Price-level determinacy, lower bounds on the nominal interest rate, and liquidity traps

We consider standard monetary-policy rules with inflation-rate targets and interest-rate or money-growth instruments using a flexible-price, perfect-foresight model. There is always a locally-unique target equilibrium. There are also below-target equilibria (BTE) with inflation always below target and constant asymptotically approaching or eventually reaching a below-target value. Liquidity traps are neither necessary or sufficient for BTE which can arise if monetary policy keeps the interest rate above a lower bound. We construct monetary-policy rules that preclude BTE, some which are monotonic in inflation but all of which are non-differentiable at a point. For standard monetary-policy rules, there are plausible fiscal policies that insure uniqueness by precluding BTE; those policies exclude perpetual surpluses and, possibly, perpetual balanced budgets.