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Over the past 20 years, U.S. import prices have become less responsive to the exchange rate. We propose that a significant portion of this decline is a result of increased trade integration. To illustrate this effect, we develop an open economy DGE model featuring demand curves with variable elasticities so that a firm's pricing decision depends on its competitors' prices. As a result, a foreign exporter finds it optimal to vary its markup in response to shocks that change the exchange rate, insulating import prices from exchange rate movements. With increased trade integration, exporters have become more responsive to the prices of their competitors, explaining a sizeable portion of the observed decline in the sensitivity of U.S import prices to the exchange rate.