I'll answer two question using a three sectors economy model (banking, household, production): a) What's the impact of changes in the MPS? b) What's the impact of investment return on output and income? For now, I'll only look at the short run model since I believe it is enough to answer you question stated above.
The short-run model
In this simple model economy, you have three main sectors: households, production, and banking. Each of them can be described by a set of accounts where income equal expenditure. For the household sector, income is composed wages and investment returns. This in turn is transformed into expenditure, through consumption and savings.
\begin{equation*}
W*N\ +\ rM_{-1} \ =\ C\ +\ \Delta M
\end{equation*}
$\displaystyle \begin{array}{{>{\displaystyle}l}}
Where:\\
W\ =\ Wage\ level\\
N\ =\ employment\ level\\
r\ =\ interest\ rate\\
M_{-1} \ =\ total\ savings\ at\ the\ previous\ period\\
C\ =\ consumption\ expense\\
\Delta M\ =\ change\ in\ savings
\end{array}$
We can add to those equation a consumption function, stating that households consume a certain part of income, a certain part of savings, and a certain level of autonomous consumption (to compensate for government expenditure) at each period:
\begin{equation*}
C\ =\ a_{0} \ +\ a_{1} YD\ +a_{2} \ M_{-1}
\end{equation*}
$\displaystyle \begin{array}{{>{\displaystyle}l}}
Where:\\
\\
YD\ =\ available\ income\ ( W*N\ +\ rM_{-1})\\
\ a_{0} \ =\ autonomous\ consumption\\
a_{1} \ =\ marginal\ propensity\ to\ consume\ income\\
a_{2} \ =\ marginal\ propensity\ to\ consume\ past\ savings
\end{array}$
As for the production sector, income will be equal to consumption and investment. This in turn is transformed into wages, depreciation payments, and interest payments.
\begin{equation*}
C\ +\ I\ =\ W*N\ +\ \delta K_{-1} \ +\ rL_{-1}
\end{equation*}
$\displaystyle \begin{array}{{>{\displaystyle}l}}
Where:\\
I\ =\ invesments\\
\delta \ =\ rate\ of\ depreciation\ of\ capital\\
K_{-1} \ =\ capital\ accumulation\ at\ previous\ period\\
L_{-1} \ =\ loan\ accumulation\ at\ previous\ period\\
r\ =\ interest\ rate
\end{array}$
The investment demand of businesses comes from previous economic output, and indicate that entrepreneurs increase their investment in growth period, and decrease investment during difficult times. Investment also provide liquidity for depreciation expenses:
\begin{gather*}
I\ =\ y\left( K^{T} -K_{-1}\right) \ +\ \delta K_{-1}\\
K^{T} \ =\ cY_{-1}
\end{gather*}
$\displaystyle \begin{array}{{>{\displaystyle}l}}
Where:\\
y\ =\ constant\ estimator\\
K^{T} =\ target\ level\ of\ capital\\
c\ =\ capital\ accumulation\ ratio\\
Y_{-1} \ =\ previous\ output
\end{array}$
Finally, it is assumed that banks act as simple financial intermediate, transforming savings into loans such that:
\begin{equation*}
rM\ =\ rL
\end{equation*}
Experimentations
a) So what happens if we change the MPS? To answer this question, we'll need to expend the output function, making it a function of available income:
\begin{gather*}
Y\ =\ C+I\\
Y=YD\ -\ \Delta M\ +\ I
\end{gather*}
So, an increase in the MPS would reduce output in the very short run. This would however be followed by a partial compensation through interest returns (see figure bellow).
b) Our second question is concerning the impact of investment returns on output. In this model, investment returns have no impact on short or long term output. This is because any changes in interest returns will be compensated by an immediate change in wages. However, interest rates become significant when we assume a different propensity to consume for wage and interest income. If the MPC is higher for wages, then any decrease in interest rate would increase short and long term output.
Reference
My post is entirely based on chapter 7 of Monetary economics by Marc Lavoie and Wynne Godley. I would encourage you to read it if you want more information, it's a pretty good book. My figure is also from this book.
