The paper revisits the long-standing question of the impact of trade openness on the inflation-output trade-off by accounting for the effects of product market competition on price flexibility. The study develops a New-Keynesian open-economy dynamic stochastic general equilibrium model with non-constant price elasticity of demand and Calvo price setting in which the frequency of price adjustment is endogenously determined. It demonstrates that trade openness has two opposing effects on the sensitivity of inflation to output fluctuations. On the one hand, it raises strategic complementarity in firms' pricing decisions and the degree of real price rigidities, which makes inflation less responsive to changes in real marginal cost. On the other hand, it strengthens firms' incentives to adjust their prices, thereby reducing the degree of nominal price rigidities and increasing the sensitivity of inflation to changes in marginal cost. The study explains the positive relationship between competition and the frequency of price adjustment observed in the data. It also provides new insights into the effects of global economic integration on the Phillips Curve.