Customer relationship and sales

I analyze a search equilibrium in a large market where customer relationship based on past trade arises endogenously together with service priority and sales. Specifically, there exists a unique equilibrium where it is optimal for a buyer to make repeat purchases from the related seller and optimal for a seller to give service priority to the related buyer. Customer relationship always improves welfare by reducing search frictions, but the equilibrium is socially efficient only when the buyer/seller ratio in the market is below a critical level. When the buyer/seller ratio exceeds this critical level, the equilibrium is inefficient because it fails to induce the coexistence of trading priority for related buyers and partial mixing of buyers for related sellers. Customer relationship induces price variations for individual sellers over time even when market conditions do not change. A seller posts a (high) regular price to sell to the related buyer and, once the seller loses the relationship, the seller posts a (low) sale price to sell to unrelated buyers until he gains a relationship. I also examine how market conditions affect the aggregate stock of relationships, markups, the size and the duration of a sale.