This paper describes a new monetary open‐economy model where firms have market power due to search frictions in the goods market, and endogenous search effort by consumers mitigates this market power. The optimal inflation rate generally depends positively on the cost of search effort, the cost of firm entry, and the cost of trade. Higher inflation always improves a country's terms‐of‐trade against its trading partners. I also characterize a general class of matching processes which offer a novel approach to modeling firm sales. (JEL D43, E40, F12)