Pairwise trade, asset prices, and monetary policy

We construct a search-theoretic model where fiat money coexists with real assets, and all assets can be used as a media of exchange. The terms of trade in bilateral matches are determined by a pairwise Pareto-efficient pricing mechanism. We do not have to appeal to exogenous liquidity constraints to generate asset prices that are consistent with the following facts: (i) fiat money can be valued despite being dominated in its rate of return; (ii) real assets with identical dividend flows can have different rates of return; and (iii) an increase in inflation raises asset prices, lowers their returns, and widens the rate-of-return differences between assets. On the normative side we show that there is a range of inflation rates that implement the first-best allocation.