Equilibrium and Efficiency in Production Economies

This book is a substantially revised and enlarged version of the monograph General Equilibrium with Increasing Returns, published by Springer-Verlag as a Lecture Notes volume in 1996. It incorporates new topics and the most recent developments in the field. It also provides a more systematic analysis of the differences between production economies with and without convex production sets. Five out of twelve chapters are new, and most of the remaining ones have been reformulated. An outline of contents appears in chapter 1. As its predecessor, this book contains a formal and systematic exposition of the main results on the existence and efficiency of equilibrium, in production economies where production sets need not be convex. There is an explicit attempt at making of it a suitable reference both for graduate students and researchers interested in theory (not necessarily specialists in mathematical economics). With this twofold purpose in mind, the work has been written according to three key principles: (i) To provide a uhified approach to the problems involved. For that we construct a basic model that is rich enough to encompass the different models appearing throughout, and to derive all the results as coroilaries of a reduced number of general theorems. (ii) To maintain a relatively low mathematical complexity. Thus, when the estimated cost of generality exceeds the benefit of simplicity, we shall state and prove the theorems under assumptions that need not be the most general ones.

Low mathematical complexity Highly self-contained exposition

Klappentext

This book deals with the analysis of production economies in which firms may exhibit increasing returns to scale, or other forms of non-convexities. The study focuses on the existence and efficiency of equilibrium allocations, and the comparison with the standard competitive equilibrium model. A number of alternative pricing rules and equilibrium concepts are considered (marginal pricing, constrained profit maximization, mark-up pricing, valuation equilibria, non-linear input-output models, etc.).

Inhalt
1 Preliminaries.- 1.1 Introduction.- 1.2 Overview.- 1.3 The setting.- 1.4 References to the literature.- 2 Consumers.- 2.1 Introduction.- 2.2 Consumption sets.- 2.3 Preferences.- 2.4 The utility function.- 2.5 Wealth restrictions.- 2.6 Consumers' behaviour.- 2.7 References to the literature.- 3 Production and Supply.- 3.1 Introduction.- 3.2 Production sets.- 3.3 Efficiency, additivity, divisibility.- 3.4 Returns to scale.- 3.5 The behaviour of competitive firms.- 3.6 References to the literature.- 4 Competitive Equilibrium.- 4.1 Introduction.- 4.2 The model.- 4.3 Assumptions and consequences.- 4.4 The existence of equilibrium.- 4.5 Equilibrium and efficiency.- 4.6 Abstract economies.- 4.7 References to the literature.- 5 Equilibrium with Non-convex Firms.- 5.1 Introduction.- 5.2 Pricing rules.- 5.3 The model.- 5.4 The existence of equilibrium.- 5.5 References to the literature.- 6 Marginal Pricing.- 6.1 Introduction.- 6.2 Preliminaries.- 6.3 Marginal pricing.- 6.4 The efficiency problem.- 6.5 References to the literature.- 7 Increasing Returns and Monopolies.- 7.1 Introduction.- 7.2 The reference model.- 7.3 Two-part marginal pricing.- 7.4 The efficiency of two-part tariffs.- 7.5 Perfect price discrimination.- 7.6 References to the literature.- 8 Loss-free Pricing Rules.- 8.1 Introduction.- 8.2 The reference model.- 8.3 Mark-up pricing.- 8.4 Constrained profit maximization.- 8.5 References to the literature.- 9 Competition and Increasing Returns.- 9.1 Introduction.- 9.2 The reference model.- 9.3 Competitive pricing.- 9.4 Classical equilibrium.- 9.5 References to the literature.- 10 Non-Convexities as Public Goods.- 10.1 Introduction.- 10.2 The model.- 10.3 Public competitive equilibrium.- 10.4 Valuation equilibrium.- 10.5 Examples.- 10.6 References to the literature.-11 Input-Output Analysis.- 11.1 Introduction.- 11.2 The linear model.- 11.3 Extensions.- 11.4 References to the literature.- 12 The Limits of the Economy.- 12.1 Asymptotic cones.- 12.2 Closed sums.- 12.3 Structural properties of the economy.- 12.4 References to the literature.