Consider the following GDP equation, consumption function, exports func$-$

tion, imports function and investment function and use them to answer the

following questions

Yt $=$ Ct $+$ It $+$ Gt $+$ EXt $$ IMt

It

$$Yt

$=$ai $$b $($Rt $$r$)$ ; $$b $>0$

Ct

$$Yt

$=$ac $+$x $$Yt; $0<$x $<1$

G $=$ag $$Yt

EX $=0$

IM $=0$

$($a$)$ Derive the IS curve as a relation between short run output $$Yt and the

real interest rate gap Rt $$r $(8$ points $)$

$5$

Find the government spending multiplier

d $$Y

d $$ag

holding the real interest

rate constant. Is the multiplier greater than one or smaller than one? Briefly

provide intuition for your answer along with mathematical reasoning. $(4$ points$)$

$($c$)$ Consider the following MP curve where monetary policy and real interest

rates now depends on the short$-$run output.

Rt $$r $=$m $($t $$$)+$n $$Yt

Derive the AD curve. $(5$ points$)$

$($d$)$ Find the government spending multiplier

d $$Y

d $$ag

$,$ holding inflation fixed.

If $$n is positive, is the multiplier higher or lower than in part c$?$

$($e$)$ Briefly explain what is Ricardian equivalence.