This paper studies economic utilities and quality of service (QoS) in a two-sided non-neutral market where Internet service providers (ISPs) charge content providers (CPs) for the content delivery. We propose new models that involve a CP, an ISP, end users and advertisers. The CP may have either a subscription revenue model (charging end users) or an advertisement revenue model (charging advertisers). We formulate the interactions between the ISP and the CP as a noncooperative game for the former and an optimization problem for the latter. Our analysis shows that the revenue model of the CP plays a significant role in a non-neutral Internet. With the subscription model, both the ISP and the CP receive better (or worse) utilities as well as QoS in the presence of the side payment at the same time. With the advertisement model, the side payment impedes the CP from investing on its contents.