Best Effort service has been the bedrock of the Internet. The simultaneous offering of Managed Service has been proposed as an efficient way to support quality of service, to make some applications feasible and many others more attractive, and give consumers greater choice. However, there is widespread concern that if a network provider is allowed to offer Managed Service and charge a per-use fee, then the network provider will find it in its short-term profit-maximizing interest to degrade the Best Effort service. Not only will consumers then face higher costs, but also fewer innovations and new applications will be created. To investigate these issues, we formulate a model in which the provider myopically maximizes its profit by setting the per-use fee and deciding on the bandwidth to provision for the Best Effort and Managed Services. We show that in the optimal solution the service offering is binary, i.e., either the Best Service or the Managed Service is offered, but not both simultaneously. Moreover, a necessary and sufficient condition gives the optimal service offering. Combining this condition with a birth-and-death model of applications, we identify a natural attractor around which the application creation process makes the service offering stable. Our finding alleviates the concern about the Managed Service. Still, the provider needs tow have foresight and the regulator needs to be vigilant, since we also show that there is a threshold number of applications belo which the stabilizing mechanism loses its effectiveness and myopic profit-maximization results in a shrinking network and application pool, which hurts both the provider and consumers.