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Previous literature shows that in the presence of staggered price setting, high trend inflation induces not only a large loss in steady-state output relative to its natural rate but also indeterminacy of equilibrium under the Taylor rule. This paper examines the implications of a "smoothed-off" kink in demand curves for the natural rate hypothesis and macroeconomic stability using a canonical model with staggered price setting. An empirically plausible calibration of the model demonstrates that the kink in demand curves mitigates the influence of high trend inflation on aggregate output through the average markup and (when relevant) the relative price distortion, thereby ensuring that the violation of the natural rate hypothesis is minor and preventing indeterminacy caused by high trend inflation. (Copyright: Elsevier)