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The product market competition affects the non-neutrality of monetary policy. This paper quantitatively assesses its impact on the slope of the Phillips curve through the channels of nominal and real rigidity. We build a New Keynesian model using the Kimball aggregator and the Calvo staggered pricing scheme. We show that a more competitive market environment has opposite effects on the slope of the Phillips curve by increasing the real rigidity and lowering the nominal rigidity. We then estimated the model using regional data of China. The Bayesian estimation shows that the response of inflation-output trade-off is larger in the region with a high degree of competition. Counterfactual experiments demonstrate that nominal rigidity has a dominant role and accounts for the majority of the difference in the Phillips curve, while the contribution of real rigidity is relatively minor. Our results highlight the key role of nominal rigidity in determining the inflation-output dynamics.