Conclusion

An increase in European money supply lowers unemployment in Europe. On the other hand, it raises inflation there. Correspondingly, an increase in European government purchases lowers unemployment in Europe. On the other hand, it raises inflation there. In the numerical example, a unit increase in money supply lowers the rate of unemployment by 1 percentage point. On the other hand, it raises the rate of inflation by 1 percentage point. Similarly, a unit increase in government purchases lowers the rate of unemployment by 1 percentage point. On the other hand, it raises the rate of inflation by 1 percentage point. For instance, let initial unemployment be 2 percent, and let initial inflation be 2 percent as well. Now consider a unit increase in money supply. Then unemployment goes from 2 to 1 percent. On the other hand, inflation goes from 2 to 3 percent. The target of the European central bank is zero inflation in Europe. The instrument of the European central bank is European money supply. Thus there is one target and one instrument. We assume that the European central bank has a quadratic loss function. The amount of loss depends on the level of inflation. The European central bank sets European money supply so as to minimize its loss. The first-order condition for a minimum loss gives the reaction function of the European central bank. Suppose the European government raises European government purchases. Then, as a response, the European central bank lowers European money supply.