of unit normals.- 7.2 Infinite dimensional linear spaces of preferences.- 7.3 Random individual demand.- 7.4 The generic approach.- 8 Mathematical Tools.- 8.1 Miscellany.- 8.2 Differential topology.- 8.3 Measure theory.- Notation.- References.
Series: Lecture Notes in Economic and Mathematical Systems
Number Of Pages: 208
Published: February 1984
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6
Weight (kg): 0.31