Exterior Differential Calculus and Applications to Economic Theory

Author(s):  Ivar Ekeland

Publisher: Edizioni della Normale

Date     : 2007

Pages    : 56

Format   : PDF

Language : English

ISBN-10  : 887642251X



During the academic year 1995/96, I was invited by the Scuola Normale Superiore to give a series of lectures. The purpose of these notes is to make the underlying economic problems and the mathematical theory of exterior differential systems accessible to a larger number of people. It is the purpose of these notes to go over these results at a more leisurely pace, keeping in mind that mathematicians are not familiar with economic theory and that very few people have read Elie Cartan.



CONTENTS

Foreword

Chapter 1- From economics to mathematics

Chapter 2- The single consumer model

Chapter 3- Exterior differential calculus

3.1. - Preliminaries

3.2. - Exterior product

3.3. - Exterior derivative

3.4. - Differential ideals

Chapter 4- The Frobenius theorem

4.1. - Statement and proof

4.2. - Application to the one consumer model

Chapter 5- The household model

5.1. - Statement of the model and Pareto optimality

5.2. - The Browning - Chiappori necessary condition

Chapter 6- Pfaff's theorem

Chapter 7- The Cartan-Kahler theorem

7.1. - An introductory example

7.2. - The general problem

7.3. - Differential ideals

7.4. - A counter example

7.5. - Regularity conditions and ordinary points

7.6. - The main result

Chapter 8- Markets





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