<p>The output defined with spending approach: <span class="math-container">$Y\equiv C+I+G+NX$</span> is an identity because it holds by definition. By definition output must be equal to sum of spending, investment government spending and net exports. However, this is actually <strong>not</strong> the equilibrium condition.</p>
<p>The equilibrium condition is that goods market demand <span class="math-container">$Z$</span> must be equal to output in the equilibrium. Hence the equilibrium condition is that <span class="math-container">$Z=Y$</span> (this is really just macro version of saying that demand = supply, since output <span class="math-container">$Y$</span> is the supply). This is the equilibrium condition not the identity <span class="math-container">$Y\equiv C+I+G+NX$</span>. However, <em>given</em> that the equilibrium condition is that <span class="math-container">$Z=Y$</span> we can from that deduce the following: <span class="math-container">$Z=Y \implies Z= C+ I + G + NX$</span> <em>in equilibrium</em>.</p>
<p>This might be easier to explain with graph. Consider the following graph from Blanchard et al. Macroeconomics a European Perspective pp 47. In the graph below the demand is the purple line while the identity <span class="math-container">$Y \equiv C+I+G$</span> (they omit net exports for simplicity) is the <span class="math-container">$45°$</span> line that just definitionally says output is equal to output.</p>
<p><a href="https://i.sstatic.net/M87kT.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/M87kT.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2020-11-21T13:36:30.227Z
2020-11-21T14:21:09.663Z
2020-11-21T14:21:09.663Z
1muflon1
<p>This is an important question which is usually covered in good undergraduate texts. You are correct in pointing out that the two <em>appear</em> to be same. But there is a subtle difference.</p>
<p>The difference comes through the definition of <span class="math-container">$I$</span>. The Income-Expenditure Identity is an accounting identity in which <span class="math-container">$I$</span> is the realized investment expenditure which includes <em>changes</em> in inventory.</p>
<p>In the Goods market equilibrium, <span class="math-container">$I$</span> (in some good texts denoted by <span class="math-container">$I_p$</span>) is the investment demand or planned investment expenditure (hence the subscript <span class="math-container">$p$</span>). This is a function of real interest rate <span class="math-container">$r$</span> which gives you IS curve with equilibrium a function of income <span class="math-container">$Y$</span> and interest rate <span class="math-container">$r$</span>. Clearly, this does not include the changes in inventory (at least not the unplanned ones).</p>
<p>You can see <a href="https://faculty.washington.edu/danby/bls324/macro/bop/1-3new.html" rel="nofollow noreferrer">this</a> link for some more details and examples.</p>

CC BY-SA 4.0
2020-11-21T13:35:18.993Z
2020-11-21T13:35:18.993Z
Dayne
<p>Is there any difference between the Income-Expenditure Identity and the Goods Market Equilibrium condition. Both are <span class="math-container">$Y=C+I+G+NX$</span>. If it is an identity, why do we solve for the equilibrium output? Shouldn't it always hold? If someone could clarify this it would be very helpful.</p>

<macroeconomics><national-accounts>
Difference between Income-Expenditure Identity and the Goods Market Equilibrium condition
MrAP
# Difference between Income-Expenditure Identity and the Goods Market Equilibrium condition

(Asked by: username_0 on 2020-11-21)

Is there any difference between the Income-Expenditure Identity and the Goods Market Equilibrium condition. Both are $Y=C+I+G+NX$. If it is an identity, why do we solve for the equilibrium output? Shouldn't it always hold? If someone could clarify this it would be very helpful.

**Tags:** macroeconomics, national-accounts

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## 2 answers

### Answer by username_1 on 2020-11-21. Score: 2

The output defined with spending approach: $Y\equiv C+I+G+NX$ is an identity because it holds by definition. By definition output must be equal to sum of spending, investment government spending and net exports. However, this is actually **not** the equilibrium condition.

The equilibrium condition is that goods market demand $Z$ must be equal to output in the equilibrium. Hence the equilibrium condition is that $Z=Y$ (this is really just macro version of saying that demand = supply, since output $Y$ is the supply). This is the equilibrium condition not the identity $Y\equiv C+I+G+NX$. However, *given* that the equilibrium condition is that $Z=Y$ we can from that deduce the following: $Z=Y \implies Z= C+ I + G + NX$ *in equilibrium*.

This might be easier to explain with graph. Consider the following graph from Blanchard et al. Macroeconomics a European Perspective pp 47. In the graph below the demand is the purple line while the identity $Y \equiv C+I+G$ (they omit net exports for simplicity) is the $45°$ line that just definitionally says output is equal to output.

[![enter image description here](https://i.sstatic.net/M87kT.png)](https://i.sstatic.net/M87kT.png)


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### Answer by username_2 on 2020-11-21. Score: 1

This is an important question which is usually covered in good undergraduate texts. You are correct in pointing out that the two *appear* to be same. But there is a subtle difference.

The difference comes through the definition of $I$. The Income-Expenditure Identity is an accounting identity in which $I$ is the realized investment expenditure which includes *changes* in inventory.

In the Goods market equilibrium, $I$ (in some good texts denoted by $I\_p$) is the investment demand or planned investment expenditure (hence the subscript $p$). This is a function of real interest rate $r$ which gives you IS curve with equilibrium a function of income $Y$ and interest rate $r$. Clearly, this does not include the changes in inventory (at least not the unplanned ones).

You can see [this](https://faculty.washington.edu/danby/bls324/macro/bop/1-3new.html) link for some more details and examples.


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