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.
I examine a two-period duopolistic market for a durable good where firms compete in prices. Consumers are heterogeneous and can be described according to the following characteristics (i) high valuation and high search intensity; (ii) high valuation and low search intensity; (iii) low valuation and high search intensity; and (iv) low valuation and low search intensity. The market exhibits a new version of the so-called Coasian dynamics. The firms engage in intertemporal price discrimination and only consumers with high valuation and low search intensity purchase the product early. This result is based on a property which dictates that the consumers with high valuation and low search intensity are the most impatient. I call this the skimming through search property. When the difference between the high and the low valuation is small, there is positive probability that the prices in the first period are lower than the prices in the second period, so each firm may set a decreasing sequence of prices in a stochastic sense. Furthermore, when the percentage of consumers with high valuation increases, all consumers pay lower prices. This inter-consumer externality resembles the positive externality caused by an increase in market transparency.
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