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We study a canonical model of decentralized exchange for a durable good or asset, where agents are assumed to have time‐varying, heterogeneous utility types. Whereas the existing literature has focused on the special case of two types, we allow agents' utility to be drawn from an arbitrary distribution. Our main contribution is methodological: we provide a solution technique that delivers a complete characterization of the equilibrium, in closed form, both in and out of the steady state. This characterization offers a richer framework for confronting data from real‐world markets and reveals a number of new economic insights. In particular, we show that heterogeneity magnifies the impact of frictions on equilibrium outcomes and that this impact is more pronounced on price levels than on price dispersion and welfare.

Banks’ ratio of the market value to book value of their equity was close to 1 until the 1990s, then more than doubled during the 1996–2007 period, and fell again to values close to 1 after the 2008 financial crisis. Some economists argue that the drop in banks’ market-to-book ratio since the crisis is due to a loss in bank franchise value or profitability. In this paper we argue that banks’ market-to-book ratio is the sum of two components: franchise value and the value of government guarantees. We empirically decompose the ratio between these two components and find that a large portion of the variation in this ratio over time is due to changes in the value of government guarantees.

We construct a continuous‐time new‐monetarist economy that displays an endogenous, nondegenerate distribution of money holdings. Properties of equilibria are obtained analytically and equilibria are solved in closed form in a variety of cases. Lump‐sum transfers financed with money creation are welfare‐enhancing when labor productivity is low whereas regressive transfers approach first best when labor productivity is high and agents are not too impatient. We introduce illiquid government bonds and draw implications for liquidity‐trap equilibria. We also study transitional dynamics under quadratic preferences and the velocity of money under heterogeneous preference shocks.