Output-inflation trade-offs and the optimal inflation rate

We show that a positive superelasticity of demand, often referred to as “Marshall's Second Law of Demand,” is a new push factor of optimal inflation in staggered price models. The positive superelasticity alters the trade-offs between output and inflation in the models. It allows higher trend inflation to steepen the slope of a model-based Phillips curve and lower the steady-state average markup, and thus reduces the inflation-related weight in a model-based welfare function for higher trend inflation and the steady-state welfare cost of higher trend inflation. Consequently, the positive superelasticity can make the optimal trend inflation rate positive and lessen the welfare difference between inflation targets of 2 percent and 4 percent.