Steps for Consider the following GDP equation, consumption function, exports function. imports function and investment function and use them to answer the following questions $1+=$ C$++$ I $+$ Gt $+$ EXt $-$ IMt It $$a $6$R F$6>0$ Ct $=$a$+$iY;$0<<1$ G $=$ agYt EX $=0$ IM $=0($a$)$ Derive the IS curve as a relation between short run output It and the real interest rate gap Rt $-$ T$.($b$)$ Find the government spending multiplier da$,)$ holding the real interest rate constant. $($c$)$ Is the multiplier derived in b$)$ greater than one or smaller than one? Briefly provide intuition for your answer along with mathematical reasoning. $($d$)$ Consider the following MP curve where monetary policy and real interest rates now depends on the short$-$run output. Derive the AD curve. $($e$)$ Find the government spending multiplier $($da$).$ If n is positive, is the multiplier higher or lower than in part c$).$