Cooperation between European Central Bank,German Government, and French Government

An increase in European money supply lowers unemployment in Germany and France. On the other hand, it raises inflation there. An increase in German government purchases lowers unemployment in Germany. On the other hand, it raises inflation there. Correspondingly, an increase in French government purchases lowers unemployment in France. On the other hand, it raises inflation there. The primary targets of the European central bank are zero inflation in Germany and France. The primary target of the German government is zero unemployment in Germany. And the primary target of the French government is zero unemployment in France. The model of unemployment and inflation can be represented by a system of four equations: (1) $${\rm u}_{\rm 1} {\rm = A}_{\rm 1} - {\rm M} - {\rm G}_{\rm 1}$$ (2) $${\rm u}_{\rm 2} {\rm = A}_{\rm 2} - {\rm M} - {\rm G2}$$ (3) $${\rm \pi }_{\rm 1} {\rm = B}_{\rm 1} + {\rm M} + {\rm G}_{\rm 1}$$ (4) $${\rm \pi }_{\rm 2} {\rm = B}_{\rm 2} + {\rm M} + {\rm G}_{\rm 2}$$ Here u1 denotes the rate of unemployment in Germany, u2 is the rate of unemployment in France, π1 is the rate of inflation in Germany, π2 is the rate of inflation in France, M is European money supply, G1 is German government purchases, G2 is French government purchases, A1 is some other factors bearing on the rate of unemployment in Germany, A2 is some other factors bearing on the rate of unemployment in France, B1 is some other factors bearing on the rate of inflation in Germany, and B2 is some other factors bearing on the rate of inflation in France. The endogenous variables are the rate of unemployment in Germany, the rate of unemployment in France, the rate of inflation in Germany, and the rate of inflation in France.