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


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 Giskard's comment, this approach is only appropriate when working in 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.

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    $\begingroup$ Isn't the dot notation exclusive to continuous time models? $\endgroup$
    – Giskard
    Oct 30 at 13:56
  • $\begingroup$ 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. $\endgroup$ Oct 30 at 14:07
  • $\begingroup$ @A_Reinhardt The difficulty with $rD$ is that again it could easily be read as two variables multiplied together. $\endgroup$ Oct 30 at 17:14
  • $\begingroup$ 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 $G_{t=4}$=$V_{t3}$ $r_{t4}$. $\endgroup$ Oct 30 at 17:46
  • $\begingroup$ 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! $\endgroup$ Oct 30 at 17:48

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