Aufgabe:
Consider the following six equation Keynesian model for a closed economy:
Y =F(K,L)
\( \begin{aligned} W / P &=F_{L}=\frac{\partial F(K, L)}{\partial L} \\ C &=C(Y-T, r), \quad 0<\frac{\partial C(Y-T, r)}{\partial Y}<1, \frac{\partial C(Y-T, r)}{\partial r}<0 \\ I &=I(r), \quad \frac{\partial I(r)}{\partial r}<0 \\ Y &=C+I+G \\ \frac{M}{P} &=m(Y, r), \quad \frac{\partial m(Y, r)}{\partial Y}>0, \frac{\partial m(Y, r)}{\partial r}<0 \end{aligned} \)
where the definition of the variables is standard and the production function has the usual properties.
(i) Linearize the equation system and bring it into matrix form.
(Hint: The endogenous variables of the model are Y , L, P , C, I and r. Exogeneous variables are K, T, G, M and W.)
