Power laws of wealth, market order volumes and market returns

Using the Generalized Lotka Volterra model adapted to deal with mutiagent s ystems we can investigate economic systems from a general viewpoint and obt ain generic features common to most economies. Assuming only weak generic a ssumptions on capital dynamics, we are able to obtain very specific predict ions for the distribution of social wealth. First, we show that in a 'fair' market. the wealth distribution among individual investors fulfills a powe r law. We then argue that 'fair play' for capital and minimal socio-biologi cal needs of the humans traps the economy within a power law wealth distrib ution with a particular Pareto exponent alpha similar to 3/2. In particular , we relate it to the average number of individuals L depending on the aver age wealth: alpha similar to L/(L - 1). Then we connect it to certain power exponents characterizing the stock markets. We find that the distribution of volumes of the individual (buy and sell) orders follows a power law with similar exponent beta similar to alpha - 3/2. Consequently, in a market wh ere trades take place by matching pairs of such sell and buy orders, the co rresponding exponent for the market returns is expected to be of order gamm a similar to 2 alpha similar to 3. These results are consistent with recent experimental measurements of these power law exponents (S. Maslov, M. Mill s, Physica A 299 (2001) 234 for beta; P. Gopikrishnan et al., Phys. Rev. E 60 (1999) 5305 for gamma). (C) 2001 Elsevier Science B.V. All rights reserv ed,