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In my microeconomics book, I read that when we have $1+\dfrac{1}{\eta}$ where $\eta$ is an elasticity coefficient, we can write $1-\dfrac{ 1}{|\eta|}$ "to avoid ambiguities stemming from the negative sign of the elasticity".

What does this mean? Is it always legitimate to perform such a transformation?

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It should be negative. –  Luigi Oct 28 '12 at 15:08
    
The reason for the care is that elasticity has been traditionally defined in two different ways, the way you are familiar with, and the negative of that. –  André Nicolas Oct 28 '12 at 16:35
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2 Answers

up vote 5 down vote accepted

If the elasticity coefficient $\eta$ is negative, then $|\eta|=-\eta$. The ambiguity arises because some people may suppress the negative sign and write it as a positive number instead. In this case, using $1+\frac{1}{\eta}$ becomes ambiguous.

For example, if $\eta=-2$ but people write it as $\eta=2$, then $1+\frac{1}{\eta}$ can mean $1-\frac{1}{2}$ or $1+\frac{1}{2}$.

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No, such a calculation is not always allowed...I'm guessing it relates to the constant itself.

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