Inflation and Unemployment in the Long Run Revisited

We construct a continuous-time, monetary model with frictional goods and labour markets to revisit the long-run relationship between inflation and unemployment. By endogenising the value of consumers’ outside options and market power in accordance with standard consumer search theory, we generate novel predictions for the slope of the long-run Phillips curve, optimal monetary policy, and outcomes at the frictionless limit. The relationship between inflation and unemployment is non-monotone and, at low inflation rates, an increase in inflation reduces unemployment. The Friedman rule is suboptimal when firms’ average bargaining power across markets is low. Markups and markdowns vanish as frictions disappear.