Which level of inflation should Central Banks be targeting? The authors investigate this issue in the context of a simplified Agent Based Model of the economy. Depending on the value of the parameters that describe the behaviour of agents (in particular inflation anticipations), they find a rich variety of behaviour at the macro-level. Without any active monetary policy, our ABM economy can be in a high inflation/high output state, or in a low inflation/low output state. Hyper-inflation, deflation and “business cycles” between coexisting states are also found. The authors then introduce a Central Bank with a Taylor rule-based inflation target, and study the resulting aggregate variables. The main result is that too-low inflation targets are in general detrimental to a CB-monitored economy. One symptom is a persistent under-realization of inflation, perhaps similar to the current macroeconomic situation. Higher inflation targets are found to improve both unemployment and negative interest rate episodes. The results are compared with the predictions of the standard DSGE model.