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Paris Metro Pricing (PMP) is a simple multi-class flat-rate pricing scheme already practiced by transport systems, specifically by the Paris Metro at one time. The name is coined after Andrew Odlyzko proposed it for the Internet as a simple way to provide differentiated services. Subsequently, there were several analytical studies of this promising idea. The central issue of these studies is whether PMP is viable, namely, whether it will produce more profit for the service provider, or whether it will achieve more social welfare. The previous studies considered similar models, but arrived at different conclusions. In this paper, we point out that the key is how the users react to the congestion externality of the underlying system. We derive sufficient conditions of congestion functions that can guarantee the viability of PMP, and provide the relevant physical meanings of these conditions.