We consider an environment where the general equilibrium assumption that every agent buys and sells simultaneously is relaxed. We show that fiat money can implement a Pareto optimal allocation only if taxes are type-specific. We then consider intermediated money by assuming that financial intermediaries whose liabilities circulate as money have an important identifying characteristic: they are widely viewed as default-free. The paper demonstrates that default-free intermediaries who issue deposit accounts with credit lines to consumers can resolve the monetary problem and make it possible for the economy to reach a Pareto optimum.