This paper studies optimal monetary policy rules in a framework with sticky prices, matching
frictions and real wage rigidities. Optimal monetary policy is given by a constrained Ramsey
plan in which the monetary authority maximizes the agents’ welfare subject to the competitive
economy relations and the assumed monetary policy rule. I find that the optimal policy rule
should respond to unemployment alongside with inflation. This is so since models with matching
frictions (unlike standard New Keynesian models) feature a congestion externality that makes
unemployment inefficiently high. A strong response to inflation remains optimal while a response
to output is always welfare detrimental.