Vertical differentiation with non‐uniform consumers' distribution

This note explores a vertical differentiation model with a continuous non‐uniform consumers' distribution. First, a result concerning the finiteness property obtained with uniform consumers' distribution is generalized. Second, we prove an existence result of price equilibrium when the distribution is concave. Finally, we exhibit a counter‐example to the existence of price equilibrium to show that the concavity assumption is not superfluous.