  We extend in a minimal way the stylized model introduced in in "Tipping
Points in Macroeconomic Agent Based Models" [JEDC 50, 29-61 (2015)], with the
aim of investigating the role and efficacy of monetary policy of a `Central
Bank' that sets the interest rate such as to steer the economy towards a
prescribed inflation and employment level. Our major finding is that provided
its policy is not too aggressive (in a sense detailed in the paper) the Central
Bank is successful in achieving its goals. However, the existence of different
equilibrium states of the economy, separated by phase boundaries (or "dark
corners"), can cause the monetary policy itself to trigger instabilities and be
counter-productive. In other words, the Central Bank must navigate in a narrow
window: too little is not enough, too much leads to instabilities and wildly
oscillating economies. This conclusion strongly contrasts with the prediction
of DSGE models.
