Question $4$: IS$-$LM Framework

Consider the following economy:

$C=700+0\mathrm{.}8(Y-0\mathrm{.}2Y)-200$

$\frac{M^d}{p}=0\mathrm{.}4Y-40R$

$\frac{M^s}{P}=1200$

$G=500$

$Nx=300-0\mathrm{.}04Y-15R$

$I=500-25R$

Use the information provided to:

a$.$ Derive the IS curve and state its slope.

b$.$ Derive the LM curve and state its slope.

$(5$ marks$)$

$(5$ marks$)$

c$.$ Calculate the equilibrium interest rate and output level. Illustrate both relationships on a graph.

$(10$ marks$)$

$($Total $20$ marks$)$ Show all working