I study a class of macroeconomic models in which all
firms can costlessly choose any price at each date from an interval
(indexed to last period's price level) that includes a positive lower
bound. I prove three results that are valid for any such half-closed
interval (regardless of how near zero the left endpoint is). First,
given any output sequence that is uniformly bounded from above by
the moneyless equilibrium output level, that bounded output sequence
is an equilibrium outcome for a (possibly time-dependent) specification
of monetary and fiscal policy. Second, given any specification of
monetary and fiscal policy in which the former is time invariant and
the latter is Ricardian (in the sense of Woodford (1995)), there is
a sequence of equilibria in which consumption converges to zero on
a date-by-date basis. These first two results suggest that standard
macroeconomic models without pricing bounds may provide a false degree
of confidence in macroeconomic stability and undue faith in the long-run
irrelevance of monetary policy. The paper's final result constructs
a non-Ricardian nominal framework (in which the long-run growth rate
of nominal government liabilities is sufficiently high) that pins
down a unique stable real outcome as an equilibrium.