The goal of this paper is to study pricing of differentiated services and its impact on the choice of service priority at equilibrium. We consider both TCP connections as well as non controlled (real time) connections. The performance measures (such as throughput and loss rates) are determined according to the operational parameters of a RED buffer management. The latter is assumed to be able to give differentiated services to the applications according to their choice of service class. We consider a best effort type of service differentiation where the QoS of connections is not guaranteed, but by choosing a better (more expensive) service class, the QoS parameters of a session can improve (as long as the service class of other sessions are fixed). The choice of a service class of an application will depend both on the utility as well as on the cost it has to pay. We first study the performance of the system as a function of the connections' parameters and their choice of service ...