In this question, we$$ll look at the IS$/$LM framework with algebraically and quantitatively.

Here are the relevant parameters and relationships to define the economy:

C $=550+0\mathrm{.}75($Y $$ T $)$

I$($r$)=40075$r

G $==750$

T $=750$

M$/$P $=0\mathrm{.}8$Y $200$r

M $=4500$

P $=4\mathrm{.}5$

$($a$)$ Derive the IS curve and LM curve, both where Y is a function of r$.($To help with

graphing, you might want to also solve IS and LM for r as a function of Y $,$ which will

graph more intuitively on the coordinate plane to which we$$re accustomed.$)$

$($b$)$ Calculate equilibrium values of r$$ and Y $$ that these IS and LM curves.

$($c$)$ Government spending increases to $1025.$ How much would this change in G shi$$ the

IS curve? What are the new values of r and Y $?$ Is the amount Y increased $($from Y $$

to the new Y $)$ the same as the change in the IS curve? Why or why not?

$($d$)$e monetary authority holds a meeting to discuss responses to this change in G$.$ One

side of the discussion advocates action to keep the interest rate at r$.$ How much will

M have to change to accomplish this goal? What will happen to output $($Y $)?$

$($e$)$e other side of the discussion is concerned about inflationary pressure if Y remains

higher than Y $$ for very long. $$ey propose action to restore output to Y $.$ How much

will M have to change to bring this result about? What will happen to the interest

rate $($r$)?$

$($f$)$ While the monetary authority is trying to decide how to act, inflation is going on in

the economy. $$e price level increases $25\%$ to $5\mathrm{.}625\%.$ With the change in G $($from

part c of this question$),$ but without any accommodating monetary policy $($discussed

in parts c or d$),$ what will this increase in the price level do to Y and r$?$