<p>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.</p>
<p><em>The short-run model</em></p>
<p>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.</p>
<p><span class="math-container">\begin{equation*}
W*N\ +\ rM_{-1} \ =\ C\ +\ \Delta M
\end{equation*}</span></p>
<p><span class="math-container">$\displaystyle  \begin{array}{{&gt;{\displaystyle}l}}
Where:\\
W\ =\ Wage\ level\\
N\ =\ employment\ level\\
r\ =\ interest\ rate\\
M_{-1} \ =\ total\ savings\ at\ the\ previous\ period\\
C\ =\ consumption\ expense\\
\Delta M\ =\ change\ in\ savings
\end{array}$</span></p>
<p>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:</p>
<p><span class="math-container">\begin{equation*}
C\ =\ a_{0} \ +\ a_{1} YD\ +a_{2} \ M_{-1}
\end{equation*}</span></p>
<p><span class="math-container">$\displaystyle  \begin{array}{{&gt;{\displaystyle}l}}
Where:\\
\\
YD\ =\ available\ income\ ( W*N\ +\ rM_{-1})\\
\ a_{0} \ =\ autonomous\ consumption\\
a_{1} \ =\ marginal\ propensity\ to\ consume\ income\\
a_{2} \ =\ marginal\ propensity\ to\ consume\ past\ savings
\end{array}$</span></p>
<p>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.</p>
<p><span class="math-container">\begin{equation*}
C\ +\ I\ =\ W*N\ +\ \delta K_{-1} \ +\ rL_{-1}
\end{equation*}</span></p>
<p><span class="math-container">$\displaystyle  \begin{array}{{&gt;{\displaystyle}l}}
Where:\\
I\ =\ invesments\\
\delta \ =\ rate\ of\ depreciation\ of\ capital\\
K_{-1} \ =\ capital\ accumulation\ at\ previous\ period\\
L_{-1} \ =\ loan\ accumulation\ at\ previous\ period\\
r\ =\ interest\ rate
\end{array}$</span></p>
<p>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:</p>
<p><span class="math-container">\begin{gather*}
I\ =\ y\left( K^{T} -K_{-1}\right) \ +\ \delta K_{-1}\\
K^{T} \ =\ cY_{-1}
\end{gather*}</span></p>
<p><span class="math-container">$\displaystyle  \begin{array}{{&gt;{\displaystyle}l}}
Where:\\
y\ =\ constant\ estimator\\
K^{T} =\ target\ level\ of\ capital\\
c\ =\ capital\ accumulation\ ratio\\
Y_{-1} \ =\ previous\ output
\end{array}$</span></p>
<p>Finally, it is assumed that banks act as simple financial intermediate, transforming savings into loans such that:</p>
<p><span class="math-container">\begin{equation*}
rM\ =\ rL
\end{equation*}</span></p>
<p><em>Experimentations</em></p>
<p>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:</p>
<p><span class="math-container">\begin{gather*}
Y\ =\ C+I\\
Y=YD\ -\ \Delta M\ +\ I
\end{gather*}</span></p>
<p>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).</p>
<p><a href="https://i.sstatic.net/kl3Zk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/kl3Zk.png" alt="enter image description here" /></a></p>
<p>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.</p>
<p><em>Reference</em></p>
<p>My post is entirely based on chapter 7 of <em>Monetary economics</em> 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.</p>

CC BY-SA 4.0
2021-12-18T03:11:34.843Z
What if the savings have appreciated? Then it is no longer true that $Y = C + \Delta M$ because that $\Delta M$ would be equal to the output not spent on consumption *and* asset appreciation.
LudwigNagasena
CC BY-SA 4.0
2021-12-19T14:23:13.570Z
The identity is Y = C + I. Output includes produced goods, which are divided in two categories, consumption goods and investments goods.
Alexandre Michaud
CC BY-SA 4.0
2021-12-19T14:54:51.457Z
Yeah, what I wanted to say is that this model doesn't seem to take into account what I am interested in. If we say that $W*N\ +\ rM_{-1} \ =\ C\ +\ \Delta M$, it means that the monetary value of savings can only change by putting a part of income there, but what if the assets simply appreciate in value?
LudwigNagasena
CC BY-SA 4.0
2021-12-22T19:45:26.120Z
What do you mean by the "assets simply appreciate in value"? Are you referring to interest returns?
Alexandre Michaud
CC BY-SA 4.0
2021-12-23T03:06:50.370Z
Like the price of a stock moving from $\$20$ to $\$25$. Or maybe even simply holding money while the price level decreases.
LudwigNagasena
CC BY-SA 4.0
2021-12-16T18:41:35.920Z
2021-12-16T18:41:35.920Z
Alexandre Michaud
<p>As I understand, in the very basic macroeconomic model we have that <span class="math-container">$Y = C+S = C+I$</span> where <span class="math-container">$Y$</span>, <span class="math-container">$C$</span>, <span class="math-container">$S$</span> and <span class="math-container">$I$</span> are real goods measured in monetary terms.</p>
<p>Assume a steady state economy that produces <span class="math-container">$\\\$10$</span> of goods, <span class="math-container">$\\\$5$</span> of which are consumed, and <span class="math-container">$\\\$5$</span> of which are saved and invested. In such case there is a savings rate of <span class="math-container">$S/Y = 50\%$</span>.</p>
<p>However, imagine if the government now prints <span class="math-container">$\\\$10$</span> each period and gives them directly to people, and people just keep them. Then, the financial income people have has increased, but the “savings rate” stays the same. However, what we actually think of savings rate in normal life has increased and it would be <span class="math-container">$75\%$</span>.</p>
<p>Or what if the capital appreciates over time (or just once, eg if a risky investment was successful). This will, again, lead to an increase in financial income, but to no change in the savings rate in the sense of <span class="math-container">$S/Y$</span>.</p>
<p>People, obviously, don’t care whether the income they get is from financial or real sources, money is fungible. This would imply that MPS is irrelevant. What am I missing?</p>

CC BY-SA 4.0
2021-12-15T02:56:18.537Z
Could you detail why you think the saving rate is irrelevant? I'll answer will more information :)
Alexandre Michaud
CC BY-SA 4.0
2021-12-15T04:26:58.983Z
I think my examples show the discrepancy. I will try to come up with a better explanation: Imagine an agent whose wealth has increased (by asset appreciation or money printing). This is a purely financial phenomenon and has no impact on Y that measures real production. But for an agent it is as real as any increase of his wealth caused by production. After all, it is all just money. So why would the total consumption depend on Y (eg as $C = a_0+a_1Y$) and not on total financial income that includes money creation and asset appreciation?
LudwigNagasena
CC BY-SA 4.0
2021-12-15T13:51:09.843Z
Consumption depends on available income, not total output. I believe you might have misread something. I can detail a simple model with bank money (I believe there's no government in your exemple) if you want. Would that help?
Alexandre Michaud
CC BY-SA 4.0
2021-12-15T14:39:06.073Z
Just to rectify, in a three sectors economy (production, banking, households), consumption depends on investment returns, savings (because you consume a part of savings), and available income.
Alexandre Michaud
CC BY-SA 4.0
2021-12-16T05:44:02.507Z
In this basic economy the whole income is disposable as people don’t spend money on taxes or anything else. It either goes to savings or consumption. This consumption function is something I have seen virtually everywhere that discusses basic macroeconomics. Yes, if you could do it, I would like to see how investment returns (if this includes asset appreciation) factor in the model. The whole thing seems confusing because what I would understand in normal life as “income” doesn’t seem to be a part of what is called “income” in the model.
LudwigNagasena
CC BY-SA 4.0
2021-12-16T18:42:23.620Z
It's done, you can comment the answer if you want more information :)
Alexandre Michaud
<macroeconomics><nonexpert>
The impact of finance in the basic macroeconomic model
LudwigNagasena
# The impact of finance in the basic macroeconomic model

(Asked by: username_0 on 2021-12-14)

As I understand, in the very basic macroeconomic model we have that $Y = C+S = C+I$ where $Y$, $C$, $S$ and $I$ are real goods measured in monetary terms.

Assume a steady state economy that produces $\\\$10$ of goods, $\\\$5$ of which are consumed, and $\\\$5$ of which are saved and invested. In such case there is a savings rate of $S/Y = 50\%$.

However, imagine if the government now prints $\\\$10$ each period and gives them directly to people, and people just keep them. Then, the financial income people have has increased, but the “savings rate” stays the same. However, what we actually think of savings rate in normal life has increased and it would be $75\%$.

Or what if the capital appreciates over time (or just once, eg if a risky investment was successful). This will, again, lead to an increase in financial income, but to no change in the savings rate in the sense of $S/Y$.

People, obviously, don’t care whether the income they get is from financial or real sources, money is fungible. This would imply that MPS is irrelevant. What am I missing?

**Tags:** macroeconomics, nonexpert
> **Comments:**
> **username_1**: Could you detail why you think the saving rate is irrelevant? I'll answer will more information :)  
> **username_0**: I think my examples show the discrepancy. I will try to come up with a better explanation: Imagine an agent whose wealth has increased (by asset appreciation or money printing). This is a purely financial phenomenon and has no impact on Y that measures real production. But for an agent it is as real as any increase of his wealth caused by production. After all, it is all just money. So why would the total consumption depend on Y (eg as $C = a_0+a_1Y$) and not on total financial income that includes money creation and asset appreciation?  
> **username_1**: Consumption depends on available income, not total output. I believe you might have misread something. I can detail a simple model with bank money (I believe there's no government in your exemple) if you want. Would that help?  
> **username_1**: Just to rectify, in a three sectors economy (production, banking, households), consumption depends on investment returns, savings (because you consume a part of savings), and available income.  
> **username_0**: In this basic economy the whole income is disposable as people don’t spend money on taxes or anything else. It either goes to savings or consumption. This consumption function is something I have seen virtually everywhere that discusses basic macroeconomics. Yes, if you could do it, I would like to see how investment returns (if this includes asset appreciation) factor in the model. The whole thing seems confusing because what I would understand in normal life as “income” doesn’t seem to be a part of what is called “income” in the model.  
> **username_1**: It's done, you can comment the answer if you want more information :)  

---

## 1 answers

### Answer by username_1 on 2021-12-16. Score: 2

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).

[![enter image description here](https://i.sstatic.net/kl3Zk.png)](https://i.sstatic.net/kl3Zk.png)

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.

> **Comments:**
> **username_0**: What if the savings have appreciated? Then it is no longer true that $Y = C + \Delta M$ because that $\Delta M$ would be equal to the output not spent on consumption *and* asset appreciation.  
> **username_1**: The identity is Y = C + I. Output includes produced goods, which are divided in two categories, consumption goods and investments goods.  
> **username_0**: Yeah, what I wanted to say is that this model doesn't seem to take into account what I am interested in. If we say that $W*N\ +\ rM_{-1} \ =\ C\ +\ \Delta M$, it means that the monetary value of savings can only change by putting a part of income there, but what if the assets simply appreciate in value?  
> **username_1**: What do you mean by the "assets simply appreciate in value"? Are you referring to interest returns?  
> **username_0**: Like the price of a stock moving from $\$20$ to $\$25$. Or maybe even simply holding money while the price level decreases.  

---

