In this paper, the authors explore a dynamical version of the Aoki and Yoshikawa model (AYM) for an economy driven by demand. They show that when an appropriate Markovian dynamics is taken into account, the AYM has different equilibrium distributions depending on the form of transition probabilities. In the version of the dynamic AYM presented here, transition probabilities depend on a parameter c tuning the choice of a new sector for workers leaving their sector. The solution of Aoki and Yoshikawa is recovered only in the case c = 0. All the other possible cases give different equilibrium probability distributions, including the Bose-Einstein distribution.