<p>In Keynesian model investment <em>is</em> saving.</p>
<p>By definition saving is (assuming no government taxes or spending to simplify math):</p>
<p><span class="math-container">$$S=Y-C \tag{*}$$</span></p>
<p>Next GDP in a close economy with no government spending is:</p>
<p><span class="math-container">$$Y=C+I \tag{**}$$</span></p>
<p>Now solve * for Y and substitute into **:</p>
<p><span class="math-container">$$S+C=C+I \implies S= I$$</span></p>
<p>Saving <em>is</em> investment. Consequently you can either write it as <span class="math-container">$Y=C+I$</span> or <span class="math-container">$Y=C+S$</span> but you can’t add both I and S that would be double counting the same thing.</p>

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2022-08-31T16:54:17.453Z
Thanks, for the quick reply, so qualitatively speaking, savings = investment because the investment goes back to paying for factor services, which will lead to a proportionate rise in savings in a linear model, right?
math and physics forever
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2022-08-31T17:21:37.370Z
@fhhh actually it’s even simpler, it’s purely definitional. Saving is any unconsumed resource, so by definition any time you are not consuming you are saving. Note in these models even unfinished production that is not consumed is considered saving and also investment (inventory investment). Hence there is no deep economic logic behind it. It’s simply because both saving and investment are simply defined as not consuming resources. Hence every portion of income you don’t consume automatically becomes saving (and at the same time investment) purely from the definition.
1muflon1
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2022-08-31T17:23:51.397Z
@fhhh it’s like in physics defining satellite as a thing that orbits another body (eg planet). Next in physics we define moon as the big white rock orbiting earth. Ergo purely from definition of satellite and moon we can say moon = satellite
1muflon1
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2022-08-31T16:49:23.827Z
2022-08-31T16:49:23.827Z
1muflon1
<p>In the simple keynesian model, the equilibrium is usually calculauted by dteremining where the aggreagate supply curve meets the aggregate demand curve curve, with the AS curve , usually taken to be a 45 degree line( So that all that is earned is spent). However, my concern is doesn't this assumption imply that Y is that Y doesn't include I(investment), whoch acts as an iincome for someone else, so shouldn't Y=C+S(consuption + investemt+ savings), and not just C+S?</p>

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2022-08-31T18:31:12.753Z
(1) Does "as income for someone else" mean that **usually consumption is income, *by barter***? (2) Does government spending in the simple Keynesian model include tax receipts, alone?
Nick Carducci for Carface Bank
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2022-09-01T10:15:32.767Z
a)Is incomeb) I think in the SKM, there are no taxes. AT least that's the model I've been taught
math and physics forever
<macroeconomics><general-equilibrium><keynesian-economics>
A question on the simple Keynesian model
math and physics forever
# A question on the simple Keynesian model

(Asked by: username_0 on 2022-08-31)

In the simple keynesian model, the equilibrium is usually calculauted by dteremining where the aggreagate supply curve meets the aggregate demand curve curve, with the AS curve , usually taken to be a 45 degree line( So that all that is earned is spent). However, my concern is doesn't this assumption imply that Y is that Y doesn't include I(investment), whoch acts as an iincome for someone else, so shouldn't Y=C+S(consuption + investemt+ savings), and not just C+S?

**Tags:** macroeconomics, general-equilibrium, keynesian-economics
> **Comments:**
> **username_1**: (1) Does "as income for someone else" mean that **usually consumption is income, *by barter***? (2) Does government spending in the simple Keynesian model include tax receipts, alone?  
> **username_0**: a)Is incomeb) I think in the SKM, there are no taxes. AT least that's the model I've been taught  

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## 1 answers

### Answer by username_2 on 2022-08-31. Score: 2 | Accepted answer

In Keynesian model investment *is* saving.

By definition saving is (assuming no government taxes or spending to simplify math):

$$S=Y-C \tag{\*}$$

Next GDP in a close economy with no government spending is:

$$Y=C+I \tag{\*\*}$$

Now solve \* for Y and substitute into \*\*:

$$S+C=C+I \implies S= I$$

Saving *is* investment. Consequently you can either write it as $Y=C+I$ or $Y=C+S$ but you can’t add both I and S that would be double counting the same thing.

> **Comments:**
> **username_0**: Thanks, for the quick reply, so qualitatively speaking, savings = investment because the investment goes back to paying for factor services, which will lead to a proportionate rise in savings in a linear model, right?  
> **username_2**: @fhhh actually it’s even simpler, it’s purely definitional. Saving is any unconsumed resource, so by definition any time you are not consuming you are saving. Note in these models even unfinished production that is not consumed is considered saving and also investment (inventory investment). Hence there is no deep economic logic behind it. It’s simply because both saving and investment are simply defined as not consuming resources. Hence every portion of income you don’t consume automatically becomes saving (and at the same time investment) purely from the definition.  
> **username_2**: @fhhh it’s like in physics defining satellite as a thing that orbits another body (eg planet). Next in physics we define moon as the big white rock orbiting earth. Ergo purely from definition of satellite and moon we can say moon = satellite  

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