<p><strong>A1:</strong></p>
<p><span class="math-container">$S=I$</span>  is purely definitional. By definition the output (I assume closed economy for simplicity) is given by:</p>
<p><span class="math-container">$$Y = C+ I + G $$</span></p>
<p>saving <em>by definition</em> is equal to net income minus consumption:</p>
<p><span class="math-container">$$S= Y-T-C$$</span></p>
<p>as a consequence of the above definitions, which are by definition true identities:</p>
<p><span class="math-container">$$S + T +C = C+ I + G$$</span></p>
<p>and once we solve for <span class="math-container">$I$</span> we get:</p>
<p><span class="math-container">$$S + T- G  = I $$</span></p>
<p>So <em>by definition</em> investment <em>must</em> be equal to private <span class="math-container">$S$</span> and government <span class="math-container">$T-G$</span> saving. Many 101 textbooks will for simplicity assume government runs balanced budget so the definition boils down to <span class="math-container">$I=S$</span>.</p>
<p>However, as a consequence what is considered investment on national account does not correspond to layman understanding of investment. For example, store building an inventory of unsold goods counts as an &quot;inventory investment&quot;, similarly for household saving you will have a catch all term called &quot;saving-investment&quot; (see the <a href="https://www.bea.gov/sites/default/files/methodologies/nipa_primer.pdf" rel="nofollow noreferrer">Measuring the Economy
A Primer on GDP and
the National Income and
Product Accounts published by BEA</a>). Consequently, any required reserves are inconsequential, investment here does not necessarily mean investment in factories.</p>
<p><strong>A2:</strong></p>
<p>The leakages and injections have to end up being equal in a given period of time. If the amount of leakages increases then amount of income must raise to offset it.  Otherwise <span class="math-container">$Y=C+I+G$</span> would be violated.</p>
<p>The leakages and injections are actually based on this expression, which as explained above is purely definitional;</p>
<p><span class="math-container">$$S + T = I + G$$</span></p>
<p>where <span class="math-container">$S$</span> and <span class="math-container">$T$</span> are leakages and <span class="math-container">$I$</span> and <span class="math-container">$G$</span> are injections (dont forget we simplified to closed economy maybe your textbook also has <span class="math-container">$M$</span> and <span class="math-container">$X$</span> there for imports and exports).</p>
<p>If there is an increase in <span class="math-container">$S$</span> then simply either:</p>
<ul>
<li>Taxes must increase</li>
<li>Investment must increase</li>
<li>Government spending must increase</li>
</ul>
<p>or some combination of the above.</p>

CC BY-SA 4.0
2022-02-15T16:38:25.407Z
2022-02-15T16:38:25.407Z
1muflon1
<p>I’ve got a couple of questions regarding the real-time validity of the S = I equation.</p>
<ol>
<li>As far as I understand, the main intuition behind it is that all savings represent investment in one shape or another and the main argument here is that banks lend out the money that they receive from depositors. But what if there is a reserve requirement of 10%? How does that saving turn into investment if it’s not being lent out?</li>
<li>The circular flow of income assumes that intended saving and intended investment represent injections and leakages in and out of the flow with a possibility for either one to exceed or fall behind the other. How is that possible if saving is always equal to investment and how is it at all that investment could outpace saving? Where would the additional money come from?</li>
</ol>

CC BY-SA 4.0
2022-02-16T00:51:37.387Z
$S=I$ as a macroeconomic tautology is not really about money, but instead stuff measured in monetary terms.  See for example https://economics.stackexchange.com/questions/25839/s-i-in-a-closed-economy
Henry
<macroeconomics>
Saving = Investment as part of the GDP identity and circular flow of income
ThomasJ
# Saving = Investment as part of the GDP identity and circular flow of income

(Asked by: username_0 on 2022-02-15)

I’ve got a couple of questions regarding the real-time validity of the S = I equation.

1. As far as I understand, the main intuition behind it is that all savings represent investment in one shape or another and the main argument here is that banks lend out the money that they receive from depositors. But what if there is a reserve requirement of 10%? How does that saving turn into investment if it’s not being lent out?
2. The circular flow of income assumes that intended saving and intended investment represent injections and leakages in and out of the flow with a possibility for either one to exceed or fall behind the other. How is that possible if saving is always equal to investment and how is it at all that investment could outpace saving? Where would the additional money come from?

**Tags:** macroeconomics

> **Comments:**
> **username_1**: $S=I$ as a macroeconomic tautology is not really about money, but instead stuff measured in monetary terms.  See for example https://economics.stackexchange.com/questions/25839/s-i-in-a-closed-economy  

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## 1 answers

### Answer by username_2 on 2022-02-15. Score: 2

**A1:**

$S=I$ is purely definitional. By definition the output (I assume closed economy for simplicity) is given by:

$$Y = C+ I + G $$

saving *by definition* is equal to net income minus consumption:

$$S= Y-T-C$$

as a consequence of the above definitions, which are by definition true identities:

$$S + T +C = C+ I + G$$

and once we solve for $I$ we get:

$$S + T- G = I $$

So *by definition* investment *must* be equal to private $S$ and government $T-G$ saving. Many 101 textbooks will for simplicity assume government runs balanced budget so the definition boils down to $I=S$.

However, as a consequence what is considered investment on national account does not correspond to layman understanding of investment. For example, store building an inventory of unsold goods counts as an "inventory investment", similarly for household saving you will have a catch all term called "saving-investment" (see the [Measuring the Economy
A Primer on GDP and
the National Income and
Product Accounts published by BEA](https://www.bea.gov/sites/default/files/methodologies/nipa_primer.pdf)). Consequently, any required reserves are inconsequential, investment here does not necessarily mean investment in factories.

**A2:**

The leakages and injections have to end up being equal in a given period of time. If the amount of leakages increases then amount of income must raise to offset it. Otherwise $Y=C+I+G$ would be violated.

The leakages and injections are actually based on this expression, which as explained above is purely definitional;

$$S + T = I + G$$

where $S$ and $T$ are leakages and $I$ and $G$ are injections (dont forget we simplified to closed economy maybe your textbook also has $M$ and $X$ there for imports and exports).

If there is an increase in $S$ then simply either:

* Taxes must increase
* Investment must increase
* Government spending must increase

or some combination of the above.


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