Should-Read: Robert Waldmann: A Dynamic Macroeconomic Model with Downward Nominal Rigidity II: "This note explores the implications of downward nominal rigidity...
...To make things clear and simple, I will assume absolute downward nominal rigidity so prices and nominal wages are never cut. This is simply assumed with a nod at US data and not explained. Downward nominal rigidity is quite different from standard assumptions about sticky wages and prices in which wage and price setting is slow but takes expected inflation into account. Downward nominal rigidity implies indeterminate equilibrium with a continuum of outcomes possible for given tastes and technology. It is possible for the economy to fall into a liquidity trap for no particular reason, and it is possible for the economy to escape from that trap for no particular reason...
