Trading leads to scale-free self-organization

► We study the simplest market model incorporating standard folklore on price formation. ► Trading inherently leads to instability of prices. ► The market self-organizes into a Pareto wealth distribution. ► The market self-organizes into a scale-free volume distribution concomitant with non-Gaussian price fluctuations. ► The tail-index of the distribution of returns depends on the activity of the traders.