Economics Stack Exchange Archive

How can I reconcile these two different equations for “Arc Elasticity”?

• posted by: Kerim Atasoy on 2012-03-27
• tagged: microeconomics, homework, elasticity
• score: 2

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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