Optimal Monetary Policy and the Welfare Cost of Inflation of a Currency Union

This paper studies the welfare cost of inflation and optimal monetary policy of a currency union between two countries using a search-theoretic framework with endogenous composition of buyers and sellers. The model includes three features of a currency union that are key to welfare and policy analysis: heterogeneous market structure (characterized by buyers' bargaining power), imperfect market integration, and immigration policy.

The model yields optimal monetary policy that deviates from the Friedman rule, with the magnitude of the optimal inflation rate and welfare cost of inflation determined by different policy regimes. The Friedman rule is suboptimal, because of a matching congestion externality in the labor market arising from the endogenous composition of buyers and sellers. Higher labor mobility reduces the cost of inflation by alleviating congestion, regardless of buyers' bargaining power. Market integration may also reduce congestion, lowering the cost of inflation, but only when sellers are relatively scarce.