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I'm aware that certain terms in economics have precise definitions that don't necessarily line up with our intuition about what they mean. I'm currently writing a paper that heavily relies on the concept of scarcity, and I'd like to make sure I am using the term properly. Currently I have this sentence written:

Suppose widgets are a scarce resource that are distributed among agents

Then I rewrite this mathematically as $\mu = \sum\limits_{i=0}^n x_i$ where $x_i$ is the number of widgets agent $i$ has. I don't see any problems with this myself, but I'd like to make sure that economists view this as orthodox. Are there any references that I could use to verify this? Is this accurate? What is the precise definition of scarcity?

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A Dictionary of Economics states scarcity is: "The property of being in excess demand at a zero price. This means that in equilibrium the price of a scarce good or factor must be positive" This is the most authoritative source I've found so far, but this doesn't seem like a rigorous definition to me - it clearly isn't mathematically defined. Am I wrong about this?

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  • $\begingroup$ Can you consider this from a post-scarcity standpoint, and see what needs to be changed to get there? The difference, will point you towards what scarcity is. $\endgroup$ – Mast Nov 11 '19 at 19:15
  • $\begingroup$ I don't understand this comment. Do you mean viewing the model from a post scarcity standpoint? $\endgroup$ – K Pomykala Nov 13 '19 at 1:18
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Your formula $\mu = \sum\limits_{i=0}^n x_i$ just denotes the total amount of goods, so this just means that $\mu$ units were distributed among $n$ agents. Scarcity (in this context) means that no matter how you distribute these $\mu$ units, as long as everything else is unchanged (ceteris paribus) at least one agent would like to get more, i.e. $\forall (x_i)_{i = 0}^n$ where $\mu = \sum\limits_{i=0}^n x_i$ there is an agent $i$ and a positive $\epsilon$ such that $$ x_i \prec_i x_i + \epsilon. $$ This is context dependent, there may be other definitions as well (e.g. ones that allow for production).

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  • $\begingroup$ What about in general? Is there even a general definition? Does scarcity mean that agents ceteris paribus "want more"? $\endgroup$ – K Pomykala Nov 11 '19 at 16:18
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    $\begingroup$ @KPomykala No, that is non-satiation. Scarcity has to be about the quantity of some resource as well as someone wanting more. To my knowledge there is no general definition, as there are many different model frameworks. $\endgroup$ – Giskard Nov 11 '19 at 18:11
  • $\begingroup$ Ah, I quite like that conceptualization, the combination of finiteness of a quantity and non-satiation. Thank you a lot! Not trying to ask too much, but if you have a good source(preferably a textbook) that treats scarcity that way I would be absolutely thrilled! $\endgroup$ – K Pomykala Nov 13 '19 at 1:21
  • $\begingroup$ @KPomykala Sorry, I have no source. Equilibrium theory usually takes an easier route and makes the stronger assumption that preferences are non-satiable (or something similar). $\endgroup$ – Giskard Nov 13 '19 at 5:48
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There are two key properties for a scarce good. First that demand can get arbitrarily high if the price is low enough. So if you plot demand on the $x$-axis and price on the $y$-axis this function is decreasing for all $x$. Second is that production cost is non zero, producing more items will always cost more money. This is always the case for physical goods but not for things like intellectual property goods.

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  • $\begingroup$ Unfortunately I'm working in an extremely elementary model that isn't in the standard supply/demand framework. Price isn't even defined in it. Hence, why I'm having such a hard time trying to figure out where scarcity fits into it all. $\endgroup$ – K Pomykala Nov 13 '19 at 1:14
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Scarcity is a term which is often used in introductory textbooks and never properly defined. According to Walras, a good is scarce, if it is "useful to us [but] only available to us in limited quantity". That gives the idea, but is still somewhat vague. If you suggest a particular precise definition, typically many economists will disagree with it. Is air a scarce ressource? It is clearly "useful", but there is also a "limited quantity" of air on the planet. On the other hand, it is not in excess demand, even though its price is zero. So is air scarce? Some say yes, some say no, some say it depends on whether it is polluted or not, or on the degree of pollution, and so on. My Econ 101 teacher used to say the only nonscarce ressource is gravity...

My personal advice would be to just avoid using the term. It doesn't really appear in economic theory, and whether or not your widgets are scarce will be implicitly defined in your model w.r.t. any definition you have in mind.

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