We analyze optimal discretionary monetary policy in an endogenous sticky prices model. Similar models with exogenous sticky prices can deliver multiple equilibria. This is a necessary condition for the occurrence of expectation traps (when private agents' expectations determine the equilibrium level of inflation). In our model, sticky-price firms are allowed to switch to flexible pricing by paying a random cost. For plausible parametrizations, our model has a unique low-inflation equilibrium. With endogenous sticky prices, the monetary authority does not validate high-inflation expectations and deviates to the Friedman rule.