The effects of entry in a model of sales

I revisit Varian's (1980) model of sales by introducing bidimensional consumer heterogeneity. In my version of the model, there are (i) informed consumers with high valuation; (ii) uninformed consumers with high valuation; (iii) informed consumers with low valuation; and (iv) uninformed consumers with low valuation. Depending on parameters, always one of the following three types of equilibrium exists: the deterministic partial participation, the probabilistic partial participation, and the deterministic full participation equilibrium. My main finding is that the impact of entry on the firms' expected price may be ambiguous. For example, when the status quo number of firms generates the probabilistic partial participation equilibrium, a new entrant may either increase or decrease the expected price.