Arc Elasticity

What Is Arc Elasticity?

Arc elasticity is a way of measuring how responsive one quantity is to a change in another, calculated over a range between two points on a curve rather than at a single point. Economists most often use it to measure how much the quantity demanded of a good changes when its price changes, which is a core part of price elasticity of demand. Because it uses the average of the starting and ending values, it gives the same answer whether you move up or down the range. This makes it useful when comparing two observed situations.

How It Works

Elasticity compares percentage changes rather than raw changes, so the result does not depend on units of measurement. Arc elasticity uses the midpoint method, in which each percentage change is calculated relative to the average of the starting and ending values. The formula is:

Arc elasticity = [(Q2 − Q1) / ((Q2 + Q1) / 2)] ÷ [(P2 − P1) / ((P2 + P1) / 2)]

Here Q1 and Q2 are the quantities before and after the change, and P1 and P2 are the prices before and after. Using averages avoids the problem of getting different answers depending on which value is treated as the starting point.

An Example

Suppose the price of a product rises from $10 to $12, and the quantity sold falls from 100 units to 80 units. The quantity changes by −20 units, and the average quantity is 90, so the quantity change is about −22.2 percent. The price changes by $2, and the average price is $11, so the price change is about 18.2 percent. Dividing the two gives an arc elasticity of about −1.22.

Because the absolute value is greater than 1, demand is considered elastic demand over this range. Buyers reduced their purchases by a larger percentage than the price increase. The negative sign reflects the usual inverse relationship between price and quantity demanded.

Advantages and Limitations

Arc elasticity is simple to calculate from two observed data points, and it does not require knowing the exact shape of the underlying demand curve. It is therefore common in introductory analysis and in situations where only a few observations are available.

Its main limitation is that it describes an average response across a range rather than behavior at one precise price. If the range is wide, the result may hide important variation. For precise measurement at a specific point, economists use point elasticity, which relies on calculus and the slope of the demand curve.

Arc elasticity is a useful bridge between the textbook concept of elasticity and real data. It helps analysts understand how sensitive sales or total revenue may be to pricing changes.