Question

Consider the following goods and money market equations. Identify the CORRECT option(s).

• A. The IS equation is \(i=73.75-0.05Y\)
• B. The LM equation is \(i=0.0133Y-13.33\)
• C. The equilibrium \(i=7\) and \(Y=1400\)
• D. If \(G\) decreases to \(200\), then new equilibrium \(i=4\) and \(Y=1200\)

Hint:

To solve IS-LM questions, first derive IS from goods market equilibrium and LM from money market equilibrium, then equate both equations to find equilibrium \(Y\) and \(i\).

Answer 1

The Correct Option is A, B

Step 1: Build the consumption line.
With $C=20+0.75(Y-T)$ and $T=-40+0.2Y$, the disposable income is $Y-T=0.8Y+40$, so
\[ C=50+0.6Y \]

Step 2: Get the IS equation.
Using $Y=C+I+G$ with $I=240-8i$ and $G=300$,
\[ 0.4Y=590-8i\;\Rightarrow\;i=73.75-0.05Y \]
So option A is correct.

Step 3: Get the LM equation.
Setting money supply $200$ equal to demand $0.2Y-15i$,
\[ i=0.0133Y-13.33 \]
So option B is correct.

Step 4: Solve for equilibrium.
Equating IS and LM gives $Y\approx1375$ and $i\approx5$, not the $1400$ and $7$ in option C, so C is wrong.

Step 5: Test the cut in G.
With $G=200$ the new solution is about $Y\approx1178$ and $i\approx2.4$, not the values in option D, so D is wrong.
\[ \boxed{(A)\text{ and }(B)} \]