We study in this paper a simple model of a two-period economy, with two states of the world in the second period, two agents and one good. Financial markets are incomplete since only inside money is available. We show that outside money, which is introduced in the model through its role as a medium of exchange, is non-neutral, in the sense that it has an effect on the equilibrium allocation. We then discuss whether a monetary policy that would aim at state-independent price levels is desirable. We illustrate that discussion with a few examples. The possible sub-optimality of a constant-across-states inflation rates target for monetary policy is to be contrasted with results from representative agent macroeconomic models.