A model in which monetary policy is about money

Optimal monetary policy is studied in a model with (i) heterogeneity in the degree to which different people are monitored (have publicly known histories); (ii) idiosyncratic shocks that give rise to heterogeneity in earning and spending realizations; and (iii) central-bank intervention in a "market" in claims or credit in which the participants are those who are heavily monitored. A special case of the model has everyone perfectly monitored. In that case, there is no role for money and no role for central-bank intervention. In the example displayed with imperfect monitoring, optimal intervention is not simple.