Monopoly and optimal nonlinear pricing: the case of route monopolies and heteregeneous demand in the air transport market

This paper explores the robustness of the one-dimensional screening model with respect to increasing the number of instruments and the number of characteristics. We study a case of nonlinear pricing (2 instruments (2 routes on which the airline provides customers with services), 2 characteristics (demand of services on these routes) and two values per characteristic (a low or a high demand of services on these routes)) and we show that none of the conclusions of the one-dimensional analysis remain valid. In particular, upward incentive compatibility constraint may be binding at the optimum. As a consequence, they may be distortion at the top of the distribution. In addition to this, we show that the optimal solution often requires bundling, while it is sometimes optimal for the monopolist to produce only one good or to exclude some buyers from the market. This means that the monopolist cannot fully apply his monopoly power and is better off selling two goods independently. We define all possible solutions in the case of a quadratic cost function for a uniform distribution of agent types and demonstrate that the range of services proposed by an airline is often larger than the corresponding range in demand.