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Due to its impact on nominal firm profits, price rigidity amplifies the response of entry and exit to adverse supply shocks, such as COVID-19. This "entry-exit multiplier" triggers substantial magnification of the welfare losses due to negative supply shocks--especially when wages are also rigid. This is in stark contrast to the benchmark New Keynesian model (NK), which predicts a positive output gap in response to that same shock under the same monetary policy. Endogenous entry-exit thus radically changes the consequences of nominal rigidities. In addition to the aggregate-demand amplification of supply disruptions, our model also reconciles the response of hours worked across the NK and RBC models. And unlike the standard NK model, our model can also be used to evaluate how monetary expansions can alleviate or even eliminate the negative output gap induced by supply disruptions.