B$2.$ Closed Economy IS$-$LM$-$FE model: The behaviour of households and $$rms in a closed economy is represented by the following equations: Desired consumption : C d $=200+0$:$8($Y T$)500$r Desired investment : I d $=200500$r Real money demand : Md P $=0$:$5$Y $250($r $+$ e $)$ where expected in$$ation is e $=0$:$10$ and taxes depend on income according to T $=20+0$:$25$Y: Government purchases are represented by G$.($a$)$ Derive an expression for the IS curve with the real interest rate on the left side of the equation. How does the position of the IS curve depend on G$?($b$)$ If the money supply is M $=9890$ derive an expression for the LM curve, with the real interest rate on the left side of the equation. How does the position of the LM curve depend on P$?($c$)$ If government purchases are G $=196,$ derive an expression for the aggregate demand curve. If the full$-$employment output level is Y $=1000,$ what is the price level and the real interest rate in general equilibrium? $($d$)$ Starting from the situation in part $($c$),$ suppose government purchases are increased to G $=216,$ what are the resulting values of Y; r$,$ P$,$ T$,$ C d and I d in the short$-$run? $($e$)$ How does the economy adjust to its new general equilibrium after the change in part $($d$)?$ What are the resulting general equilibrium values of Y; r$,$ P$,$ T$,$ C d and I d