Full text: Size Distributions in Economics

SIZE DISTRIBUTIONS IN ECONOMICS 999 
paths depending on age of firm, age of equipment, 
age of the management, etc.). For example, the 
short-run and long-run cost curves are inevitably 
mixed up in a cross section of firms. [See Cross- 
section analysis.] 
How much “stability” and why. The starting 
point of the theories here reviewed is the stability 
of distributions, but stability must not be taken 
literally. The distributions do change in time, but 
the change is usually slow. The tail of the distribu 
tion of firms or, to a lesser extent, of wealth is 
composed of very old units, and time must pass 
before it can be affected by, for example, a change 
in new entry rates or in growth rates of firms. 
Thus, the reason for the quasi stability of distribu 
tions is that the stock of firms, etc., revolves only 
slowly. Indirectly this also accounts for the quasi 
stability of the distribution of incomes, because in 
come is largely determined by wealth or its equiva 
lent in the form of education. An even more 
enduring influence on the income distribution is 
the differentiation of skills and professions, which 
evolves slowly, as a secular process. 
The explanations advanced in this article do not 
exclude the possibility that distribution patterns 
may change abruptly—for example, as a conse 
quence of taxation, in the case of net incomes; or 
as a consequence of a big merger movement, in 
the case of firms. 
Josef Steindl 
[Directly related is the entry Rank-size relations. 
See also Lebergott 1968.] 
bibliography 
►Allais, Maurice 1968 Pareto, Vilfredo: I. Contribu 
tions to Economics. Volume 11, pages 399-411 in In 
ternationa/ Encyclopedia of the Social Sciences. Edited 
by David L. Sills. New York: Macmillan and Free 
Press. 
Champernowne, D. G. 1953 A Model of Income Distri 
bution. Economic Journal 63:318-351. 
Frechet, Maurice 1939 Sur les formules de repartition 
des revenus. International Statistical Institute, Revue 
7:32-38. 
Gibrat, Robert 1931 Les inegalites economiques. Paris: 
Sirey. 
Ijiri, Yuji; and Simon, Herbert A. 1964 Business 
Firm Growth and Size. American Economic Review 
54:77-89. 
Kalecki, Michael 1945 On the Gibrat Distribution. 
Econometrica 13:161-170. 
►Lebergott, Stanley 1968 Income Distribution: II. 
Size. Volume 7, pages 145-154 in International En 
cyclopedia of the Social Sciences. Edited by David L. 
Sills. New York: Macmillan and Free Press. 
Mansfield, Edwin 1962 Entry, Gibrat’s Law, Innova 
tion, and the Growth of Firms. American Economic 
Review 52:1023-1051. 
Rutherford, R. S. G. 1955 Income Distributions: A 
New Model. Econometrica 23:277-294. 
Simon, Herbert A. (1955) 1957 On a Class of Skew 
Distribution Functions. Pages 145-164 in Herbert 
A. Simon, Models of Man: Social and Rational. New 
York: Wiley. -» First published in Volume 42 of 
Biometrika. 
Simon, Herbert A.; and Bonini, Charles P. 1958 The 
Size Distribution of Business Firms. American Eco 
nomic Review 48:607-617. 
Steindl, Josef 1965 Random Processes and the Growth 
of Firms: A Study of the Pareto Law. London: Griffin; 
New York: Hafner. 
Wold, H. O. A.; and Whittle, P. 1957 A Model Ex 
ploring the Pareto Distribution of Wealth. Econo 
metrica 25:591-595. 
Zipf, George K. 1949 Human Behavior and the Prin 
ciple of Least Effort: An Introduction to Human 
Ecology. Reading, Mass.: Addison-Wesley. 
Postscript 
The diffusion process assumed in some of the 
above models has been studied directly on the basis 
of individualized data for German retail firms 
(Steindl 1965) but more recently also for Austrian 
manufacturing firms (Steindl 1972a). The variance 
of the logarithm of sales is shown to increase with 
time at a rate that is different in different industries. 
The question arises whether this diffusion constant 
has an economic meaning; it is tentatively sug 
gested that it might be regarded, in some sense, as 
a measure of the “dynamics” of an industry (tech 
nological change in the widest sense, with resulting 
competition). 
Wold and Whittle’s model of wealth distribution 
has been reformulated by Steindl (1972b) using 
an age-dependent branching process. The Pareto 
coefficient of wealth distribution is seen to depend 
on the speed of accumulation over the generations 
within a wealth dynasty, and on the rate at which 
new wealth dynasties appear. 
It is noted that a constant Pareto coefficient is 
compatible with growing concentration of wealth 
in a few hands, if the sample of wealth holders 
grows in time, and wealth sizes, which before were 
mere theoretical possibilities, become actualized. 
Josef Steindl 
ADDITIONAL BIBLIOGRAPHY 
^/Champernowne, D. G. 1973 The Distribution of In 
come Between Persons. New York: Cambridge Univ. 
Press. 
Ijiri, Yuji; and Simon, Herbert A. 1967 A Model of 
Business Firm Growth. Econometrica 35:348-355. 
j Ijiri, Yuji; and Simon, Herbert A. 1971 Effects of 
Mergers and Acquisitions on Business Firm Concen 
tration. Journal of Political Economy 74:314-322.
	        

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