  The dynamics of generalized Lotka-Volterra systems is studied by theoretical
techniques and computer simulations. These systems describe the time evolution
of the wealth distribution of individuals in a society, as well as of the
market values of firms in the stock market. The individual wealths or market
values are given by a set of time dependent variables $w_i$, $i=1,...N$. The
equations include a stochastic autocatalytic term (representing investments), a
drift term (representing social security payments) and a time dependent
saturation term (due to the finite size of the economy). The $w_i$'s turn out
to exhibit a power-law distribution of the form $P(w) \sim w^{-1-\alpha}$. It
is shown analytically that the exponent $\alpha$ can be expressed as a function
of one parameter, which is the ratio between the constant drift component
(social security) and the fluctuating component (investments). This result
provides a link between the lower and upper cutoffs of this distribution,
namely between the resources available to the poorest and those available to
the richest in a given society. The value of $\alpha$ %as well as the position
of the lower cutoff is found to be insensitive to variations in the saturation
term, that represent the expansion or contraction of the economy. The results
are of much relevance to empirical studies that show that the distribution of
the individual wealth in different countries during different periods in the
20th century has followed a power-law distribution with $1 < \alpha < 2$.
