In a closed economy, the consumption function is given by C $=200+$

$0\mathrm{.}75($Y$-$T$).$ The investment function is I $=20025$r$.$ Government purchases and taxes are both $100.$

The money demand function in the economy is $($M$/$P$)$d $=$ Y $100$r$.$ The money supply M is $1,000$

and the price level P is $2.$

a$.$ Derive the equations of IS and LM curves.

b$.$ Find the equilibrium interest rate r and the equilibrium level of income Y$,$ given the

price is fixed. Graph the IS and LM curves and the equilibrium r and Y$.$

c$.$ Derive an equation for the aggregate demand curve in this economy