Continuous Cross Subsidies And Quantity Restrictions

This article provides a model of loss leader pricing and quantity restrictions for a competitive multiproduct industry when individual consumers have continuous (and independent) demands for the set of available goods. Utilizing a generalization of the model proposed by Bliss [1988], we demonstrate the importance of consumer heterogeneity for the existence of cross subsidies when there is complete information and individual consumers have smooth, downward sloping demands. Continuous cross subsidies arising from consumer heterogeneity are also shown to exist in Hotelling models. Our use of continuous rather than ‘unit’ demands allows us to analyze issues related to welfare, which in turn exposes a strong incentive for the firm to place binding quantity restrictions on consumers. We also show how the presence of quantity restrictions can be used to distinguish between continuous cross subsidies arising from heterogeneous consumers versus those arising from classic demand complementarity with homogeneous agents.