  The mean-field variant of the model of limit order driven market introduced
recently by Maslov is formulated and solved. The agents do not have any
strategies and the memory of the system is kept within the order book. We show
that he evolution of the order book is governed by a matrix multiplicative
process. The resulting stationary distribution of step-to-step price changes is
calculated. It exhibits a power-law tail with exponent 2. We obtain also the
price autocorrelation function, which agrees qualitatively with the
experimentally observed negative autocorrelation for short times.
