Table Of ContentTheory and Applications of
ECONOMIC INDICES
Proceedings of an International Symposium
Held at the University of Karlsruhe April-June 1976
Edited by
W. Eichhorn, R. Henn, 0. Opitz, R.W. Shephard
at the Universities of Karlsruhe and Berkeley
Springer-Verlag
Berlin Heidelberg GmbH
1978
ClP-Kurztitelaufnahme der Deutschen Bibliothek
Theory and applications of economic indices:
proceedings of an internat. symposium held at the
L"niv. of Karlsruhe. April June 1976 I ed. by
W. Eichhorn . . . -Wlirzburg, Vienna : Physica
Verlag. 1978.
:\L bchhorn. Wolfgang [Hrsg.]; Universit<it
Karlsruhe>
This hook. or parts thereof, may not be translated or reproduced in any form
without written permission of the publisher
ISBN 978-3-7908-0191-0 ISBN 978-3-662-41486-6 (eBook)
DOI l 0.1007/978-3-662-41486-6
© Springer-Verlag Berlin Heidelberg 1978
Originally published by Physica-Verlag, RudelfLiebing GmbH+ Co., Wurzburg in 1978.
Preface
An international symposium on economic indices was held at
the University of Karlsruhe April, May, and June of 1976, invol
ving participants from Belgium, Canada, Finland, Great Britain,
Luxembourg,Sweden, Switzerland, and the USA. Also many partici
pants from German universities and other German institutions made
contributions. Karlsruhe supplied the predominant part of the
German contributors.
This symposium was a follow-on of a similar symposium held
during May, June, and July of 1973 on production theory, stimu
lated by the results there obtained. (The proceedings of the
1973 symposium were published under the title PRODUCTION THEORY,
with the same editors, by Springer-Verlag, Berlin-Heidelberg-
New York 1974, Lecture Notes in Economics and Mathematical Systems,
Vol. 99).
For the discussions of the seminar 32 papers spanning a large
part of the field of economic indices were presented and these
papers are herewith published as a coherent collection under the
title: THEORY AND APPLICATIONS OF ECONOMIC INDICES.
Part I on methodological topics contains three papers in
volving an axiomatic foundation for economic indices, the rela
tionship of cluster analysis to the theory of economic indices
and a philosophcal discussion of object and number logic for
price indices.
Part II on price indices contains several papers with an axio
matic approach to various issues in the formation of price indi
ces, and papers dealing with cost of living indices, purchasing
power parity methods, comparisons of price indices, stochastic
and dynamic price indices, and a paper on an extension of Gorman's
price aggregation theorem.
III
Part III on other economic indices contains a paper on a
true wage index as kind of a counterpart to the true cost of
living index, a treatment of indices of income inequality, a
paper on indices of preference inequality, an application of a
new definition of the degree of monopoly, a treatment of a
household production function as a measure of satisfaction, a
dynamic formulation of indices for the theory of cost and pro
duction, a treatment of index properties of ray-homothetic
dynamic production structures and a paper considering the sensi
tivity of key sector indices.
Part IV on topics related to economic indices contains a
variety of papers, which include problems of aggregation in
various fields of research and an investigation of neutral changes
in utility and tastes which is useful for defining both taste
dependent true cost of living indices and wage indices.
It is interesting that nearly one half of the 32 papers
deal with or contain functional equations or systems of them,
pointing perhaps to new roles of mathematics in index number
theory.
We take this opportunity to acknowledge indebtedness to
Stiftung Volkswagenwerk (Volkswagen Foundation) for financial
means to carry out the symposium, and express our sincere appre
ciation for this support.
Karlsruhe and Berkeley W. Eichhorn, R. Henn,
October 1977 0. Opitz, R.W. Shephard
Editors
IV
TABLE OF CONTENTS
List of Contributors . VIII
PART I
Methodological Topics Concerning
Economic Indices
EICHHORN, W.: What is an Economic Index?
An Attempt of an Answer . . 3
MENGES, G.: Semantics and "Object Logic" of
Price Indices . . 43
OPITZ, 0.: On the Relationship Between Numerical
Taxonomy and the Theory of Economic Indices . 55
PART II
Price Indices
AFRIAT, S.N.: On Wald's "New Formula"for the
Cost of Living . . . . ... 67
BLACKORBY, Ch., PRIMONT, D., and R.R. RUSSELL: An
Extension and Alternative Proof of Gorman's Price
Aggregation Theorem 109
DIEHL, H.: Examination of Purchasing-Power-Parity
Methods with a View to Choosing the Most Appropriate
Method for a European-Community Purchasing-Power-
Parity Model 143
FUCHS-SELIGER, S.: Revealed Preference and the
Economic Theory of Index Numbers 161
FUNKE, H. and J. VOELLER: A Note on the Characterization
of Fisher's "Ideal Index" . 177
GEHRIG, W.: Price Indices and Generalized
Associativity . 183
v
HASENKAMP, G.: Economic and Atomistic Index
Numbers: Contrasts and Similarities .•• 207
HILD, C., and G. HACKER: A Note on Criteria
for Price Index Systems • . . . . • . . • 245
MUNDLOS, B., and J. SCHWARZE: Basic Ideas on
Stochastic Indices . . . 257
VARTIA, Y.O.: Fisher's Five Tines Fork and Other
Quantum Theories of Index Numbers . 271
VOGT, A.: Divisa Indices on Different Paths . • . • . . • . 297
PART III
Other Economic Indices
BURK, R., and W. GEHRIG: Indices of Income
Inequality and Societal Income. An Axiomatic
Approach . . . . . . . . . . . . . . . . 309
F~RE, R.: Separability and Index Properties of
Ray-Homothetic Dynamic Production Structures 357
HECKER, R.: A System of Indices for the External
Analysis of the Earning Capacity Standard and
Financial Power of Industrial Joint Stock Companies . . . 381
KOGELSCHATZ, H., and B. GOLDSTEIN: On the Sensitivity
of Key Sector Indices . . . • . . . • . . . . . . . 389
PHLIPS, L.: A Taste-Dependent True Wage Index . 401
SHEPHARD, R.W.: A Dynamic Formulation of Index
Functions for the Theory of Cost and Production 417
SHEPHARD, R.W.: On Household Production Theory .. 449
SPREMANN, K.: The Degree of Monopoly and Multivariable
Sales Policies . . . . • . . . . . . . . . . 487
STEHLING, F.: Indices of Preference Inequality and
the Construction of Social Preference Relations 535
PART IV
Topics Related to Economic Indices
ACZEL, J.: Some Recent Applications of Functional
Equations to Cornbinatorics, Probability Distributions,
Information Measures and to the Theory of Index
Numbers in Mathematical Economics . . • . . . . . . . . 565
BECKMANN, M.J.: Neutral Changes in Tastes
and Utility ...•....•. 591
BERTSCH, K.-H.: Some Considerations on Related
Discrete and Continuous Dynamic Economic Models 599
CONRAD, C.: Dynamic Utility and Aggregator Functions
for the Allocation of Private Consumption in Input-
Output-Models; An Econometric Analysis . • . . • 623
FARE, R.: Production Theory Dualities for Optimally
Realized Values . . . . • . . . . • . . • • 657
HARTTER, E.: Linear Models with Variable Coefficients 667
POKROPP, F.: Aggregation of Substitutional Production
Functions by Functional Equation Methods . . • • . 683
REEH, K.: On the Problem of Using Aggregate Predictions. . . 703
UEBE, G.: On a Flexibility Theorem of Diewert ....•.. 719
Author Index 731
Subject Index 739
VII
List of Contributors
J. ACZEL, Faculty of Mathematics, University of Waterloo,
Waterloo, Ontario, Canada.
S.N. AFRIAT, Department of Economics, University of
Ottawa, Ottawa, Ontario, Canada K1N 6N5.
MARTIN J. BECKMANN, Department of Economics, Brown
University, Providence, Rhode Island, 02912, U.S.A.,
and: Institut flir Angewandte Mathematik, Technische
Universitat Mlinchen, D-8000 Mlinchen, Germany.
KARL-HEINZ BERTSCH, Fachbereich Rechts- und Wirtschafts
wissenschaften, Universitat Mainz, D-6500 Mainz,
Federal Republic of Germany.
CHARLES BLACKORBY, Department of Economics, University of
British Columbia, British Columbia, Canada V6T 1W5.
RALPH BURK, Institut flir Wirtschaftstheorie und Operations
Research, Universitat Karlsruhe, D-7500 Karlsruhe,
Federal Republic of Germany.
KLAUS CONRAD, Sonderforschungsbereich 21, Universitat
Bonn, D-5300 Bonn, Federal Republic of Germany.
HELMUT DIEHL, Office Statistique des Communaut~s Europeennes,
Boite Postale 1907, Luxembourg.
WOLFGANG EICHHORN, Institut flir Wirtschaftstheorie und Operations
Research, Universitat Karlsruhe, D-7500 Karlsruhe,
Federal Republic of Germany.
ROLF FARE, Department of Economics, University of Lund,
S-22005 Lund 5, Sweden.
SUSANNE FUCHS-SELIGER, Institut flir Wirtschaftstheorie und
Operations Research, Universitat Karlsruhe, D-7500 Karlsruhe,
Federal Republic of Germany.
HELMUT FUNKE, Institut flir Wirtschaftstheorie und Operations
Reserach, Oniversitat Karlsruhe, D-7500 Karlsruhe,
Federal Republic of Germany.
WILHELM GEHRIG, Institut flir Wirtschaftstheorie und Operations
Research, Universitat Karlsruhe, D-7500 Karlsruhe,
Federal Republic of Germany.
VIII
BERND GOLDSTEIN, Lehrstuhl fur Statistik und 5konometrie,
Gesamthochschule Siegen, D-5900 Siegen, Federal Republic
of Germany.
GUNTER HACKER, Institut fur Wirtschaftstheorie und Operations
Research, Universitat Karlsruhe, D-7500 Karlsruhe,
Federal Republic of Germany.
ERICH HARTTER, Fachbereich Rechts- und Wirtschaftswissen
schaften, Universitat Mainz, D-6500 Mainz, Federal Republic
of Germany.
GEORG HASENKAMP, Sonderforschungsbereich 21, Universitat
Bonn, D-5300 Bonn, Federal Republic of Germany.
RAINER HECKER, Philips GmbH, Apparatefabrik Krefeld,
D-4150 Krefeld 12, Federal Republic of Germany.
CLAUS HILD, Lehrstuhlfur Statistik und 5konometrie, Gesamt
hochschule Siegen, D-5900 Siegen, Federal Republic of
Germany.
HARTMUT KOGELSCHATZ, Institut flir Statistik und Mathematische
Wirtschaftstheorie, Universitat Karlsruhe, D-7500 Karlsruhe,
Federal Republic of Germany.
GUNTER MENGES, Lehrstuhl fur Wirtschafts- und Sozialstatistik,
Universitat He~delberg, D-6900 Heidelberg, Federal Republic
of Germany.
BERND MUNDLOS, Lehrstuhl fur Statistik und 5konometrie, Techni
sche Universitat Braunschweig, D-3300 Braunschweig, Federal
Republic of Germany.
OTTO OPITZ, Institut fur Entscheidungstheorie und Unternehmens
forschung, Universitat Karlsruhe, D-7500 Karlsruhe, Federal
Republic of Germany.
LOUIS PHLIPS, Center for Operations Research and Econometrics,
Universite Catholique de Louvain, B-1348 Louvain-La-Neuve,
Belgium.
FRITZ POKROPP, Institut flir Statistik und 5konometrie,
Universitat Hamburg, D-2000 Hamburg 13, Federal Republic of
Germany.
DANIEL PRIMONT, Department of Economics, University of Massa
chusetts, Boston, Massachusetts, U.S.A.
KLAUS REEH, Seminar fur 5konometrie und Statistik der Universitat
Mlinchen, D-8000 Mlinchen 22, Federal Republic of Germany.
R. ROBERT RUSSELL, Department of Economics, University of
California, San Diego, La Jolla, California 92093, U.S.A.
IX
