2003/01 LEM Working Paper Series

Maximum Entropy Power Laws: An Application to the Tail of Wealth Distributions
Mishael Milakovic'
Wealth distribution, power laws, statistical equilibrium, maximum entropy.

  JEL Classification:
C60, D31, E10.

Statistical equilibrium denotes the distribution of wealth that can beachieved in the largest number of ways while satisfying a firstmoment constraint on the rate of growth in wealth portfolios. Maximizing entropy subject to a logarithmic constraintyields a power law distribution whose characteristic exponentdepends positively on the minimum wealth level, and inversely onthe rate of growth and the average number of changes in thecomposition of wealth portfolios. Put differently, the distribution ofwealth will be more unequal the faster the rate of growth inwealth and also the higher the number of turnovers.

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