Parts a$-$e of this problem are the same as Problem $5$ in Chapter $10$ of this workbook.$)$ Suppose that the following equations describe an economy $($C$,$ I, G$,$ T$,$ and Y are measured in billions of dollars and $r$ is measured in percent; for example. $r=10$ means $r=10$ percent$)$:

$C=170+0\mathrm{.}6(Y-T)$

$T=200$

$I=100-4r$

$G=350$

$(\frac{M}{P}{)}^d=L=0\mathrm{.}75Y-6r$

$\frac{M^S}{P}\frac{?}{b}=ar\frac{M}{\frac{?}{?}}$bar $(P)=735$

a$.$ Derive the equation for the IS curve. $($Hint: It is easier to solve for real output $Y$ here.$)$

b$.$ Derive the equation for the LM curve. $($Hint: Again, it is easier to solve for real output Y$.)$

c$.$ Now express both the IS and LM equations in terms of $r.$ Plot and graph both curves and calculate their slopes.

d$.$ Use the equations from Parts a and $b$ to calculate the equilibrium levels of real output $Y,$ the interest rate $r,$ planned investment I, and consumption $C.$

e$.$ At the equilibrium level of real output $Y,$ calculate the value of the government budget surplus.

f$.$ Suppose that $G$ increases by $36$ to $386.$ Derive the new IS and LM equations and plot and draw these curves on the graph you drew for Part c$.$

g$.$ What is the horizontal shift in the IS curve and$/$or the LM curve in Part $f($that is$,$ if $r$ remains constant, by how much does $Y$ increase on each curve$)?$

h$.$ Refer to the IS and LM equations you derived in Partf. With Y on the left$-$hand side of the equations, calculate the new equilibrium levels of real output $Y,$ the interest rate $r,$ planned investment I, and consumption $C.$

i$.$ Instead of increasing G$,$ suppose that the Fed sought to achieve the equilibrium CH level of real output $Y$ in Part $h$ through expansionary monetary policy alone. By how much would the Fed have to increase the money supply? $($Hint: Start by drawing the appropriate shifts in the IS curve and$/$or the LM curve in Parts $f$ and i$.)$

j$.$ Compare the equilibrium levels of consumption $C,$ government spending $G,$ an planned investment I in Parts $h$ and i$.$ Based on this comparison, why might some economists prefer expansionary fiscal policy while others prefer expansionary monetary policy?