Counterfeiting, screening and government policy

We construct a search theoretic model of money in which counterfeit money can be produced at a cost, but agents can screen for fake money, also at a cost. Counterfeiting can occur in equilibrium when both costs and the inflation rate are sufficiently low. Optimal monetary policy is the Friedman rule. However, the rationale for the Friedman rule in an economy with circulation of counterfeit money differs from the conventional mechanism that holds in the model when counterfeiting does not occur. We also study optimal anti-counterfeiting policy that determines the counterfeiting cost and the screening cost.