Result

The targets of the European central bank are zero inflation in Germany and France. The instrument of the European central bank is European money supply. We assume that the European central bank has a quadratic loss function. The amount of loss depends on inflation in Germany and France. The European central bank sets European money supply so as to minimize its loss. The firstorder condition for a minimum loss gives the reaction function of the European central bank. Suppose the German government raises German government purchases. Then, as a response, the European central bank lowers European money supply.

The target of the German government is zero unemployment in Germany. The instrument of the German government is German government purchases. We assume that the German government has a quadratic loss function. The amount of loss depends on unemployment in Germany. The German government sets German government purchases so as to minimize its loss. The first-order condition for a minimum loss gives the reaction function of the German government. Suppose the European central bank lowers European money supply. Then, as a response, the German government raises German government purchases.