L-stability and multiplicative variation of income

  • Benoit B. Mandelbrot


This paper describes a theory of the stationary stochastic variation of income based on a new family of nonGaussian random functions, U ( t). This approach is intimately connected with random walks of log U(t), but no use is made of the “principle of proportionate effect.” Instead, the model is based upon the fact that there exist limits for sums of random functions, in which the effect of chance in time is multiplicative. This feature provides a new type of motivation for the widespread, convenient, and frequently fruitful use of the logarithm of income, considered as a “moral wealth.”

I believe that these new stochastic processes will play in linear economics, for example in certain problems of aggregation. The reader will fine that the results are easily rephrased in terms of diverse economic quantities other than income. As a result, the tools to be introduced may be as important as the immediate results to be achieved. In particular, the distribution and variation of city sizes raises very similar problems.


Random Walk Main Diagonal Aggregate Income Stable Sequence Asymptotic Scaling 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Benoit B. Mandelbrot
    • 1
  1. 1.Mathematics DepartmentYale UniversityNew HavenUSA

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