This paper addresses the issues of charging, rate control and routing for a communication network carrying elastic traffic, such as an ATM network offering an available bit rate service. A model is described from which max–min fairness of rates emerges as a limiting special case; more generally, the charges users are prepared to pay influence their allocated rates. In the preferred version of the model, a user chooses the charge per unit time that the user will pay; thereafter the user’s rate is determined by the network according to a proportional fairness criterion applied to the rate per unit charge. A system optimum is achieved when users ’ choices of charges and the network’s choice of allocated rates are in equilibrium. 1