<p>Are you sure that <span class="math-container">$Y$</span> is a constant? Look at the right side of your equation.
<span class="math-container">$Y$</span> is determined by the variables included in the right side, so each time one of these variables changes, <span class="math-container">$Y$</span> changes.</p>
<p>From a mathematical point of view, you cannot say if a quantity represented by a symbol is a constant or not just looking at an equation, it should be said aside, that is it must be said outside the equation, for example &quot;<span class="math-container">$\alpha$</span> is a constant in <span class="math-container">$\mathbb{R}$</span>&quot;, &quot;<span class="math-container">$G$</span> is a constant&quot;, and so on.</p>
<p>And in an economic model it is the same:  in a model must be established <em>a</em> <em>priori</em>, in advance, which quantities are <em>exogenous</em> variables (that is, taken as fixed, determined <em>outside</em> the model) and which are <em>endogenous</em> variables, determined <em>by</em> the model (that is, the unknowns of the system of equations that constitute the model).</p>
<p>These are basic and very important notions when you study macroeconomic models.</p>
<p><strong>[edit]</strong>: you have modified your question, so my answer now is less appropriate.</p>
<p>As for your new question, if <span class="math-container">$Y$</span> is a constant, you can, of course, in principle, have a non constant variable on the right side. This implies, simply, that when the non constant variable, as <span class="math-container">$I(r)$</span>, varies, there is an other variable on the right side that varies at the same time, as to mantain <span class="math-container">$Y$</span> constant, at the same level.</p>
<p>This is true in general from a mathematical point of view, I don't understand very well what's your particular problem in your example.</p>
<p>If <em>all</em> variables are fixed except <span class="math-container">$Y$</span> it is not possible have <span class="math-container">$Y$</span> fixed and <span class="math-container">$I$</span> changing arbitrarily.</p>
<p>Maybe, you want to solve for <span class="math-container">$r$</span> so that you find the value of <span class="math-container">$r$</span> that makes the equality true, as when one wants to construct the IS curve.
But this just my guess.</p>

CC BY-SA 4.0
2022-09-10T16:21:43.037Z
Hi, thank you very much for your answer! You wrote: " when the non constant variable, as I(r), varies, there is an other variable on the right side that varies at the same time, as to mantain Y constant, at the same level." Could this be the variable C(.)? How could it be, when it depends on Y and T, which are constant? Thanks!
student
CC BY-SA 4.0
2022-09-10T16:41:59.637Z
What you say is true in general, if there are other variables, besides $I$ that can vary. Think of an equation as $10 = 6+2+ x$. The equality is true if $x=2$. You cannot change $x$ and give it a value different from $2$. But if you write $10=6+y+x$ you can change $x$ as you want, provided that you change also $y$ as to mantain the equality. I wrote also "If all variables are fixed except  it is not possible have  fixed and  changing arbitrarily." So, if Y, T, etc, are all fixed, you can't change $I$, you can't give to $I$ a value different from the value that fulfils the equality.
BakerStreet
CC BY-SA 4.0
2022-09-10T16:47:57.590Z
A different question is if you are looking for a value of $r$, for which the investment $I(r)$ (investment depends on $r$) fulfils the equation, for a given value of $Y$. This Is what we do when we look for the equation of the $IS$ curve.
BakerStreet
CC BY-SA 4.0
2022-09-11T06:19:35.860Z
Hi, thank you very much for your answer! So in that case, can we assume that I (Investment) is fixed, so I(r) is also fixed, although I(r) it doesn't have the 'constant' symbol?
student
CC BY-SA 4.0
2022-09-11T08:19:09.060Z
Yes, If the equality must hold, for a given value of $Y$ ,the investment must be fixed at the level that ensures equality. If $Y$ changes,  also this value of $I$ has to change. The 'constant symbol on $Y$ means that $Y$ has a given value, from which we can calculate the equilibrium $I(r)$.
BakerStreet
CC BY-SA 4.0
2022-09-11T12:51:13.627Z
You are welcome!
BakerStreet
CC BY-SA 4.0
2022-09-10T11:49:22.983Z
2022-09-10T14:12:25.697Z
2022-09-10T14:12:25.697Z
BakerStreet
<p>How could we include I(r), a non-constant variable, while Y̅, on the other side of the equation, is constant?</p>
<p>Thank you!</p>

<macroeconomics><mathematical-economics><economic-growth>
Question regarding the Y̅=C(Y̅–T̅)+I(r)+G̅ function
student
# Question regarding the Y̅=C(Y̅–T̅)+I(r)+G̅ function

(Asked by: username_0 on 2022-09-09)

How could we include I(r), a non-constant variable, while Y̅, on the other side of the equation, is constant?

Thank you!

**Tags:** macroeconomics, mathematical-economics, economic-growth

---

## 1 answers

### Answer by username_1 on 2022-09-10. Score: 1

Are you sure that $Y$ is a constant? Look at the right side of your equation.
$Y$ is determined by the variables included in the right side, so each time one of these variables changes, $Y$ changes.

From a mathematical point of view, you cannot say if a quantity represented by a symbol is a constant or not just looking at an equation, it should be said aside, that is it must be said outside the equation, for example "$\alpha$ is a constant in $\mathbb{R}$", "$G$ is a constant", and so on.

And in an economic model it is the same: in a model must be established *a* *priori*, in advance, which quantities are *exogenous* variables (that is, taken as fixed, determined *outside* the model) and which are *endogenous* variables, determined *by* the model (that is, the unknowns of the system of equations that constitute the model).

These are basic and very important notions when you study macroeconomic models.

**[edit]**: you have modified your question, so my answer now is less appropriate.

As for your new question, if $Y$ is a constant, you can, of course, in principle, have a non constant variable on the right side. This implies, simply, that when the non constant variable, as $I(r)$, varies, there is an other variable on the right side that varies at the same time, as to mantain $Y$ constant, at the same level.

This is true in general from a mathematical point of view, I don't understand very well what's your particular problem in your example.

If *all* variables are fixed except $Y$ it is not possible have $Y$ fixed and $I$ changing arbitrarily.

Maybe, you want to solve for $r$ so that you find the value of $r$ that makes the equality true, as when one wants to construct the IS curve.
But this just my guess.

> **Comments:**
> **username_0**: Hi, thank you very much for your answer! You wrote: " when the non constant variable, as I(r), varies, there is an other variable on the right side that varies at the same time, as to mantain Y constant, at the same level." Could this be the variable C(.)? How could it be, when it depends on Y and T, which are constant? Thanks!  
> **username_1**: What you say is true in general, if there are other variables, besides $I$ that can vary. Think of an equation as $10 = 6+2+ x$. The equality is true if $x=2$. You cannot change $x$ and give it a value different from $2$. But if you write $10=6+y+x$ you can change $x$ as you want, provided that you change also $y$ as to mantain the equality. I wrote also "If all variables are fixed except  it is not possible have  fixed and  changing arbitrarily." So, if Y, T, etc, are all fixed, you can't change $I$, you can't give to $I$ a value different from the value that fulfils the equality.  
> **username_1**: A different question is if you are looking for a value of $r$, for which the investment $I(r)$ (investment depends on $r$) fulfils the equation, for a given value of $Y$. This Is what we do when we look for the equation of the $IS$ curve.  
> **username_0**: Hi, thank you very much for your answer! So in that case, can we assume that I (Investment) is fixed, so I(r) is also fixed, although I(r) it doesn't have the 'constant' symbol?  
> **username_1**: Yes, If the equality must hold, for a given value of $Y$ ,the investment must be fixed at the level that ensures equality. If $Y$ changes,  also this value of $I$ has to change. The 'constant symbol on $Y$ means that $Y$ has a given value, from which we can calculate the equilibrium $I(r)$.  
> **username_1**: You are welcome!  

---

