  We provide an exact solution to the ideal-gas-like models studied in
econophysics to understand the microscopic origin of Pareto-law. In these class
of models the key ingredient necessary for having a self-organized scale-free
steady-state distribution is the trading or collision rule where agents or
particles save a definite fraction of their wealth or energy and invests the
rest for trading. Using a Gibbs ensemble approach we could obtain the exact
distribution of wealth in this model. Moreover we show that in this model (a)
good savers are always rich and (b) every agent poor or rich invests the same
amount for trading. Nonlinear trading rules could alter the generic scenario
observed here.
