Customer Relationship and Sales

I construct a search model to formalize the intuitive idea that sellers hold sales to attract buyers and build customer relationships. The market consists of a large number of buyers and sellers. All sellers sell a homogeneous good and all buyers have the same publicly known valuation of the good. Buyers know the terms of trade offered by sellers before choosing which seller to visit. A buyer is related to a seller if the buyer just bought a good from the seller and the relationship is broken if the buyer fails to continue to buy from the seller. Sellers are restricted to offer the same price to all buyers, but they are allowed to give priority to their related buyers. I prove that there is an equilibrium in which a seller gives priority to the related buyer and a buyer makes repeat purchases from the related seller. In the equilibrium, a seller who does not have a related buyer posts a low (sale) price to attract the buyers who are unrelated to any seller and, once the seller is related to a buyer after a trade, the seller will post a high (regular) price to sell only to the related buyer. The fraction of related sellers is endogenous in the equilibrium. I calibrate the steady state of the model to the data and find that the sale price represents a sizable markdown, and the regular price a sizable markup, on the marginal cost. With the calibrated model, I examine comparative statics and dynamics of the equilibrium with respect to changes in the cost of and the demand for the good.