Category pricing with state-dependent utility

There is substantial literature documenting the presence of state-dependent utility with packaged goods data. Typically, a form of brand loyalty is detected whereby there is a higher probability of purchasing the same brand as has been purchased in the recent past. The economic significance of the measured loyalty remains an open question. We consider the category pricing problem and demonstrate that the presence of loyalty materially affects optimal pricing. The prices of higher quality products decline relative to those of lower quality when loyalty is introduced into the model. Given the well-known problems with the confounding of state dependence and consumer heterogeneity, loyalty must be measured in a model which allows for an unknown and possibly highly nonnormal distribution of heterogeneity. We implement a highly flexible model of heterogeneity using multivariate mixtures of normals in a hierarchical choice model. We use an Euler equations approach to the solution of the dynamic pricing problem which allows us to consider a very large number of consumer types.