Let's recompute the first four cycles using an MPC of 0.96.
### Part (a):
We start with an initial spending of [tex]$100.00 billion per year.
#### Cycle 1:
- Change in Spending: $[/tex]100.00 billion
- Cumulative Increase: [tex]$100.00 billion
#### Cycle 2:
- Change in Spending: \(100.00 \times 0.96 = 96.00\) billion
- Cumulative Increase: \(100.00 + 96.00 = 196.00\) billion
#### Cycle 3:
- Change in Spending: \(96.00 \times 0.96 = 92.16\) billion
- Cumulative Increase: \(196.00 + 92.16 = 288.16\) billion
#### Cycle 4:
- Change in Spending: \(92.16 \times 0.96 = 88.47\) billion
- Cumulative Increase: \(288.16 + 88.47 = 376.63\) billion
So, the table will be filled as follows:
\begin{tabular}{|c|c|c|c|c|}
\hline \multirow[b]{2}{*}{\begin{tabular}{l}
Spending \\
Cycles
\end{tabular}} & \multicolumn{2}{|c|}{$[/tex]M P C=0.75[tex]$} & \multicolumn{2}{|c|}{$[/tex]M P C=0.96[tex]$} \\
\hline & \begin{tabular}{l}
Change in Spending \\
during Cycle \\
(Billions per Year)
\end{tabular} & \begin{tabular}{l}
Cumulative Increase \\
in Spending (Billions \\
per Year)
\end{tabular} & \begin{tabular}{l}
Change in Spending \\
during Cycle \\
(Billions per Year)
\end{tabular} & \begin{tabular}{l}
Cumulative Increase \\
in Spending (Billions \\
per Year)
\end{tabular} \\
\hline 1 & $[/tex]\[tex]$ 100.00$[/tex] & [tex]$\$[/tex] 100.00[tex]$ & $[/tex]\[tex]$ 100.00$[/tex] & [tex]$\$[/tex] 100.00[tex]$ \\
\hline 2 & 75.00 & 175.00 & 96.00 & 196.00 \\
\hline 3 & 56.25 & 231.25 & 92.16 & 288.16 \\
\hline 4 & 42.18 & 273.44 & 88.47 & 376.63 \\
\hline
\end{tabular}
### Part (b):
Calculate the additional consumption that occurs in the first four cycles when the MPC is 0.96 compared to when the MPC is 0.75.
- Cumulative increase after 4 cycles with MPC 0.96: 376.63 billion
- Cumulative increase after 4 cycles with MPC 0.75: 273.44 billion
Additional consumption \( = 376.63 - 273.44 = 103.2\) billion
So, the additional consumption is \( \$[/tex] 103.2 \) billion.
### Part (c):
Calculate the value of the multiplier.
#### Multiplier if MPC = 0.75:
[tex]\[
\text{Multiplier} = \frac{1}{1 - 0.75} = \frac{1}{0.25} = 4.00
\][/tex]
So, the multiplier if the MPC is 0.75 is 4.00.
