Inflation and unemployment are central issues in macroeconomics. While progress has been made on these issues recently using models that explicitly incorporate search-type frictions, existing models analyze either unemployment or inflation in isolation. We develop a framework to analyze unemployment and inflation together. This makes contributions to disparate literatures, and provides a unified model for theory, policy, and quantitative analysis. We discuss optimal fiscal and monetary policy. We calibrate the model, and discuss the extent to which it can account for salient aspects of a half century's experience with inflation, unemployment, interest rates, and velocity. Depending on some details concerning how one calibrations certain parameters, the model can do a good job matching the data.