The paper compares the welfare properties of two competing organizations of the monetary system: The current fractional reserve banking system versus a narrow banking system where inside money is fully backed by outside money issued by the central bank. Using a New Monetarist model, the analysis shows that fractional reserve banking is beneficial because of the interest payments on inside money. Since inside money funds loans, it pays interest, compensating the agents for the in ation tax and thus reducing the welfare costs of in ation. Since narrow banking provides no such compensation fractional reserve banking typically dominates narrow banking in terms of welfare. This also holds if outside money pays interest. Only if fractional reserve banking is sufficiently constrained, narrow banking can yield higher welfare.