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Über dieses Buch

The analysis of this volume represents an attempt to apply modern mathematical techniques to the problems arising from large and significant indivisibilities. While the classical microeconomic theory refers to assumptions about the convexity of production sets and consumer preferences, this book directs the attention to indivisible commodities. It investigates the influence of the assumed indivisibilities of factors and goods on the results of the microeconomic theory of the firm, the theory of the household and market theory.

Inhaltsverzeichnis

Frontmatter

Chapter I. Microeconomic Theory with Respect to Indivisibilities

Abstract
Indivisible goods and factors constitute a subject of economic theory associated with a series of unsolved problems. Even advanced works on microeconomic theory like Varian (1992) or Jehle (1991) refrain from the consideration of indivisible goods and factors to provide a structure for the analysis where relatively simple mathematical methods can be applied. The Handbook of Mathematical Economics also does not contain any approach treating explicitly the integer problem. While Green, Heller (1981) present the instrument of convex analysis with respect to economic applications in the first chapter, a corresponding work dealing with the indivisibility of goods and factors is missing. Even in Brown (1991), who introduces an equilibrium analysis with nonconvex technologies in Chapter 36, the problem of indivisibility is merely of minor importance.
Hagen Bobzin

Chapter II. Microeconomic Foundations

Abstract
In an economy composed of many economic agents two groups of individual economic decision units may be stressed: households and firms. The theory of the household deals with the question how to satisfy the household’s needs, whereas the theory of the firm concentrates on the production of new goods.
Hagen Bobzin

Chapter III. Microeconomic Theory of Individual Agents

Abstract
The notion of duality is used differently and is often misleading.1 Usually, the attention is drawn to certain symmetry properties of statements or optimization problems. For example, we can formulate in accordance with mathematical logic the subsequent duality principle for the statements A and B which are either “true” or “false”: if the word “and” is exchanged everywhere with the word “or” in the two semantically equivalent statements H1 and H2 which are only composed of the functional words “and”, “or”, and “not”, then the resulting dual statements H1* and H2* are semantically equivalent, too.2 When the text stresses this dual view of different statements, then such a substitution principle is intended bearing the symmetry properties in mind.3
Hagen Bobzin

Chapter IV. Theory of Market Equilibria

Abstract
In every economy it is necessary to know who can dispose of what quantities of goods and for what purpose. The examination of these problems assumes that the property rights of goods are exerted personally by individual persons, i.e. common property is ruled out.
Hagen Bobzin

Chapter V. Critique

Abstract
In treating indivisible goods and factors we follow a path which is based on well known approaches in microeconomic theory.
Hagen Bobzin

Backmatter

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