Consider the following numerical example of the IS-LM model:

\[
\begin{aligned}
C & =100+0.3 Y_{D} \\
I & =150+0.2 Y-1000 i \\
T & =100 \\
G & =200 \\
\bar{i} & =.01
\end{aligned}
\]

a. Find the equation for aggregate demand \((Y)\).

b. Derive the IS relation.

c. Derive the LM relation if the central bank sets an interest rate of \(1 \%\).

d. Solve for the equilibrium values of output, interest rate, \(C\) and \(I\).

e. Expansionary monetary policy. Suppose that the central bank increases money supply to 1500 . What is the impact of this expansionary monetary policy on the IS and LM curves? Find the new equilibrium values of output, interest rate, \(C\) and \(I\).

f. Expansionary fiscal policy. Suppose that the government increases its spending \(G\) to 300 . What is the impact of this expansionary fiscal policy on the IS and LM curves? Find the new equilibrium values of output, interest rate, \(C\) and \(I\).