تنظیم قیمت، پراکندگی قیمت و ارزش پول: یا قانون دو قیمتی

We study models combining search, money, price posting, and preference shocks. We show how these features interact to influence the price level and price dispersion. First, price-posting equilibria exist with valued fiat currency. Second, although both are possible, price dispersion is more common than a single price. Third, we prove that generically there cannot be more than two prices. We provide intuition for this law of two prices, show it also holds in some nonmonetary search models, and discuss variations of the assumptions under which it may not hold.

We analyze search-based models of monetary exchange along the lines of Shi (1995) or Trejos and Wright (1995), but in contrast to the majority of papers in this literature, we assume sellers post prices ex ante rather than having traders bargain after they meet. Price posting is a common assumption in nonmonetary models, and it seems natural to explore its implications in monetary theory. However, in the standard Shi–Trejos–Wright model, equilibria with valued fiat currency do not even exist with price posting. To see why, recall Diamond's (1970) result from nonmonetary models: there is a unique price-posting equilibrium, it has a single price, and this price gives all the gains from trade to sellers. In a monetary model, since buyers get no gains from trade, the value of fiat currency falls to zero—i.e., the monetary equilibrium unravels and the unique equilibrium is the nonmonetary equilibrium.

We have analyzed a model that combines search, money, price setting and random preference shocks. As a contribution to monetary economics, we showed that equilibria with valued fiat currency exist, something that is not true when preferences are constant or when preferences differ permanently across agents. As a contribution to the literature on price dispersion, we showed that a nondegenerate distribution is possible, and indeed in simple cases price dispersion is actually more common than a single price. We also derived the law of two prices: with KK possible values for the shock, the natural extension of Diamond (1970) is that there are exactly KK reservation values, but we prove that in equilibrium there will be (generically) at most two of these KK values actually posted. Although the strict law requires purely match-specific shocks, a weaker version applies more generally.