In this paper a discrete choice model is suggested which generates unambiguously lower prices, if oligopolists discriminate by price. In a setting of two groups of consumers and two firms this is due to a different ranking of the elasticity of demand of the two groups by the two firms. Here, this ranking results from switching costs. It is argued that firms can prevent price discrimination which lowers their profits, if firms are symmetric. However, with asymmetric firms price discrimination cannot always be prevented by simple threats to pay back in kind. In this case there is an incentive to use price discrimination and it enhances welfare.