This paper analyses how systematic stabilisation policy by monetary authorities may change individual price adjustment decision. The model is a stochastic dynamic menu cost model that results in (S,s)-price rules where the price is fixed inside a band. The resulting price rigidity causes output to fluctuate, and hence there is room for stabilisation policy. This paper shows that such a policy might actually be destabilising in the sense that the zone of fixed prices widens, leading to larger output fluctuations. In fact, output can be completely stabilised by a policy that amplifies shocks.