<p>If you are going to use <span class="math-container">$RG$</span> for rate of growth, then it is clearer not to make the <span class="math-container">$G$</span> into a subscript.  So <span class="math-container">$RG_{t4}$</span> is better than <span class="math-container">$R_{Gt4}$</span>.</p>
<p>However, using two letters together for rate of growth, or any other variable, is potentially confusing as a reader might assume <span class="math-container">$R$</span> is one variable and <span class="math-container">$G$</span> is another, so that <span class="math-container">$RG$</span> is two variables multiplied together.  So best would be to use a single letter for rate of growth, a common notation in economics being <span class="math-container">$g$</span>.</p>
<p>An alternative approach widely used in economics is dot notation, that is, placing a dot over a variable to indicate a rate of change of that variable.  If for example <span class="math-container">$Y$</span> is income, then <span class="math-container">$\dot{Y}$</span> would be rate of change of income. Note however that, as pointed out in Giskard's comment, this approach is only appropriate when working in <a href="https://en.wikipedia.org/wiki/Discrete_time_and_continuous_time" rel="nofollow noreferrer">continuous time</a>. So it would not be appropriate to use it to represent a rate of change between, say, income in one year and income in the next year.</p>

CC BY-SA 4.0
2021-10-30T13:56:04.567Z
Isn't the dot notation exclusive to continuous time models?
Giskard
CC BY-SA 4.0
2021-10-30T14:07:10.913Z
Thank you! It makes sense. How about using the small italic r for rate and then capital D: $rD$? I usually see both capital and small letters being used for rates, but I could not figure out the reason.
A_Reinhardt
CC BY-SA 4.0
2021-10-30T17:14:17.723Z
@A_Reinhardt  The difficulty with $rD$ is that again it could easily be read as two variables multiplied together.
Adam Bailey
CC BY-SA 4.0
2021-10-30T17:46:45.307Z
Thank you very much, Adam for your kind responses. As per your suggestion, I will go with two different single letters for these two rates (e.g., $r$ for rate of growth and $p$ for rate of depreciation. However, I also would to ask whether the convention with rates is to use small letters instead of capitals?
Another question is whether I use the time identifiers correctly. For example, if say “… the growth at t4 ($G_{t4}$) equals 50 million as per the below equation: $G_{t4}$=$V_{t3}$ $r_{t4}$” or should I state this as $G_{t=4}$=$V_{t3}$ $r_{t4}$.
A_Reinhardt
CC BY-SA 4.0
2021-10-30T17:48:59.600Z
Or (!) is the best practice to give a general formula for time t, as: $G_{t}$=$V_{t-1}$ $r_{t}$. Should I not use equations for specific years in my examples? Thanks and sorry for the bombardment of questions!
A_Reinhardt
CC BY-SA 4.0
2021-10-30T18:20:34.483Z
@A_Reinhardt I'm not sure what exactly you mean by $G$. But if it is the absolute amount of increase in $V$ in a period then your formula $G_t=V_{t−1}r_t$ is good, albeit whether it should be $r_t$ or $r_{t−1}$ would depend on how exactly the variables are defined (eg value at start or end of period, or total / average over period). Note that a more useful formula may be $V_t=V_{t−1}(1+r_t)$ which facilitates calculating values of $V$ over a number of periods. If you want to specify a particular period you don't usually need $G_{t4}$ or $G_{t=4}$: in most contexts you can just write $G_4$.
Adam Bailey
CC BY-SA 4.0
2021-10-30T18:38:48.270Z
Thank you Adam; that was exactly what I wanted to say. Regarding the question on time identifiers, someone wrote in a forum that one should never use a notation such as  $r_{t4}$, but should choose either $r_{4}$ or  $r_{t=4}$. This did not make sense to me, because I saw in economics and management journals that people use notation like  $r_{t4}$  $V_{t0}$ etc. I want to explain a hypothetical example in a few different years, since different events are supposed to occur in them.
A_Reinhardt
CC BY-SA 4.0
2021-10-30T12:11:39.630Z
2021-10-30T17:11:36.903Z
2021-10-30T17:11:36.903Z
Adam Bailey
<p>I need to write a couple of simple equations for a homework project. I wonder what the convention is with subscripts. I do not want to use Greek letters and keep it simple. I have a few variables such as as growth (G), asset value (V), and depreciation (D). But I also have rates that derive from them (e.g., rate of growth, rate of depreciation). How should I label these rate variables in equations (example below) ? Thank you!
<a href="https://i.sstatic.net/PLKFn.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/PLKFn.jpg" alt="enter image description here" /></a></p>

<macroeconomics><interest-rate><discount-rate>
Question on notation
A_Reinhardt
# Question on notation

(Asked by: username_0 on 2021-10-30)

I need to write a couple of simple equations for a homework project. I wonder what the convention is with subscripts. I do not want to use Greek letters and keep it simple. I have a few variables such as as growth (G), asset value (V), and depreciation (D). But I also have rates that derive from them (e.g., rate of growth, rate of depreciation). How should I label these rate variables in equations (example below) ? Thank you!
[![enter image description here](https://i.sstatic.net/PLKFn.jpg)](https://i.sstatic.net/PLKFn.jpg)

**Tags:** macroeconomics, interest-rate, discount-rate


---

## 1 answers

### Answer by username_1 on 2021-10-30. Score: 2 | Accepted answer

If you are going to use $RG$ for rate of growth, then it is clearer not to make the $G$ into a subscript. So $RG\_{t4}$ is better than $R\_{Gt4}$.

However, using two letters together for rate of growth, or any other variable, is potentially confusing as a reader might assume $R$ is one variable and $G$ is another, so that $RG$ is two variables multiplied together. So best would be to use a single letter for rate of growth, a common notation in economics being $g$.

An alternative approach widely used in economics is dot notation, that is, placing a dot over a variable to indicate a rate of change of that variable. If for example $Y$ is income, then $\dot{Y}$ would be rate of change of income. Note however that, as pointed out in username_2's comment, this approach is only appropriate when working in [continuous time](https://en.wikipedia.org/wiki/Discrete_time_and_continuous_time). So it would not be appropriate to use it to represent a rate of change between, say, income in one year and income in the next year.

> **Comments:**
> **username_2**: Isn't the dot notation exclusive to continuous time models?  
> **username_0**: Thank you! It makes sense. How about using the small italic r for rate and then capital D: $rD$? I usually see both capital and small letters being used for rates, but I could not figure out the reason.  
> **username_1**: @username_0  The difficulty with $rD$ is that again it could easily be read as two variables multiplied together.  
> **username_0**: Thank you very much, Adam for your kind responses. As per your suggestion, I will go with two different single letters for these two rates (e.g., $r$ for rate of growth and $p$ for rate of depreciation. However, I also would to ask whether the convention with rates is to use small letters instead of capitals? Another question is whether I use the time identifiers correctly. For example, if say “… the growth at t4 ($G_{t4}$) equals 50 million as per the below equation: $G_{t4}$=$V_{t3}$ $r_{t4}$” or should I state this as $G_{t=4}$=$V_{t3}$ $r_{t4}$.  
> **username_0**: Or (!) is the best practice to give a general formula for time t, as: $G_{t}$=$V_{t-1}$ $r_{t}$. Should I not use equations for specific years in my examples? Thanks and sorry for the bombardment of questions!  
> **username_1**: @username_0 I'm not sure what exactly you mean by $G$. But if it is the absolute amount of increase in $V$ in a period then your formula $G_t=V_{t−1}r_t$ is good, albeit whether it should be $r_t$ or $r_{t−1}$ would depend on how exactly the variables are defined (eg value at start or end of period, or total / average over period). Note that a more useful formula may be $V_t=V_{t−1}(1+r_t)$ which facilitates calculating values of $V$ over a number of periods. If you want to specify a particular period you don't usually need $G_{t4}$ or $G_{t=4}$: in most contexts you can just write $G_4$.  
> **username_0**: Thank you Adam; that was exactly what I wanted to say. Regarding the question on time identifiers, someone wrote in a forum that one should never use a notation such as  $r_{t4}$, but should choose either $r_{4}$ or  $r_{t=4}$. This did not make sense to me, because I saw in economics and management journals that people use notation like  $r_{t4}$  $V_{t0}$ etc. I want to explain a hypothetical example in a few different years, since different events are supposed to occur in them.  

---

