Answered

Instructions: Round your responses to two decimal places.

a. Recompute the first four cycles using an MPC of 0.96.

\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow[b]{2}{*}{\begin{tabular}{l}
Spending \\
Cycles
\end{tabular}} & \multicolumn{2}{|c|}{[tex]$MPC=0.75$[/tex]} & \multicolumn{2}{|c|}{[tex]$MPC=0.96$[/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]$100.00 & \$[/tex]100.00 & \[tex]$100.00 & \\
\hline
2 & 75.00 & 175.00 & & \\
\hline
3 & 56.25 & 231.25 & & \\
\hline
4 & 42.18 & 273.44 & & \\
\hline
\end{tabular}

b. Given that the MPC is higher, how much more consumption occurs in the first four cycles when the MPC is 0.96 compared to when the MPC is 0.75?
\$[/tex] [tex]$\square$[/tex] billion

c. What is the value of the multiplier?

1. if the MPC [tex]$= 0.75$[/tex] ?
[tex]$\square$[/tex]



Answer :

GinnyAnswer
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.