The Collected Economics Articles of Harold Hotelling

186 Pages·1990·14.54 MB·English

by  Adrian C. Darnell (auth.)

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
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Typeset by Asco Trade Typesetting Ltd., Hong Kong.
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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comprises some 13,000 separate items and contains numerous unpublished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).