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# Arc Elasticity

## A Primer on Arc Elasticity

One of the problems with the standard formulas for elasticity that are in many freshman texts is the elasticity figure you come up with is different depending on what you use as the start point and what you use as the end point. An example will help illustrate this.

When we looked at Price Elasticity of Demand we calculated the price elasticity of demand when price went from \$9 to \$10 and demand went from 150 to 110 was 2.4005. But what if we calculated what the price elasticity of demand when we started at \$10 and went to \$9? So we'd have:

Price(OLD)=10
Price(NEW)=9
QDemand(OLD)=110
QDemand(NEW)=150

First we'd calculate the percentage change in quantity demanded: [QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)

By filling in the values we wrote down, we get:

[150 - 110] / 110 = (40/110) = 0.3636 (Again we leave this in decimal form)

Then we'd calculate the percentage change in price:

[Price(NEW) - Price(OLD)] / Price(OLD)

By filling in the values we wrote down, we get:

[9 - 10] / 10 = (-1/10) = -0.1

We then use these figures to calculate the price-elasticity of demand:

PEoD = (% Change in Quantity Demanded)/(% Change in Price)

We can now fill in the two percentages in this equation using the figures we calculated earlier.

PEoD = (0.3636)/(-0.1) = -3.636

When calculating a price elasticity, we drop the negative sign, so our final value is 3.636. Obviously 3.6 is a lot different from 2.4, so we see that this way of measuring price elasticity is quite sensitive to which of your two points you choose as your new point, and which you choose as your old point. Arc elasticities are a way of removing this problem.

Be Sure to Continue to Page 2 of "Arc Elasticities"

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