# How can I reconcile these two different equations for “Arc Elasticity”? [migrated]

Well, I've encountered a problem which seemed me like a wrong answered one so, I Google'd for the formulas of both "Arc Elasticity" and "Arc Elasticity of Demand" So far, I've found myself in some kind of paradox that is caused by some different educational theories about Economics.

Here, I'm giving the numbers of the problem which was asked for the "Arc Elasticity": $$P_0=100, \; \; \; Q_0=25 \\ P_1=300, \; \; \; Q_1=15 \\ \large{\bf{E_{arc}^{d}}}= \; ?$$

And, here're some formulas about the "Arc Elasticity":

$$Formula \; 1:$$ $$\large{E_{arc}^{d}= \; \frac{\frac{Q_1-Q_0}{Q_1+Q_0}} {\frac{P_1-P_0}{P_1+P_0}}} \\\$$ $$Formula \; 2:$$ $$\large{E_{arc}^{d}= \; \frac{\frac{Q_1-Q_0}{\frac{Q_1+Q_0}{2}}} {\frac{P_1-P_0}{\frac{P_1+P_0}{2}}}} \\\$$

So, which formula I've to apply to find the $E_{arc}^{d}$ ?

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## migrated to math.stackexchange.com by Jason B♦May 1 '12 at 19:55

This question belongs on our site for people studying math at any level and professionals in related fields.