A New Axiom System for Price Indices
In the above quotation Kaiser (1971) refers to Fisher (1941a:193). Kaiser (1970:1,1974:51) coined the term “societal sciences” meaning “sciences treating society” without the side-meaning “solidarity” of the attribute “social”. He entiteled his lecture 19
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Last Note from the Authors The formula on the cover page (formula (1.47) in the book) looks tremendous. In fact, it corresponds to the most simple path in the price-commodity-space (linear path, see figure on page 16). In this context the exponential path (figure on page 32, formulas (1.50), (1.51)) is noteworthy as well. April 1997
Arthur Vogt and Hmos Barta
Fisher (left) in 1945 on television with his world map
Arthur Vogt · Janos Barta
The Making of Tests for Index Numbers Mathematical Methods of Descriptive Statistics
Published in Honour of the 50th Anniversary of the Death of Irving Fisher
With 8 Figures
Springer-Verlag Berlin Heidelberg GmbH
Dr. Arthur Vogt Ahornweg 16 CH-3400 Burgdorf, Switzerland Dipl. math. Janos Barta Via Navone 21 CH-6942 Savosa, Switzerland
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Vogt, Arthur: The making of tests for index numbers: mathematical methods of descriptive statistics; published in honor of the 50th anniversary of the death ofIrving Fisher I Arthur Vogt; Janos Barta. ISBN 978-3-7908-2456-8 ISBN 978-3-662-13179-4 (eBook) DOI 10.1007/978-3-662-13179-4 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 he obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1997 Originally published by Physica-Verlag Heidelberg in 1997 Softcover reprint of the hardcover 1st edition 1997
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. Photograph on p. II from "Fisher: My Father Irving Fisher (1956), Comet Press Books, New York" Cover Design: Erich Kirchner, Heidelberg SPIN 10573770
88/2202-5 4 3 2 I 0 - Printed on acid-free paper
Foreword This book on the field called measurement in economics contains so many different "indices" that the question of a common origin of them may reasonably be asked. Another question arises immediately: What kind of mechanism produces an index from a set of economic figures or objects? The reader may like to get answers to these questions. The variety of examples in this book may suggest the following definition: In economics an index is a measure, i.e. a function F:D~R
which maps, on the one hand, a set of economically interesting objects D into the set R of real numbers, and which satisfies, on the other hand, a system of economically relevant condit
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