When two-part tariffs are not enough: mixing with nonlinear pricing

We determine explicitly the fully nonlinear equilibrium tariffs in a simple tractable model where two firms compete for consumers whose private preferences for products and quantities are correlated because they mix both goods. Contrary to the existing literature assuming uncorrelated preferences, neither full exclusivity nor two-part tariffs can arise in equilibrium. The equilibrium tariff sorts consumers through decreasing marginal prices even when goods are almost homogeneous. The market splits endogenously between one-stop and two-stop shopping customers. This conclusion also holds when consumers differ in total demand.