The authors construct a search-theoretic model in which fiat money coexists with real assets, and no restrictions are placed on the use of assets as means of payment. The terms of trade in bilateral matches are determined by a pairwise Pareto-efficient pricing mechanism. From the view point of agents with a financing need, this mechanism replicates the explicit liquidity constraints found in Kiyotaki and Moore (2005) or Lagos (2006) that are needed to generate asset pricing facts found in the data. A critical difference, however, is that the authors do not impose any such constraints in our environment. They show that fiat money can be valued despite being dominated in its rate of return. Moreover, real assets can generate different rates of returns even if agents are risk-neutral. An increase in inflation raises assets' prices, lowers their returns, and widens the rate-of-return differences between real assets. Finally, there is a range of inflation rates that implement the first-best allocation.

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