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
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Frechet, Maurice 1939 Sur les formules de repartition
des revenus. International Statistical Institute, Revue
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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
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Review 52:1023-1051.
Rutherford, R. S. G. 1955 Income Distributions: A
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Biometrika.
Simon, Herbert A.; and Bonini, Charles P. 1958 The
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Steindl, Josef 1965 Random Processes and the Growth
of Firms: A Study of the Pareto Law. London: Griffin;
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Wold, H. O. A.; and Whittle, P. 1957 A Model Ex
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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.