Central Bank and Governments Decide Sequentially

The static model. As a point of reference, consider the static model. It can be represented by a system of three equations:

$$ \begin{array}{*{20}l} {{\rm{u}}_1 {\rm{ = }}} & {{\rm{B}}_1 {\rm{ - \gamma M - \delta G}}_1 } & {\left( {\rm{1}} \right)} \\ {{\rm{u}}_2 {\rm{ = }}} & {{\rm{B}}_2 {\rm{ - \gamma M - \delta G}}_2 } & {\left( 2 \right)} \\ {{\rm{u = }}} & {0.5{\rm{u}}_1 + 0.5{\rm{u}}_2 } & {\left( 3 \right)} \\ \end{array} $$

Of course this is a reduced form. u₁ denotes the rate of unemployment inGermany, u₂ is the rate of unemployment in France, u is the rate of unemployment in Europe, M is European money supply, G₁ is German government purchases, G₂ is French government purchases, γ is the monetary policy multiplier, δ is the fiscal policy multiplier, B₁ is some other factors bearing on the rate of unemployment in Germany, and B₂ is some other factors bearing on the rate of unemployment in France.

The endogenous variables are the rates of unemployment in Germany, France and Europe. According to equation (1), 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 (2), the rate of unemployment in France is a negative function of European money supply and a negative function of French government purchases. According to equation (3), the rate of unemployment in Europe is the average of the rates of unemployment in Germany and France.