(Solved): 1) Using the formula for the consumption function ( C=A+[mpcx income]) and the formula for the savi ...

1) Using the formula for the consumption function ( $\mathrm{C}=\mathrm{A}+[\mathrm{mpc}\mathrm{x}$ income]) and the formula for the savings function $(\mathrm{S}=-\mathrm{S}+[\mathrm{mps}\mathrm{x}$ income] $)$ calculate consumption, average propensity to consume, savings, and average propensity to save at the following levels of income. Autonomous consumption (consumption when income $=\$0$ ) is $\$5000$ and mupe is .9. (mope is the percentage of an increase in one's income that is consumed; $.9=90\%$ of an increase in income will be consumed) Example: income $=\$15,000$ \begin{tabular}{|c|c|c|c|} \hline $\mathrm{C}=\$19,000$ & $\$3500$ & $APC=1.23$ & APS $=-23$ \\ \hline \begin{tabular}{l} $\$15,000$ income \\ $\times .9\times$ wos \\ \end{tabular} & \begin{tabular}{l} Income - consumption \\ $\$15,000-\$18,500$ \end{tabular} & \begin{tabular}{l} Consumption/ \\ Income \end{tabular} & \begin{tabular}{l} 1-APS \\ $1-1.23$ \end{tabular} \\ \hline$\$13,500$ & the negative & $\$18,500/$ & \\ \hline \begin{tabular}{l} $\$5000$ (ALWAYS ADD \\ Autonomous consumption \end{tabular} & means dissaving & $\$15,000$ & \\ \hline \end{tabular} $=\$18,500$ a) Income $=\$25,000$ $\mathrm{C}=$ $\mathrm{S}=$ $\mathrm{APC}=$ APS= b) income $=\$50,000$ $\mathrm{C}=\mathrm{S}=$ $\mathrm{APC}=$ APS= c) income $=\$100,000$ $\mathrm{C}=\mathrm{S}=$ $\mathrm{APC}=$ APS= 2) calculate the spending multiplier when Formula $=1/($ mps + mpi) stepe one: calculate mps by doing 1 -mmp step 2; plug that mps into the formula for the multiplier If the $\mathrm{MPC}=.8$ and ${}_{212}=.13$, calculate the multiplier Step $1;\mathrm{mps}=.2(1-.8)$ Step $2:1/(.2+.13)=1/.33=3$ a) $\mathrm{mpc}=.85$, ${\mathrm{mpi}}^{-1}=1$ b) ${\mathrm{mpC}}^2=.95,\mathrm{mpi}=.05$ c) $\mathrm{mpc}=.6$, $\mathrm{mpi}=.1$ 3) based on the multiplier calculated in (a), a $\$200$ million increase in autenomus spending will lead to a increase in GDP. (increase $x$ multiplier) 5) based on the multiplier calculated in (A), a GDP gap of $\$100$ million can be closed with an increase of (GDP gap divided by the multiplier) in spending, also called the recessionary gap.