Specifically, we discuss the two newly discovered scaling results that appear to be 'universal', in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent -4 extending over 102 standard deviations (a factor of 108 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2. Zajdenweber D., Equité et Jeu de Saint-Petersbourg. Not logged in pp 185-194 | doi = "10.1088/0953-8984/14/9/301". @article{9b6ffe8def2142d19a711aba121db443. N2 - This paper discusses some of the similarities between work being done by economists and by computational physicists seeking to contribute to economics. In particular, we review two such new results. Inequalities for Stochastic Processes ( Mc Graw Hill, New York, 1965 ). D) attributed to economies of scale. We use the terms scale and translation invariance throughout the paper to avoid any confusion with the relative ( r) and absolute ( a) measures of inequality of opportunity, which we will introduce in section2. Barton Ch. “Scale invariance” is not a common expression in economics, and expressions like “self similarity” or “self affinity” are scarcely used. adshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A © 2020 Springer Nature Switzerland AG. Isard W., Location and Space economy ( Wiley, New York, 1956 ). Scale invariance and universality in economic phenomena. Kolmogorov (Cambridge U. Press, 1995 ). journal = "Journal of Physics Condensed Matter", https://doi.org/10.1088/0953-8984/14/9/301. We discuss a curious 'symmetry breaking' for values of ∑ above a certain threshold value ∑c; here ∑ is defined to be the local first moment of the probability distribution of demand Ω-the difference between the number of shares traded in buyer-initiated and seller-initiated trades. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behaviour of the response function at the critical point (zero magnetic field) leads to large fluctuations. Gibrat R., Les Inégalités Economiques (Paris, 1930). We discuss a curious 'symmetry breaking' for values of ∑ above a certain threshold value ∑c; here ∑ is defined to be the local first moment of the probability distribution of demand Ω-the difference between the number of shares traded in buyer-initiated and seller-initiated trades. Cite as. Zipf G.K., Human Behavior and the Principle of Least Effort (Cambridge, Mass, 1949 ). tions on the utility function for scale invariance of the preference relation, which is a topic that is not treated here, and was dealt with in seminal work by Skiadas (2009 (Chapters 3 and 6), 2013); (ii) scale invariance of an optimality equation, in the form of a differential equation, which is … 1Scale invariant and translation invariant inequality measures are also known as relative and absolute inequal-ity measures respectively. I 3rd ed Ed. Dubins L.E. This famous sociologist and economist of the end of the XIXth century found numerous examples of power laws in income size-distributions [3]. We also introduce extensions of Benford’s Law beyond the rst digit phenomenon to calculating the empirical frequencies of the second, third, and any given digit or sequence of digits. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. Mandelbrot B., The Pareto Levy Law and the Distribution of Income. 2 H. E. Stanley*, L. A N Amaral, P. Gopikrishnan, V. Plerou, M. A. Salinger, Research output: Contribution to journal › Article › peer-review. By continuing you agree to the use of cookies. Recently, Dr Stanley and his collaborators have been exploring the degree to which scaling concepts give insight into economics and … Specifically, we discuss the two newly discovered scaling results that appear to be 'universal', in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent -4 extending over 102 standard deviations (a factor of 108 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2. display either one tail with a power law (for obvious reasons most economic size-distributions can only take a positive value) or two tails (all stock market prices, since they have positive and negative variations). Barton Ch. Specifically, we discuss the two newly discovered scaling results that appear to be 'universal', in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent -4 extending over 102 standard deviations (a factor of 108 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2.

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