Fundamentals of Production Theory
This graduate text develops production theory from a set of reasonable axioms. The theory is presented both in a primal and dual as well as in an indirect (constrained) framework. The basic model leads to a set of efficiency measures which can be readily
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Rolf Färe
Fundamentals of Production Theory
Lectu re Notes in Economics and Mathematical Systems Managing Editors: M. Beckmann and W. Krelle
311 Rolf Fare
Fundamentals of Production Theory
Spri nger-Verlag Berlin Heidelberg GmbH
Editorial Board
H.Aibach M. Beckmann (Managing Editor) P. Dhrymes G. Fandel G. Feichtinger J. Green W. Hildenbrand W. Krelle (Managing Editor) H.P. Kl.inzi K. Ritter R. Sato U. Schittko P. Schonfeld R. Selten Managing Editors
Prof. Dr. M. Beckmann Brown University Providence, Rl 02912, USA Prof. Dr. W. Krelle lnstitut fGr Gesellschafts- und Wirtschaftswissenschaften der Universitiit Bonn Adenauerallee 24-42, D-5300 Bonn, FRG Author
Prof. Rolf Fare Department of Economics, Southern Illinois University Carbondale, IL 62901, USA
ISBN 978-3-540-50030-8 DOI 10.1007/978-3-642-51722-8
ISBN 978-3-642-51722-8 (eBook)
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1988 Originally published by Springer-Verlag Berlin Heidelberg New York in 1988 2142/3140-54321 0
To Carolina and Shawna
PREFACE During my visit at the economics department at Vanderbilt University I had the opportunity to teach a class in production theory.
This text is the lecture notes
that I developed for that occasion. As a student of the late Professor Ronald W. Shephard, it is natural for me to treat production theory within an axiomatic framework.
The axiomatic approach on which
this monograph rests is strongly influenced by Professor Shephard's book "Theory of Cost and Production," and our joint book "A Dynamic Theory of Production Correspondences." The text is by nature somewhat mathematical, however, the mathematics is rather standard and a student with advanced undergraduate mathematics training should have no problems with the text.
To make full use of the book, students need to solve the
problems, since they are extensions of the text, and often introduce additional concepts.
Also, see the notes for references to additional literature.
Special thanks are given to Mariann Baratta for her outstanding work and patience in preparing this manuscript. Rolf Fare February, 1988 Carbondale, Illinois
CONTENTS
PREFACE INTRODUCTION 2
THE PRODUCTION STRUCTURE 2.0
Introduction
2.1
The Production Technology
2.2
The Axiomatic Framework
2.3
Notions of Efficiency
11
2.4
Properties of the Efficient Input and Output Sets
14
3 4 6
Appendix: On the Consistency and the Independence of the Maintained Axioms 2.P
3
4
Problems
20
Notes
21
REPRESENTING
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