In this paper, we show that strategic complementarities?such as firm-specific factors or quasikinked demand?have crucial implications for the design of monetary policy and for the welfare costs of output and inflation variability. Recent research has mainly used log-linear approximations to analyze the role of these mechanisms in amplifying the real effects of monetary shocks. In contrast, our analysis explicitly considers the nonlinear properties of these mechanisms that are relevant for characterizing the deterministic steady state as well as the second-order approximation of social welfare in the stochastic economy. We demonstrate that firm-specific factors and quasi-kinked demand curves yield markedly different implications for the welfare costs of steady-state inflation and inflation volatility, and we show that these considerations have dramatic consequences in assessing the relative price distortions associated with the Great Inflation of 1965-1979.