Economists’ Mathematical Manual Knut Sydsæter · Arne Strøm · Peter Berck Economists’ Mathematical Manual Fourth Edition 123 Professor Knut Sydsæter University of Oslo Department of Economics P.O. Box 10955 Blindern NO-0317 Oslo Norway
[email protected] Associate Professor Arne Strøm University of Oslo Department of Economics P.O. Box 10955 Blindern NO-0317 Oslo Norway
[email protected] Professor Peter Berck University of California, Berkeley Department of Agricultural and Resource Economics Berkeley, CA 94720-3310 USA
[email protected] ISBN 978-3-540-26088-2 e-ISBN 978-3-540-28518-2 DOI 10.1007/978-3-540-28518-2 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009937018 c Springer-Verlag Berlin Heidelberg 1991, 1993, 1999, 2005, Corrected Second Printing 2010 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface to the fourth edition The fourth edition is augmented by more than 70 new formulas. In particular, we have included some key concepts and results from trade theory, games of incomplete information and combinatorics. In addition there are scattered additions of new formulas in many chapters. Again we are indebted to a number of people who has suggested corrections, improvements and new formulas. In particular, we would like to thank Jens-Henrik Madsen, Larry Karp, Harald Goldstein, and Geir Asheim. In a reference book, errors are particularly destructive. We hope that readers who find our remaining errors will call them to our attention so that we may purge them from future editions. Oslo and Berkeley, May 2005 Knut Sydsæter, Arne Strøm, Peter Berck From the preface to the third edition The practice of economics requires a wide-ranging knowledge of formulas from mathematics, statistics, and mathematical economics. With this volume we hope to present a formulary tailored to the needs of students and working professionals in economics. In addition to a selection of mathematical and statistical formulas of