Small Union of Three Countries

The model can be captured by a system of four equations: (1)$$ {{\text{Y}}_{{\text{1}}}} = {\text{ c}}{{\text{Y}}_{{\text{1}}}} + {\text{ }}{{\text{I}}_{{\text{1}}}} + {\text{ }}{{\text{G}}_{{\text{1}}}} + {\text{ he }} - {\text{ q}}{{\text{Y}}_{{\text{1}}}} + {\text{ m}}{{\text{Y}}_{{\text{2}}}} + {\text{ m}}{{\text{Y}}_{{\text{3}}}} $$(2)$$ {{\text{Y}}_{{\text{2}}}} = {\text{ c}}{{\text{Y}}_{{\text{2}}}} + {\text{ }}{{\text{I}}_{{\text{2}}}} + {\text{ }}{{\text{G}}_{{\text{2}}}} + {\text{ he }} + {\text{ m}}{{\text{Y}}_{{\text{1}}}} - {\text{ q}}{{\text{Y}}_{{\text{2}}}} + {\text{ m}}{{\text{Y}}_{{\text{3}}}} $$(3)$$ {{\text{Y}}_{{\text{3}}}} = {\text{ c}}{{\text{Y}}_{{\text{3}}}} + {{\text{I}}_{{\text{3}}}} + {\text{ }}{{\text{G}}_{{\text{3}}}} + {\text{ he }} + {\text{ m}}{{\text{Y}}_{{\text{1}}}} + {\text{ m}}{{\text{Y}}_{{\text{2}}}} - {\text{ q}}{{\text{Y}}_{{\text{3}}}} $$(4)$$ {\text{M }} = {\text{ k}}{{\text{Y}}_{{\text{1}}}} + {\text{k}}{{\text{Y}}_{{\text{2}}}} + {\text{k}}{{\text{Y}}_{{\text{3}}}} $$ 1 stands for union country 1, 2 for union country 2, and 3 for union country 3. Equations (1), (2) and (3) are the goods market equations. Equation (4) is the money market equation. The union countries are the same size and have the same behavioural functions. The parameters of the model are the marginal consumption rate c, the exchange rate sensitivity of exports h, the income sensitivity of money demand k, the marginal import rate relative to another union country m, and the overall marginal import rate q. The exogenous variables are national government purchases G_i? national investment I_i? and union money supply M. The endogenous variables are the union exchange rate e and national income Y_i.