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We present a theory of differences of liquidity across assets, based on an endogenous ranking of assets as media of exchange arising from their relative quality as hedging devices. When assets have two distinct roles, as intertemporal media of exchange and hedging devices, buyers have generically a strict preference for paying sellers with the asset which is the relative better hedging device for sellers. The consequence of this preference is that there are three monetary policy regimes, and these regimes differ in which assets serve as media of exchange, whether assets carry a liquidity premium, and in the impact that monetary policy has on asset prices.