A customer market model in which firms and customers form long-term relations is developed and integrated into the canonical New Keynesian framework. This leads to two important differences compared to the standard model. First, the purely forward-looking Phillips curve is replaced by a hybrid variant where current inflation also depends on past inflation. Second, the welfare cost of inflation is much lower, which leads to an optimal monetary policy where relatively more weight is put on output gap stabilization than previously found in the literature.