Introduction to Modern Austrian Capital Theory

204 Pages·1979·7.752 MB·English

by  Prof. Dr. Malte Faber (auth.)

Lectu re Notes
in Economics and
Mathematical Systems
Managing Editors: M. Beckmann and H. P. KUnzi
Mathematical Economics
167
Malte Faber
Introduction to
Modern Austrian Capital Theory
Springer-Verlag
Berlin Heidelberg New York 1979
Editorial Board
H. Albach· A. V. Balakrishnan' M. Beckmann (Managing Editor)
p. Dhrymes . J. Green' W. Hildenbrand' W. Krelle
H. P. Kunzi (Managing Editor) . K. Ritter' R. Sato . H. Schelbert
p. Schonfeld
Managing Editors
Prof. Dr. M. Beckmann Prof. Dr. H. P. Kunzi
Brown University Universitat Zurich
Providence, RI 02912/USA 8090 Zurich/Schweiz
Author
Prof. Dr. Malte Faber
Alfred-Weber-Institut
der Universitat Heidelberg
Seminargebaude
Grabengasse 14
6900 Heidelberg/FRG
AMS Subject Classifications (1970): 90-02, 90A99
ISBN-13: 978-3-540-09121-9 e-ISBN-13: 978-3-642-48310-3
001: 10.1007/978-3-642-48310-3
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© by Springer-Verlag Berlin Heidelberg 1979
2142/3140-543210
To
Peter Bernholz
mentor and friend
Preface
During the fifties and the sixties the neoclassical concept of the
production function was criticized in numerous papers. In particular,
the aggregation of different capital goods into a single number was
reprehended. A second essential disadvantage, namely the neglect of
the time structure of the production process, found, however, rela
tively little attention.
While up to the thirties the Austrian capital theory which stressed
the time aspect of production was an important school, it fell into
oblivion after the great capital controversies of the thirties. It
took over thirty years, i.e. till the beginning of the seventies be
fore it came to a renaissance of the Austrian capital theory by var
ious writers. We may roughly classify the different attempts of Hits
rebirth in modern economics" into three groups:
1. The approach of ~ [1970, 1973, 1973a] has received most of
the attention in the literature (Burmeister [1974], Faber [1975],
Fehl [1975], ~[1975], Hagemann and ~ [1976]). It will be
shown in Chapter 9 that ~ is only in so far a Neo-Austrian as
he does explicitly take into consideration the vertical time
structure of the production process. But he does not use the
Austrian concepts of superiority of roundabout methods, of time
preference and of the period of production.
2. The latter concept has been revived by the second group, to which
Tintner [1970], von Weizs~cker [1971a, 1971b, 1974], ~ [1971,
1976 and ~ [1973, 1975, 1976] belong. The discussion of the
thirties mentioned above, however, showed that the period of pro
duction is a dubious tool for the analysis of problems of capital
theory (see e.g. Morgenstern [1935]).
3. The authors forming the third group try to employ the concepts of
superiority of roundabout methods and of time preference to prove
that the rate of interest is positive. Jaksch [1975a, 1975b]
shows in a linear multiperiod multisector model that investment
implies a positive rate of interest under certain rather strong
conditions. In contrast to ~, Bernholz [1971] started with
a linear two-period two-sector model which has successively been
extended by Bernholz and the present writer in a series of papers
during the last seven years. In addition we have tried to relate
our neo-Austrian approach to the Marxian labor theory of value,
the von Neumann-model, neoclassical growth theory and Hicks'
neo-Austrian theory of capital.
VI
Bernholz [1971] began with a rather intuitive concept of superiority
of roundabout methods, which we grad~ally deve19ped into a rigorous
form. Since we broke, in some respects, new ground, it is not surpris
ing that some readers had difficulties to understand our papers. Of
course, these were aggravated by the fact that we continuously changed
our definitions and notations. The present author, therefore, thought
it to be appropriate to unify our papers and to supplement several
missing links in such a way that our approach is accessibl~ in the
form of a text-book. A further reason for the publication of this
volume was that some of the relevant material was only accessi~le to
German speaking readers.
After the introduction, von Bohm-Bawerk's theory of capital and
interest is presented. For this purpose I use the interpretations by
Wicksell [1893], Dorfman [1958/59, 1959] and ~ [1967]. To my mind,
the further development of the traditional Austrian capital theory is
best stated by a presentation of an article by von Stackelberg [1941/
43], which at the same time may be considered a temporary termination
of this school of thought. Von Stackelberg develops four models, in
which not only the questions put forward by Wicksell and Akerman are
examined, but the problem of recycling (Rtickversetzung) of goods is
analyzed as well. Since von Stackelberg's important contribution is
entirely unknown in the English literature (the same is almost true
for the German one), I have presented it in detail. A critical assess
ment of the traditional Austrian theory of capital and interest closes
Chapter 2. The von Neumann-model is described in Chapter 3. Special
emphasis is put on its assumptions and its economic interpretation.
It will be shown that von Neumann's approach already indicated a way
out of the dead-ends in which the Austrian capital and interest theory
found itself at the end of the thirties. Having set the stage in Part
I, it is demonstrated in Part II how the law of greater productivity
of roundabout production can be introduced in a modified special case
of the generalized von Neumann-model, namely a generalized Leontief
technology. In Chapter 4 a two-period two-sector model is employed
to introduce the ideas of our neo-Austrian approach: the model is
extended to n periods in Chapter 5. It is generalized to a multi
sector model in Chapter 6, however, with the restriction that there
is an economic horizon of only two periods. (Work is in progress to
generalize it: see ~ [1978]). While the production programs are
not restricted to the class of proportional ones (steady states) in
Chapter 4 to 6, they are restricted to stationary programs in Chapter
7, where I take up the famous controversy between von Bohm-Bawerk and
VII
schumpeter on the zero rate of interest in a stationary economy.
Some relationships between other approaches to capital theory and ours
are shown in Part III. The neoclassical steady state theory is dealt
with in Chapter 8 and Hicks' approach in Chapter 9.
Bernholz and myself [1971, 197~] have also related our approach to
the labor theory of value. Since Bernholz [1972, Chapter 3, pp.85-95]
has already treated this subject in a text-book and since there has
been a voluminous literature on the labor theory of value\during the
last decade, it did not seem to be necessary to deal with it once
again.
The absence of a discussion of the Cambria!e U.K. theory of capital
explains itself quite different. I accept it to be a deficiency of
this book and can only apologize for this with the proverb that "Rome
was not built in a day." Perhaps I have also been influenced by
a letter from Professor Joan Robinson in which she wrote to me:
"I am afraid it is a hopeless task to reconcile the Sraffa system with
BOhm-Bawerk because they take different views of the operation of the
capitalist system." I, however, am not quite so pessimistic in that
respect, since there seems to be a relationship between Sraffa's and
our approach via the von Neumann-model' (see Burmeis'ter [1974] and
Schefold [1978]).
The manuscript for this book was used for a course at the Univer
sity of Heidelberg in winter-semester 1977/78. Thus the problems at
the end of each chapter have been tested. The students were in the
'Hauptstudium', i.e. senior undergraduate level and first year gradu
ate students. Though mathematical requirements consist only of an
elementary form of the Kuhn-Tucker conditions and ~'s rule, the
reading of this book is in some passages demanding. This holds for
Chapter 5, especially Section 5.3, and in particular for Chapter 6,
the multisector model. Some students told me that it helped them to
start Part II with Chapter 7.
Throughout this volume I have tried to make the assumptions, defini
tions and propositions of all models explicit to enable the reader to
compare the models more easily. I also took pains to avoid phrases
like "it is easily seen';" nas the reader finds after several transfor
mations." Some readers, therefore, may find some derivations too
lengthy.
There are many persons to whom I am indebted. I hope that the ded
ication of this book gives the reader an impression how much lowe to
Peter Bernholz. As stated above, his 1971 paper gave rise to our
VIII
collaboration. A rendition of this article is presented in Chapter 4.
A comparison of this chapter with the following three chapters of
Part II shows how much it influenced our later research. It should,
however, be mentioned that Peter Bernholz has actually continued his
earlier research on Austrian capital theory in 1971, since he wrote
his dissertation on the law of greater productivity of roundabout
methods in 1955 and two papers on impatience to consume in 1964 and
1965. Besides Peter Bernholz I would like to thank also my co-authors
Johann Irsigler, Winfried Reiss, and Gunther Stephan for letting me
use material from previously published joint articles. Furthe~ I am
grateful to Klaus Jaeger [1974], Hans Jurgen Jaksch [1975a] and 2£!
Schweizer [1978], who took up in one form or the other papers by ~
holz and me. Their valuable criticisms and constructive suggestions
helped and stimulated us in many respects.
I am also grateful to my students, in particular to my English
speaking ones, Grover Mc Arthur and Anthony Sagoe, who corrected my
English; Gregory Capellari translated the second and third chapters
into English.
My assistants Friedrich Breyer, Alexander Gerybadze, Johann Irsig
l!E, Gerhard Pross, Winfried Reiss supported me in various ways to
prepare the manuscript. Johann Irsigler helped to formulate the prob
lems at the end of each chapter. Friedrich Breyer and Johann Irsigler
carefully read three versions of the manuscript, which led to a con
siderable mathematical, economic and stylistic improvement. Joachim
Weisbrod proofread the whole manuscript. Of course, I assume full
responsibility for any remaining errors.
Thanks are due to Wolfgang KBstlin, who enabled me in various ways
to spend more time on capital theory than would have been possible
without his help.
I gratefully acknowledge the permission of the publishers of Kyklos,
Zeitschrift fUr die gesamte Staatswissenschaft and Journal of Economic
Theory for letting me use material previously published.
Finally I thank Hanna Streubel for her accurate and most of all
patient typing of various versions of the manuscript.
Con ten t s
PART I: AUSTRIAN CAPITAL THEORY AND THE VON NEUMANN-MODEL
1. Introduction 3
1.1 Problems 7
2. The Austrian Theory of Interest 10
2.1 von B5hm-Bawerk 10
2.2 von Stackelberg 20
2.3 An Assessment of Austrian Interest Theory 29
2.4 Problems 34
3. The von Neumann-Model and its Relations to Austrian
Capital and Interest Theory 38
3.1 Introduction 38
3.2 The Meaning, Import and Historical Point of
Departure of the Ideas of the von Neumann-Model 38
3.3 The von Neumann-Model 40
3.4 Criticism and Generalization of the von Neumann_
Model 51
3.5 Solutions to Problems of Austrian Capital
Theory 53
3.6 The Interest Rate in the Stationary State 55
3.7 Problems 56
PART II: MODERN AUSTRIAN CAPITAL THEORY
4. A Two-Period Two-Sector Neo-Austrian Model 61
4.1 Outline of the Procedure 61
4.2 The Technology 61
4.3 The Transformation Curve 64
4.4 Condition for Roundaboutness 70
4.5 Condition for Superiority 71
4.6 Prices in a Planned Economy 73
4.7 The Rate of Interest in a Planned Economy 77
4.8 Decentralizing the Decisions 85
4.9 Problems 87
5. A Multiperiod Two-Sector Model 90
5.1 Extension of the Model 90
5.2 A Model with n-Period Horizon 90
5.3 A Model with Two Techniques Using a Capital Good 98
5.3.1 The Model 98
x
5.3.2 The Sign of the Rate of Interest 104
5.4 Problems 109
6. A Multisector Model 111
6.1 The Problem and the Main Results 111
6.2 The Model 113
6.3 Superiority, Roundaboutness and Positive Rate
117
of Interest
6.4 A Finite Economic Horizon with More than ~wo
Periods 128
129
6.5 Problems
7. The Schumpeter-von Bohm-Bawerk Controversy on the
Rate of Interest in the Stationary State 131
131
7.1 Introduction
7.2 The Origins of the Controversy 133
135
7.3 The Rate of Interest in a Stationary State
140
7.4 Schumpeter's Dynamic Theory of Interest
142
7.5 Problems
PART III: RELATIONSHIP TO OTHER APPROACHES TO CAPITAL THEORY
8. A Comparison with Results of Neoclassical Capital and
Growth Theory 145
8.1 Introduction 145
8.2 A Simple Growth Model 145
8.3 A Neoclassical Version for Steady States 150
8.3.1 Factor-Price Frontier for T~ and T~ 150
8.3.2 Factor-Price Frontier for Tl and T2 154
8.3.3 Consumption-Growth Frontier 155
8.3.4 The Relationship between the Interest Rate
and the Growth Rate 157
8.4 Charcteristics of Optimal Steady State Programs 159
8.5 Problems 163
9. Hicks' Neo-Austrian Theory of Capital 164
9.1 Introduction 164
9.2 Hicks' Model 166
9.3 The Index of Improvement in Efficiency 168
9.4 Hicks' New Classification of Technological
Change 169
9.5 Superiority and the Index of Efficiency 174
9.6 Concluding Remarks 178
9.7 Problems 179
References 181
Author Index 192
Subject Index 194
Part I:
AUSTRIAN CAPITAL THEORY AND THE
VON NEUMANN-MODEL