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I've been reading quite a bit about elasticity of demand. There seems to be an argument among texts as to whether elasticity of demand should be represented as negative or as an absolute value. The argument for one method over the other depends on the text, but generally boils down to "because this is how we do it." I'm looking for a more meaningful discussion about this topic.

What are the pros and cons of using the negative? Of the absolute value?

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  • $\begingroup$ Can you please point to some sources about this argument? It is somewhat surprising to hear of it, as functional elasticity is a mathematical concept and I would think one cannot change the sign merely because one does not like it. Of course linguisticually it is usually easier to talk about the absolute value of the price elasticity of demand. But perhaps you would like to retain some difference between the sign of price elasticity of demand and income elasticity of demand? $\endgroup$ – Giskard Apr 18 '17 at 21:31
  • $\begingroup$ @denesp I don't have my books on hand, but here is an example from some lecture notes that I just found online; it touches on my question: "Textbooks differ on whether to take the absolute value or not. If you don't take the absolute value, you'll get a negative elasticity, which means that the demand curve is downward sloping. But to keep things positive, we'll always take the absolute value." $\endgroup$ – c4sadler Apr 19 '17 at 12:41
  • $\begingroup$ There seems to be no argument there, merely an explanation about the difference. $\endgroup$ – Giskard Apr 19 '17 at 14:30
  • $\begingroup$ What I'm gathering is that when reporting elasticity results, the decision use negative or absolute value is a matter of discression. Since there are instances in which elasticity results are actually positive, I assume that the person reporting such results would indicate that the presentation is a positive number and not just a matter of convention. Essentially, any time elasticity of demand is reported as a positive number, assume it's the absolute value unless otherwise noted. Does this sound correct? $\endgroup$ – c4sadler Apr 19 '17 at 15:16
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    $\begingroup$ I guess, people use absolute value because they are accustomed to positive numbers. AFAIK, negative numbers appear later then positive numbers and even fractions in history. $\endgroup$ – beroal Apr 20 '17 at 18:08
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Elasticity of demand is almost always assumed to be negative. It is assumed that there is an inverse relationship between price and quantity demanded. If you want to buy 2 hamburgers for $5 each you aren't suddenly going to want to buy 3 hamburgers if they now cost $10 each. If this isn't the case it means that consumers aren't rational which blows up 99% of the models economics has to offer.

Because the elasticity of demand is always negative it can be assumed that if I say X is the elasticity of demand I mean X is negative because elasticity of demand is always negative. If I say -X is the elasticity of demand you can still assume that it is negative because a) I said it explicitly, and b) it is always true.

At this point it's just a matter of preference and doesn't matter either way, I just wanted to explain why it really doesn't matter since someone who understands what elasticity of demand means will understand that it will always be negative in almost all scenarios.

Personally, I think that explicitly saying that the elasticity of demand is negative is a better choice since I can imagine some fringe scenarios where a product being expensive leads to that product being sold more often, (I think of caviar as an example for these types of products, where consumers buy it precisely because its expensive) but for most economic models the assumption holds.

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