Using a monetary search model, Rocheteau, Rupert and Wright (2007) show that the relationship between inflation and unemployment can be positive or negative depending on the primitives of the model. The key features are indivisible labor, nonseparable preferences and bargaining. Their results are derived only for a special case of the bargaining solution, take-it-or-leave-it offer by buyers. Instead of bargaining, this paper considers competitive search (price posting with directed search). I show that the results in Rocheteau, Rupert and Wright (2007) can be generalized in an environment where both buyers and sellers have nonseparable preferences. In addition, the relationship between inflation and unemployment is robust to allowing free entry by sellers, which cannot be studied in Rocheteau, Rupert and Wright (2007).