Price setting, price dispersion, and the value of money - or - The law of two prices

We study models that combine search, monetary exchange, price posting by sellers, and buyers with preferences that differ across random meetings - say, because sellers in different meetings produce different varieties of the same good. We show how these features interact to influence the price level (i.e., the value of money) and price dispersion. First, price-posting equilibria exist with valued fiat currency, which is not true in the standard model. Second, although both are possible, price dispersion is more common than a single price. Third, perhaps surprisingly, we prove generically there cannot be more than two prices in equilibrium.