Question $3$: Comparative statics

A macro economy can be characterised by the following set of equations:

$S(Y,\frac{M}{P})+T(Y)=I(r)+G_0$

$L(Y,r)=\frac{M}{P}$

where $P$ is the price level and $\frac{M}{P}$ is referred to as "real balances". It is usually assumed that

a$)$ Find the Jacobian of this system and determine its sign.

b$)$ Write down the equilibrium identities with respect to $G_0$ and $P.$

c$)$ Analyse the comparative statics of the model when there is change in government

expenditures

d$)$ Find $\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}\text{p}}$ and discuss its economic interpretation