An Analysis of Economic Size Distributions

117 Pages·1977·2.041 MB·English

by  Bertil Näslund (auth.)

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continuation on page 101
Lectu re Notes
in Economics and
Mathematical Systems
Managing Editors: M. Beckmann and H. P. Kunzi
143
Bertil Naslund
An Analysis of Economic
Size Distributions
Springer-Verlag
Berlin· Heidelberg· New York 1977
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
Bertil Naslund
The Stockholm School of Economics
Box 6501
S-113 83 Stockholm/Sweden
Library of Congress Cataloging in Publication Data
N~slund, Bertil, 1933-
An analysis of economic size distributions
D
(Lecture notes in economic and mathematical systems ;
143)
Bibliography: p.
1. Equilibrium (Economics) 2. Incame distribution.
3. Industries, Size of. I. Title. II. Series.
HB145.N3~ 330'.01'8 77-4270
AMS Subject Classifications (1970):
ISBN-13: 978-3-540-08142-5 e-ISBN-13: 978-3-642-95296-8
DOl: 10.1007/978-3-642-95296-8
This work is subject to copyright. All rights are reserved, whether the whole or
part of the material is concerned, specifically those of translation, reprinting,
re-use of illustrations, broadcasting, reproduction by photocopying machine or
similar means, and storage in data banks.
Under § 54 of the German Copyright Law where copies are made for other
than private use, a fee is payable to the publisher, the amount of the fee to
be determined by agreement with the publisher.
© by Springer-Verlag Berlin· Heidelberg 1977
To the stimulating maximizers of disorder
Erik, Karin and Robert
CONTENTS
PREFACE IX
BACKGROUND AND SUMMARY XI
CHAPTER 1 INTRODUCTION 1
1.1 The log normal distribution 2
1.2 The Pareto distribution 4
1.3 Randomness and economic markets •••••••..•..•.•••••••••...•.•• 6
1.4 A more precise presentation 10
1.5 The derivation of an equilibrium distribution by maximizing
entropy ••••....••••••••..••••••••••••.•••••••••••.•.•.•.•••• 12
1.6 Conclusions 16
PART 1 EQUILIBRIUM
CHAPTER 2 SOME EQUILIBRIUM CONDITIONS FOR STATISTICAL MARKETS 18
2.1 A formulation considering explicit market transactions 18
2.2 More general formulations . . . . . • • . • . • • • • . . . . • • . • • • . • • • • • • • • • • 23
2.2a Constrained maximization 23
2.2b Dividing society into systems 25
2.3 The information theory approach ••.••••.•.••••••••..••.•••••• 27
2.4 Conclusions 29
2.5 Appendix 29
CHAPTER 3 SIZE DISTRIBUTIONS OF INCOME 32
3.1 The consumption function 35
3.2 Empirical tests 36
3.3 Conclusions 42
VI
CHAPTER 4 THE FUNCTIONAL DISTRIBUTION OF INCOME 44
4.1 Neo-c1assical theory 44
4.2 Neo-Keynesian theory 46
4.3 Derivation of the functional distribution of income 47
4.4 Conclusions 50
GHAPTER 5 SIZE DISTRIBUTIONS AND THE OPTIMAL SIZE OF FIRMS 51
5.1 The theory of the firm and size distributions 51
5.2 Some basic facts about the method of analysis 54
5.3 The relation between profit and size 58
5.4 The Pareto distribution 59
5. 5 Some data 63
5.6 A relation between the size distributions of income and firms 65
5.7 Conclusions 66
PART 2 DISEQUILIBRIUM
CHAPTER 6 THE ANALYSIS OF DISEQUILIBRIUM MARKETS 69
6.1 The equilibrium situation 69
6.2 Disequilibrium 73
6.3 Conclusions 76
CHAPTER 7 ECONOMIC GROWTH AND DISTRIBUTION 77
7.1 The origin of growth 77
7.2 An assumption about the transfer of income 78
7.3 Conclusions 82
VII
CHAPTER B DISTRIBUTION - INFLATION - UNEMPLOYMENT B4
B.1 The background B4
B.2 Inflation and unemployment ....•••.••....•.......•.•....•.... B6
B.3 Concluding discussion B7
CHAPTER 9 FINAL REMARKS 9G
REFERENCES 92
PREFACE
The basic idea behind this book is that in a market economy there is
endless variety, people die and are born, new products and processes
emerge and old ones disappear etc. Some firms grow others decline.
Some people get high salaries others get unemployed. Opportunities,
disasters and capabilities are to a large extent random.
An economy has a certain amount of resources to divide among its members.
These resources may vary over time but the rate of change is fairly small.
The number of persons in society may also vary but the rate of change is
limited.
For a society such as the one described above I was interested in deriving
equilibrium distributions of various kinds and make some tests of the
distributions found against data for different countries. I have
studied the following types of distributions
a) Income distribution
b) Functional distribution of income
c) Size distributions of firms.
Since the above mentioned distributions are related; another main purpose
of the book has been to develop a similar method for the analysis of all
three distributions in order to simplify the understanding of their
relations.
The main purpose of the book is however to develop a framework for the
analysis of dis-equilibrium. Societies like the one described above are
often not·in equilibrium. Forces such as economic growth will - more or
x
less permanently - put the economy in a state of disequilibrium of a very
special form. Once the equilibrium situation is well understood it is
possible to extend the method of equilibrium analysis to disequilibrium.
My main motivation for deriving a method for more rigorous analysis of
disequilibrium was a hope to understand better the inflation-unemployment
dilemma.
This I hoped to achieve by starting from the type of society described in
the first paragraph but injecting an element of planning into it. Thereby
making it more similar to our western economies. A formal analys of these
economies requires a non-equilibrium analysis.
After an introductory chapte~ the book is divided in two parts. Part one
deals with the analysis of distributions at an equilibrium and begins
with a presentation of the methodology. Chapter 3 is devoted to the distri
bution of personal income. The results from chapter 3 are used in chapter 4
to derive the distribution of income between labor and capital. In chapter 5
size distributions of firms are analyzed and the relations between distri-,
butions of firms and of personal income are shown.
In Part two chapter 6 is devoted to the presentation of the methodology
for analyzing non~equilibrium distributions. In chapter 7 the method is
used to show the effect of economic growth on income distribution and in
chapter 8 relations between inflation, growth and unemployment are shown
using the method derived in chapter 6. Chapter 9 is devoted to some final
conclusions.
The work has been financed by a grant from Sparbankernas Forskningsstiftelse
and Statens Rad for Samhallsforskning.
BACKGROUND AND SUMMARY
Background
The origin of a more rigorous treatment of distribution is due to
Ricardo. He explained distribution in society mainly by using two
mechanisms
(1) Wages were kept at sUbsistence level
(2) The rent was determined by the difference between the
average productivity and marginal productivity of land
(3) The return on capital is a residue. The total result
from production is given to labor and landowners according
to (1) and (2) and what is left goes to capital.
The introduction of marginal utility due to Jevons diverted the
interest from social classes and gave the treatment of the economy an
atomistic character. Everybody was endowed with preferences and pro
ductive capacity and no social classes were seen. However, for
distribution theory the embarrasing fact which always plagued this
theory was that in order for distribution to be determined by a pricing
process within a market, one had to postulate some pre-existing income
distribution before the exchange began which was not a very satisfactory
state of affairs.
The distribution of income according to the neo-classical doctrine
became determined by the marginal productivity of labor and capital.
Thus the idea of marginal productivity was taken over from Ricardo but
it was to be applied not only to resources given by nature but also to
something called capital created and constructed by man. This doctrine