Central Bank and Governments Cooperate

As a starting point, consider the model of inflation and unemployment. It can be represented by a system of four equations:

$${\rm{\pi }}_{\rm{1}} = {\rm{A}}_{\rm{1}} + {\rm{\alpha M + \beta G}}_{\rm{1}}$$

((1))

$${\rm{\pi }}_2 = {\rm{A}}_2 + {\rm{\alpha M + \beta G}}_2$$

((2))

$${\rm{u}}_{\rm{1}} = {\rm{B}}_{\rm{1}} {\rm{ - \gamma M - \delta G}}_{\rm{1}}$$

((3))

$${\rm{u}}_2 = {\rm{B}}_2 {\rm{ - \gamma M - \delta G}}_2$$

((4))

Of course this is a reduced form. π₁ denotes the rate of inflation in Germany, π₂ is the rate of inflation in France, u₁ is the rate of unemployment in Germany, u₂ is the rate of unemployment in France, M is European money supply, G₁ is German government purchases, G₂ is French government purchases, α is the monetary policy multiplier with respect to inflation, β is the fiscal policy multiplier with respect to inflation, γ is the monetary policy multiplier with respect to unemployment, and δ is the fiscal policy multiplier with respect to unemployment. The endogenous variables are the rates of inflation and the rates of unemployment, in Germany as well as in France.

According to equation (1), the rate of inflation in Germany is a positive function of European money supply and a positive function of German government purchases. According to equation (2), the rate of inflation in France is a positive function of European money supply and a positive function of French government purchases. According to equation (3), the rate of unemployment in Germany is a negative function of European money supply and a negative function of German government purchases. According to equation (4), the rate of unemployment in France is a negative function of European money supply and a negative function of French government purchases.

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.