Question

Consider the following equations for a closed economy:

Hint:

In dynamic macroeconomic models, first impose the equilibrium condition \(S=I\), then derive the recursive relation connecting current and previous income levels.

Answer 1

Correct Answer: 3600

Step 1: Use the equilibrium rule.
In this closed economy saving equals investment, so with $S_t=aY_t$ and $I_t=g(Y_t-Y_{t-1})$,
\[ aY_t=g(Y_t-Y_{t-1}) \]

Step 2: Put in the numbers.
With $a=0.5$ and $g=0.6$,
\[ 0.5Y_t=0.6Y_t-0.6Y_{t-1} \]

Step 3: Rearrange.
\[ 0.1Y_t=0.6Y_{t-1}\;\Rightarrow\;Y_t=6Y_{t-1} \]

Step 4: Step forward from Y0.
With $Y_0=100$, we get $Y_1=6(100)=600$.

Step 5: One more step.
\[ Y_2=6(600)=3600 \]
\[ \boxed{3600} \]