Optimal monetary policy, endogenous sticky prices, and multiple equilibria

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.