In this paper, I introduce money in the standard labor-matching model (Mortensen and Pissarides 1999, Pissarides 2000). A double coincidence problem makes Fiat Money necessary as a medium of exchange. In the long-run, a rise in the rate of money growth leads to higher inflation and higher unemployment, so the long-run Phillips curve is not vertical. The optimal monetary growth rate decreases with the workers’ bargaining power, the level of unemployment benefits and the payroll tax rate.