This article develops three views of the dynamics of inflation and unemployment: the expectations-augmented Phillips curve model, a monetarist model of the relation of monetary change to both inflation and unemployment, and a rational expectations model. Based on each of these models, estimates of the cost of reducing inflation are presented. Finally, the size of the permanent per period gains associated with eradicating inflation that would justify incurring these temporary costs are estimated using both the Phillips curve and monetarist models.