# Mathematical Theory of Economic Dynamics and Equilibria

• V. L. Makarov
• A. M. Rubinov
Book

1. Front Matter
Pages i-xv
2. V. L. Makarov, A. M. Rubinov
Pages 1-58
3. V. L. Makarov, A. M. Rubinov
Pages 59-92
4. V. L. Makarov, A. M. Rubinov
Pages 93-160
5. V. L. Makarov, A. M. Rubinov
Pages 161-196
6. V. L. Makarov, A. M. Rubinov
Pages 197-210
7. V. L. Makarov, A. M. Rubinov
Pages 211-233
8. Back Matter
Pages 234-253

### Introduction

This book is devoted to the mathematical analysis of models of economic dynamics and equilibria. These models form an important part of mathemati­ cal economics. Models of economic dynamics describe the motion of an economy through time. The basic concept in the study of these models is that of a trajectory, i.e., a sequence of elements of the phase space that describe admissible (possible) development of the economy. From all trajectories, we select those that are" desirable," i.e., optimal in terms of a certain criterion. The apparatus of point-set maps is the appropriate tool for the analysis of these models. The topological aspects of these maps (particularly, the Kakutani fixed-point theorem) are used to study equilibrium models as well as n-person games. To study dynamic models we use a special class of maps which, in this book, are called superlinear maps. The theory of superlinear point-set maps is, obviously, of interest in its own right. This theory is described in the first chapter. Chapters 2-4 are devoted to models of economic dynamics and present a detailed study of the properties of optimal trajectories. These properties are described in terms of theorems on characteristics (on the existence of dual prices) and turnpike theorems (theorems on asymptotic trajectories). In Chapter 5, we state and study a model of economic equilibrium. The basic idea is to establish a theorem about the existence of an equilibrium state for the Arrow-Debreu model and a certain generalization of it.

### Keywords

Finite Gleichgewicht Mathematica Wachstum boundary element method character development form function games growth mathematical analysis model theorem tool

#### Authors and affiliations

• V. L. Makarov
• 1
• A. M. Rubinov
• 1
1. 1.Siberian Branch of the Academy of SciencesRussia

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-9886-1
• Copyright Information Springer-Verlag New York 1977
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-9888-5
• Online ISBN 978-1-4612-9886-1