Since the collapse of the Bretton Woods monetary system, the monies of the developed world have been unbacked by any formal promise of convertibility. Yet, inflation has typically undershot, not overshot, central bank targets over the past couple decades. The low, while generally positive, inflation rate has (more arguably) been associated with low output and low growth. In this paper, I consider these observations through the lens of a class of representative agent rational expectations models with nominal (price-setting) frictions and the possibility of firm entry/exit. I show that for any level of nominal frictions (no matter how small) and for any monetary policy rule that satisfies a set of weak restrictions, there is a large set of equilibria that exhibit permanently low inflation, low output, and low nominal interest rates. These equilibria can only exhibit positive long-run inflation if growth is low and the specification of nominal frictions (that is, the Phillips curve) takes an unconventional but nonetheless empirically plausible form.