We examine the theoretical and numerical properties of a prototypical New Keynesian DSGE model featuring endogenous capital accumulation and labour supply. We find that this completely conventional model yields implausible impact results following unanticipated and temporary shocks when the monetary closure rule is changed from a policy rule setting nominal interest rates (a Taylor Rule) to a fixed money supply rule. We compare and contrast a variety of New Keynesian models, featuring aggregate price stickiness, with their New Classical counterparts featuring perfectly flexible prices. In line with the literature we find that under a Taylor Rule the impulse-response functions following a technology shock are very similar. In contrast, with a fixed money supply the impact effects for the New Keynesian model are implausible. We demonstrate the robustness of this Implausible Result to alternative parameter values and show that it is ultimately caused by the inflexibility of the capital stock relative to that of the real money supply. We suggest several model extensions which will eliminate the Implausible Result from New Keynesian sticky-price models.