In the workhorse DSGE model, the optimal steady state inflation rate is near to zero or slightly negative and inflation is almost completely stabilized along the business cycle (Schmitt-Grohe and Uribe, 2011). We reconsider the issue, allowing for agent heterogeneity in the access to the market for interest bearing assets. We show that inflation reduces inequality and that LAMP can justify relatively high optimal ination rates. When we calibrate the share of constrained agents to he wealth Gini index for the US, the optimal inflion rate is well above 2%. The optimal response to shocks is also affected. Rather than using public debt to smooth tax distortions, the Ramsey planner front loads tax rates and reduces public debt variations in order to limit the redistributive effects of debt service payments.