ebook img

The Collected Economics Articles of Harold Hotelling PDF

186 Pages·1990·14.54 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview The Collected Economics Articles of Harold Hotelling

The Collected Economics Articles of Harold Hotelling The Collected Economics Articles of Harold Hotelling Edited by and with an Introduction by Adrian C. Darnell With 10 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Adrian C. Darnell The Department of Economics University of Durham Durham DHI 3LE England Mathematics Subject Classifications (1980): 90Axx, 90AIO, 90All, 90A12, 90A14, 90A15, 90A16 Library of Congress Cataloging-in-Publication Data Hotelling, Harold, 1895- The collected economic articles of Harold Hotelling. Includes bibliographical references. I. Hotelling, Harold, 1895- . 2. Economics, Mathematical. 3. Mathematical Statistics. I. Darnell, A. C. II. Title. HB1l9.H68 1989 330'.01'51 89-21666 ISBN-13 :978-1-4613-8907-1 © 1990 by Springer-Verlag New York Inc. Softcover reprint of the hardcover 1st edition 1990 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the puplisher (Springer-Verlag, 175 Fifth Avenue, New York, New York 10010, U.S.A.), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this pUblication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Typeset by Asco Trade Typesetting Ltd., Hong Kong. 9 8 7 6 543 2 1 ISBN-13 :978-1-4613-8907 -1 e-ISBN-13 :978-1-4613-8905-7 DOl: 10.1007/978-1-4613-8905-7 Preface In 1985 I first began my research on the life and work of Harold Hotel ling. That year, Harold Hotelling's widow had donated the collection of his private p:;tpers, correspondence and manuscripts to the Butler Library, Columbia University. This is a most appropriate place for them to reside, in that Hotelling's most productive period as an active researcher in eco nomics and statistics coincides with the years when he was Professor of Mathematical Economics at Columbia (1931-1946). The Hotelling Collection comprises some 13,000 separate items and contains numerous unpublished letters and manuscripts of great importance to historians of economics and statistics. In the course of the following year I was able, with the generous financial assistance of the Nuffield Foundation, the Economic and Social Research Council, the British Academy and the University of Durham, to spend six weeks over the Easter period working on the collection. I returned to New York in September 1986 while on sabbatical leave from the University of Durham, and I spent most of the following eight months examining the many documents in the collection. During that academic year I was grateful to Columbia University who gave me the title of Visiting Research Professor and gave me the freedom to work in their many well-stocked libraries. Since then I have been engaged in the process of writing up my research, which has become a large project examining Hotelling's role in the history of economics. This volume is the first fruit ofthose labours. It comprises a lengthy introductory chapter which seeks first to describe Hotelling's life, and then proceeds to identify the nature and importance of his seminal contributions to economics. His published articles in economics (excepting two obituaries, of Schultz and Roos, an entry in Encyclopedia Americana and all his book reviews) are reprinted here, having corrected only original typographic errors; all page references have also been changed to the pagination of the reprints. His work covers diverse fields of economics, but is unified by its use of sophisticated mathematical techniques. This collection will, hopefully, be of interest to all economists, but especially to those whose research lies in the history of our subject. Additionally, many economists today find inspiration vi Preface for their work in the path-breaking papers Hotelling published some fifty years ago, and it is to be hoped that this collection will itself provide further inspiration for research in the general field of mathematical economics-the field in which Hotelling was certainly one of the most successful twentieth century pioneers. A reading of his papers will not prove relaxing, necessarily, but it will prove most rewarding. Acknowledgements First and foremost I would like to thank both Mrs. Harold Hotelling and Professor Harold Hotelling, 1nr. for their most generous and kind assistance and encouragement in this research. Additionally, I would like to thank the staff of the Butler Library and particularly the Librarian of Rare Books and Manuscripts, Dr. K. Lohf, for all the assistance given; I also acknowledge the help given by the staff at the Archive of The Food Research Institute, Stanford. I am indebted to Professors Kenneth Arrow, Mark Blaug, Denis O'Brien and Ingram Olkin, and to Dr. 1. Lynne Evans for their encouragement and for their comments upon my work. Last, but by no means least, my thanks go to Angela Darnell for her invaluable work as an unpaid research assistant on a preliminary visit to Columbia in April 1986. I acknowledge, with most grateful thanks, the permission given by Mrs. Harold Hotelling and by Dr. K. Lohf to quote from the papers in the Hotelling Collection at Columbia University, and I also acknowledge the co-operation of the publishers of Hotelling's articles who have granted permission to reprint copyright material originally published by them. All work reprinted is without alteration from the original, with the exception of the correction of typographic errors and the imposition of internally consistent pagination. Generous financial assistance from the Nuffield Foundation (Grant No. SOCj181(1412), the British Academy, the Economic and Social Research Council (Grant No. B 0023 2184) and the University of Durham is gratefully acknowledged. Contents Preface v Acknowledgements vii The Life and Economic Thought of Harold Hotelling Bibliography of Harold Hotelling 29 Reprints of the Published Economics Papers by Harold Hotelling 1925 A general mathematical theory of depreciation. Journal of the American Statistical Association, 20, 340-53. 36 1929 Stability in competition. Economic Journal, 39,41-57. 50 1931 The economics of exhaustible resources. Journal of Political Economy, 39, 137-75. 64 1932 Edgeworth's taxation paradox and the nature of demand and supply functions. Journal of Political Economy, 40,577-616. 93 1933 Note on Edgeworth's taxation phenomenon and Professor Garver's additional condition on demand functions. Econometrica, 1,408-9. 123 1935 Demand functions with limited budgets. Econometrica, 3, 66-78. 125 1936 Curtailing production is anti-social. Columbia Alumni News, 28(4), 3 and 16. 137 1938 The general welfare in relation to problems of taxation and of railway and utility rates. Econometrica, 6, 242-69. 141 1939 The relation of prices to marginal costs in an optimum system. Econometrica,7,151-6. 166 1939 A final note. Econometrica, 7, 158-60. 171 1943 Income-tax revision as proposed by Irving Fisher. Econometrica, 11,83-7. 174 The Life and Economic Thought of Harold Hotelling I. INTRODUCTION Harold Hotelling was one of the most important of the twentieth-century pioneers of mathematical economics and mathematical statistics.1 In both fields he is recognised for his powerful theoretical contributions2 and he was a most effective and caring teacher. His influence, both as an economist and as a statistician, is felt not only through his publications (a large number of which are seminaI3), but also through his students, amongst whom one can count many of the leading economists and statisticians of the next generation.4 Hotelling's career spans one of the most creative and formative periods in the development of both mathematical economics and mathematical statistics, and few figures have displayed a comparable originality; fewer still have publication records which bear comparison. Most importantly, his published papers are today seen as the starting point of much contemporary research. Indeed, his name is familiar to a remarkably wide range of professionals, 1 There are, surprisingly, few secondary sources on Hotelling; additional details on his life and career may be found in Madow (1960), Samuelson (1960), Smith (1978), Pfouts and Leadbetter (1979), the American Economic Review (1974), Arrow (1987) and Darnell (1988). 2 His numerous papers in mathematical statistics did have immediate impact; however, during his own lifetime, many of his contributions to economics were not properly recognised (for reasons discussed in this introductory chapter). His publications (in all fields) are listed in a complete bibliography at the end of this work. This current volume is concerned with his writings in economics, and of those, only his work in spatial economics (1929) and in welfare economics (1938, 1939 and 1939a) may be said to have had contemporary impact. 3 His publications in economics are the real concern of this work; see Hotelling (1925,1929,1931, 1932,1933,1935,1936,1938,1939, 1939a and 1943), all of which are reprinted immediately after this introductory chapter. However, in the field of mathematical statistics see, especially, the seminal contributions in Hotelling (1931a, 1933a, 1936a and 1940), and for an appreciation of Hotelling the statistician, see Neyman (1960) in Olkin, Ghuye, HoefTding, Madow and Mann (1960). 4 The list is far too large to catalogue. Nevertheless, suffice to note that while at Columbia, he taught Friedman statistics, supervised Arrow's PhD, and worked with Stigler in the Statistical Research Group. 2 Harold Hotelling a range which includes, naturally, economists and statisticians but which also includes educationalists and psychologists. He is, however, best known as a mathematical economist and mathematical statistician: in economics there is Hotelling's Law,5 Hotelling's Lemma6 and Hotelling's Rule,7 and in statistics there is Hotelling's T2 statistic.8 II. BIOGRAPHIA Hotelling's biographical details are not widely available,9 yet they provide a significant insight into his motivations as an economist and into his explicit dependence upon mathematical methods. Harold Hotelling was born on 29 September 1895 in Fulda, Minnesota, of ancestors long American but originally of English and Dutch extraction. When he was nine his family moved to Seattle in order that the five children, of whom Harold was the oldest, might enjoy a better education and have access to better opportunities than those available in Fulda. He attended high school in Seattle and, on leaving, began studying journalism at the University of Washington, financing his studies working for small newspapers; he further supplemented his income by carrying out small re-wiringjobs having studied the rudimentary principles of electricity through his own private reading (rather than through any formal tuition). His studies were interrupted by the First World War and he notes n a biographical sketch10 that, on being called to war service: Having studied mathematics, science and classics at school and college, was considered by [the] army authorities competent to care for mules. The result was [that] a temperamental mule temporarily broke his leg and thereby saved his life, as the rest of the division was sent to France and [was] wiped out. Thus Hotelling was, fortuitously, never engaged in active service and he resumed his course in journalism having been discharged from the army on 4 February 1919; however, Hotelling found that the Department of Journalism 5 The Law refers to the observation that spatial competition may lead to a clustering of com petitors. See Hotelling (1929). 6 The Lemma refers to HotelIing's work on integrability and duality in the context of the theory of the producer, and refers to the fact that the first partial derivative of a cost function with respect to the price of factor i is the demand function for that factor. See HotelIing (1932). 7 The Rule refers to HotelIing's work on exhaustible resources, and states that the optimal production schedule of an irreplaceable resource is such that it generates a rate of increase of its price which is identical to society's discount rate (thus if society's discount rate is r, then the price of an exhaustible resource should also rise at rate r). See Hotelling (1931). 8 The T2 statistic is used to make simultaneous tests of the equality of several characteristics of many variables. It is a generalisation ofStudenfs t statistic. See HotelIing (1931a). 9 See the references given in footnote 1. 10 This sketch was written cryptically and in the third person as a press notice for an invited lecture HotelIing gave in 1932 for the Chemical Society of New York. HotelIing lectured on the title of "The economics of obsolescence". The Life and Economic Thought of Harold Hotelling 3 had been severely disrupted by the war and he began to study some economics. In a letter to the University of Washington, dated 14 December 1962, he wrote:11 I have a first degree in journalism from Washington but at the time the School of Journalism was badly disorganised because ofthe First World War and they let me substitute so much economics for journalism that the degree might just have well been in it. Anyhow, the journalism degree got me a job on the Washington Standard in Olympia. Its economic component, plus later studies of mathematics at Seattle, Chicago and Princeton gave enough color to the idea that I was an economist to give me ajob as Professor of Economics at Columbia University. I actually did teach economics there, but it was economics so mathematical that no member ofthe distinguished economics faculty there could understand it. In the light of consultation with university records. Hotelling's own report makes puzzling reading: he earned a total of only nine credits in economics from just three courses. One was in "Railway and Marine Rates" and another in "Marine Insurance"; the description of the third is, unfortunately, not available. This represents only a very small part of his degree, being less than three-quarters of his final year studies. He was awarded his BA in journalism in 1919 and joined the staff of a local newspaper. Hotelling records in other autobiographical notes12 that he was stimulated as a very young man by "[the family's] Methodist interest in social justice and race equality, and the family tradition of active concern with public problems.",13 and it was with these sentiments that he became a journalist. He soon became disillusioned: Journalism had seemed to offer both a means oflivelihood and an opportunity to stimulate proper action on public matters. Later I concluded that it had been overrated in both respects.14 Much of his disappointment stemmed from his inability to write sufficiently quickly and many of his pieces were not published due to their consequent lack of topicality. With the encouragement of one of the teachers at Washington, Eric Temple Bell, the great mathematician and historian of mathematics,ls Hotelling returned to the university on 1 January 1920 to study mathematics II This letter was written by Hotelling in answer to an enquiry from the University of Washington who were, at the time, seeking information on their celebrated alumni. 12 These autobiographical notes come from "Western Hotelling and Allied Families on Epic of Migration", an unpublished, undated, typescript Hotelling wrote which traces the history of his family and background. It is better described as a family history than as an autobiography of Harold Hotelling. 13 Hotelling was never an active church-goer; he was, however, a teetotaller and always looked unfavourably upon the consumption of alcohol. 14 Also quoted from "Western Hotelling ... ". 15 Bell is particularly well known for his work on the history of mathematics, notably his Men of Mathematics (1937).

Description:
In 1985 I first began my research on the life and work of Harold Hotel­ ling. That year, Harold Hotelling's widow had donated the collection of his private p:;tpers, correspondence and manuscripts to the Butler Library, Columbia University. This is a most appropriate place for them to reside, in th
See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.