We model a specific two-sided monopoly market in which agents can switch from a side to the other. We define two periods of time. In the first period, agents buy the platform services on each side and in the second period of time, they can possibly enhance their satisfaction by going to the other face of the platform. We analyze the link between mobility, consumer’s utility, prices and profit. We show that mobility is a valuable feature which can be compared with an increase of product quality. Finally, the firm is able to capture the mobility in its monopoly’s profit. The relative size of each group then appears as a strategical variable for the firm.