Cost and Production Functions
This study is the result of an interest in the economic theory of production intermittently pursued during the past three years. Over this period I have received substantial support from the Office of Naval Research, first from a personal service consulti
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194 Ronald W. Shephard
Cost and Production Functions Reprint of the First Edition
Springer-Verlag Berlin Heidelberg New York 1981
Editorial Board
H. Albach A.V. Balakrishnan M. Beckmann (Managing Editor) P. Dhrymes J. Green W. Hildenbrand W. Krelle
H. P. Kunzi (Managing Editor) K. Ritter R. Sato H. Schelbert P. SchOnfeld R. Selten Managing Editors
Prof. Dr. M. Beckmann Brown University Providence, RI 02912, USA Prof. Dr. H. P. Kunzi Universitat Zurich CH-8092 Zurich, Schweiz Author
Ronald W. Shephard 1089 Keeler Avenue Berkeley, CA 94708, USA
Reprint of the 1953 edition, published by Princeton University Press
ISBN 978-3-540-11158-0 ISBN 978-3-642-51578-1 (eBook) DOI 10.1007/978-3-642-51578-1 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to ·Verwertungsgesellschaft Wort", Munich.
© Ronald W. Shephard 1981
2142/3140-543210
FORWARD Ronald Shephard's book Cost and Production Functions ranks as one of the most original contributions to economic theory of all time.
This
remarkable book contains a full development of three seminal ideas: 1.
The duality between cost and production functions.
Shephard's
central idea. is that technologies can be determined from two alternative and completely equivalent points of view:
The production function and
marginal productivities of the inputs on the one hand and the cost function and the demands for the inputs conditional on output on the other. Shephard's treatment of duality is based on convex analysis and is completely modern in its orientation. 2.
Shephard's lemma.
Part of the duality between cost and produc-
tion functions is based on the equality between derivatives of the cost function with respect to price and factor demands conditional on output. Shephard had a full appreciation of the central importance of this idea fOL econometric description of technologies (see, for example, pages 28 and 52).
Shephard's lemma has had far reaching influence on applied
eocnometrics over the past decade, beginning with the work of Erwin Diewert. 3.
Homotheticity and homothetic separability.
Shephard developed
the notion of a homo the tic production function and employed the idea in function and formulating the concept of homothetic separability.
The
critical importance of homothetic separability to duality in the theory of aggregation and index numbers was fully appreciated by Shephard. Like many of the most profound contributions to economic theory, Augustin Cournot's Researches into the Mathematical Principles of the Theory of Wealth being another notable example, Shephard's book began its distinguished history with a period of relative obscurity.
Hirofumi
Uzawa played an important role in promoting Shephard's point of
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