Pré-publication, Document de travail: This paper analyzes the long-run effect of monetary policy when credit constraints are taken into account. This analysis is carried on in a heterogeneous agents framework in which infinitely lived agents can partially self-insure against income risks by using both financial assets and real balences. First we show theoretically that financial borrowing constraints give rise to an heterogeneity in money demand, leading to a real effect of inflation. Secondly, we show that inflation has a quantitative positive impact on output and consumption in economies which closely match the wealth distribution of the United States. Thirdly, we find that the average welfare cost of inflation is much smaller compared to a complete market economy, and that inflation induces important redistributive effects across households.