A unique feature of the book compared to classical monographs on GE is its emphasis on the historical nature of the subject, and not only the mathematical nature. Students are expected to learn that those mathematically formidable techniques are indeed necessary for tackling many economic problems which have been significant not only in the mathematical or technical context, but also in the historical and traditional context.
The aim of this book is to incorporate Marshallian ideas such as external increasing returns and monopolistic competitions into the general equilibrium framework of Walrasian tradition. New chapters and sections have been added to this revised and expanded edition of General Equilibrium Analysis of Production and Increasing Returns (World Scientific, 2009).The new material includes a presentation of equilibrium existence and core equivalence theorems for an infinite horizon economy with a measure space of consumers. These results are currently the focus of extensive studies by mathematical theorists, and are obtained by an application of an advanced mathematical concept called saturated (super-atomless) measure space.The second major change is the inclusion of a simple toy model of a liberal society which implements the difference principle proposed by J Rawls as a principle of distributive justice. This new section opens up a possibility to connect theoretical economics and political philosophy.Thirdly, the author presents the marginal cost pricing equilibrium and discusses welfare properties of the external increasing returns, which also belong to Marshall/ Pigou tradition of the Cambridge school.Finally, a new mathematical appendix treats basics of singular homology theory. Although the fixed point theorem is originally a theorem of algebraic topology, most economic students know its proof only in the context of the differentiable manifold theory presented by J Milnor. Considering the significance of the fixed point theorem and its playing a key role in general equilibrium theory, the purpose of this new appendix is to provide readers with the idea of a proof of Brower's fixed point theorem from the 'right place'.This volume will be helpful for graduate students and researchers of mathematical economics, game theory, and microeconomics.
This is a book on general equilibrium in which firms are allowed to exhibit increasing returns to scale (more precisely, in which the convexity of production sets is not assumed). As such, it provides a full fledged general equilibrium model and analyzes the chief questions concerning existence and optimality. Increasing returns is a topic which many economists find it to be simultaneously very imponant, very difficult and very discouraging. It is very important because it refers to a well established technological phenomenon which is essentially incompatible with the functioning of competitive markets. It is very difficult because the standard concepts and tools for the analysis fail (in particular, the supply mappings are not well defined). It is very discouraging because the available models do not seem to solve the basic questions: Normative models where nonconvex firms follow marginal pricing do not achieve efficient outcomes, and positive models cannot incorporate monopolistic competition as a way of defming the behavior of those firms with increasing returns to scale. I would like to think that this monograph will contribute to show that "the increasing returns question" is neither too difficult nor too discouraging. Concerning the difficulty, it will be shown that the analysis can be carried out with essentially the same tools as those applicable to the standard competitive model. As for the relevance of the results available, let me point out the following.
The aim of this book is to incorporate Marshallian ideas such as external increasing returns and monopolistic competitions into the general equilibrium framework of Walrasian tradition. New chapters and sections have been added to this revised and expanded edition of General Equilibrium Analysis of Production and Increasing Returns (World Scientific, 2009).The new material includes a presentation of equilibrium existence and core equivalence theorems for an infinite horizon economy with a measure space of consumers. These results are currently the focus of extensive studies by mathematical theorists, and are obtained by an application of an advanced mathematical concept called saturated (super-atomless) measure space.The second major change is the inclusion of a simple toy model of a liberal society which implements the difference principle proposed by J Rawls as a principle of distributive justice. This new section opens up a possibility to connect theoretical economics and political philosophy.Thirdly, the author presents the marginal cost pricing equilibrium and discusses welfare properties of the external increasing returns, which also belong to Marshall/ Pigou tradition of the Cambridge school.Finally, a new mathematical appendix treats basics of singular homology theory. Although the fixed point theorem is originally a theorem of algebraic topology, most economic students know its proof only in the context of the differentiable manifold theory presented by J Milnor. Considering the significance of the fixed point theorem and its playing a key role in general equilibrium theory, the purpose of this new appendix is to provide readers with the idea of a proof of Brower's fixed point theorem from the 'right place'.This volume will be helpful for graduate students and researchers of mathematical economics, game theory, and microeconomics.
Conventional analysis in the trade-industrial-organization literature suggests that, when a country has some market power over an imported good, some small level of protection must be welfare improving. This is essentially a terms-of-trade argument that is reinforced if the imported goods are substitutes for domestic goods produced with increasing returns to scale, goods that are initially underproduced in free-trade equilibrium. This paper notes that this result may not hold when (1) the imports are intermediates used in a domestic increasing-returns industry, and/or (2) the intermediates are complements for domestic inputs produced with increasing returns. We then demonstrate such an outcome with respect to Mexican protection against imported auto parts using an applied general-equilibrium model of the North American auto industry.
This study analyzes increasing returns to scale using general equilibrium theory to take into account the interactions between production in the public and private sectors. It also explores how the redistribution of income has been effected by financing the private sector.
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.
This is a new kind of textbook in microeconomic theory. In place of the usual concentration on partial equilibrium analysis and discussion of a standard series of topics, the authors seek to introduce the student from the start to the general equilibrium approach to microeconomics, in the form of the two-sector model. This model is then applied to a variety of subjects in different special fields of economic analysis: welfare economics, international trade, public finance and income distribution. This book represents a very different approach to the teaching of micro-economic theory than normally followed, and one that will be of greater long-run value to the serious student of economics. In place of the usual textbook development of the subject as traditionally conceived through topics of increasing complexity and analytical difficulty, using partial equilibrium techniques of analysis, the book concentrates on the exposition and application of a more logically integrated set of tools that have been found of greater use in the analysis of problems arising not only in traditional micro-economics but also in a number of fields of economics that have customarily been hived off into separate specialized advanced courses. General Equilibrium Analysis starts with the description of the two-sector model and how these two sectors are built based on the individual micro-units in which they made up of and how they fit into the concept of the circular flow of income. Subsequent chapters deal with the evaluation of changes in factor endowment, demand preferences and technical progress by means of the model; and the theory of government, which includes both the theory of government expenditure, or public goods, and the theory of government tax and/or subsidy programmes-changes in budgetary scale, tax substitution and expenditure substitution. The model is then extended to an open economy-the so-called "two by two by two"--to consider both the normative effect of inte
