# Arc Elasticity Explained: Definition, Formula, and Example

![Arc Elasticity](https://www.investopedia.com/thmb/8qyocmkrcVt3DsRWF736na4ItRY=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/arc-elasticity.asp-final-0cd81d49db2f4a9db123b12c6f8d5a23.png)

*— Investopedia / Julie Bang*

## What Is Arc Elasticity?

Arc elasticity is the elasticity of a variable between two points. It's used in economics to measure changes in demand in relation to changes in price. For instance, a product is considered elastic if the demand also changes significantly when its price changes. Elasticity is calculated by a formula.

### Key Takeaways

*   Arc elasticity measures the elasticity of one variable with respect to another between two specific points.
*   It's commonly used in economics to assess changes in quantity demanded concerning price changes.
*   The arc elasticity formula calculates elasticity at the midpoint between two points on a demand curve.
*   Unlike price elasticity, arc elasticity provides consistent results regardless of the direction of price change.
*   Arc elasticity of demand is particularly useful when there is a significant change in price.

## Exploring Arc Elasticity in Economics

In economics, arc elasticity is commonly used in relation to the [law of demand](https://www.investopedia.com/terms/l/lawofdemand.asp) to measure percentage changes between the quantity of goods demanded and prices.

There are two possible ways of calculating elasticity: price (or point) elasticity of demand and arc elasticity of demand. [Price elasticity of demand](https://www.investopedia.com/terms/p/priceelasticity.asp) measures the responsiveness of quantity demanded to a price. It takes the elasticity of demand at a particular point on the [demand curve](https://www.investopedia.com/terms/d/demand-curve.asp), or between two points on the curve. Arc elasticity of demand uses a midpoint between the two points.

## Calculating Price Elasticity of Demand With the Point Method

  
﻿﻿ $PE_d = \dfrac{\text{\% Change in Qty}}{\text{\% Change in Price}}$﻿﻿

## Step-by-Step Guide to Price Elasticity Calculation

**1\. Identify the initial and final prices and quantities:** Gather data on the initial price (P1) and final price (P2), as well as the initial quantity demanded (Qd1) and final quantity demanded (Qd2).  
**2\. Compute the percentage change in quantity:** Use the formula \\((Qd\_2 - Qd\_1) / Qd\_1\\) to find the change in quantity.  
**3\. Compute the percentage change in price:** Use the formula \\((P2 - P1) / P1\\) to find the change in price.  
4\. **Calculate elasticity:** Divide the percentage change in quantity by the percentage change in price to get the price elasticity.

## Applying the Arc Elasticity Formula

A problem with the price elasticity of demand formula is it gives different results if the price goes up or down. If we use different start and end points—assuming the price went from $8 to $10 and quantity demanded fell from 60 to 40—the Pe\_d will be:

*   **% change in quantity demanded** = (40 – 60) / 60 = -0.33
*   **% change in price** = (10 – 8) / 8 = 0.25
*   **PEd** = -0.33 / 0.25 = 1.32, which is much different from 2.5

## Steps to Determine Arc Elasticity of Demand

To eliminate this problem, the arc elasticity of demand can be used. Arc elasticity of demand measures elasticity at the midpoint between two selected points on the demand curve by using a midpoint between the two points. The arc elasticity of demand can be calculated as:

*   **Arc Ed** = \[(Qd2 – Qd1) / midpoint Qd\] ÷ \[(P2 – P1) / midpoint P\]

Using the earlier example, let's calculate the arc elasticity:

*   **Midpoint Qd** = (Qd1 + Qd2) / 2 = (40 + 60) / 2 = 50
*   **Midpoint Price** = (P1 \+ P2) / 2 = (10 + 8) / 2 = 9
*   **% change in qty demanded** = (60 – 40) / 50 = 0.4
*   **% change in price** = (8 – 10) / 9 = -0.22
*   **Arc Ed** = 0.4 / -0.22 = 1.82

With arc elasticity, it doesn't matter which point you start or end with; the elasticity value stays the same regardless of price changes.

> **Important**
>
> Arc elasticity is more useful than price elasticity when there's a big price change.

## What Is Elasticity in Economics?

In the context of economics, elasticity is used to measure the change in the quantity demanded for a product in relation to its price movements. A product is considered to be elastic if the demand for it changes substantially when its price changes.

## What Is the Law of Demand?

The law of demand is a fundamental economic concept. It states that when prices rise, the demand for a good or service will decrease. 

## What Are the Benefits of Arc Elasticity of Demand?

The formula for arc elasticity of demand measures elasticity between two selected points by using a midpoint between the two points. As a result, it is particularly useful when there is a substantial change in price.

## The Bottom Line

Arc elasticity is commonly used in economics to determine the percentage of change between the demand for goods and their price. Elasticity can be calculated in two ways—price elasticity of demand and arc elasticity of demand. The latter is more useful when there is a significant change in price.

> **Article Sources**
>
> 1.  Federal Reserve Bank of St. Louis. “[Elasticity of Demand - The Economic Lowdown Podcast Series](https://www.stlouisfed.org/education/economic-lowdown-podcast-series/episode-16-elasticity-of-demand).”
>     
> 2.  University of Minnesota. “[The Price Elasticity of Demand](https://open.lib.umn.edu/principleseconomics/chapter/5-1-the-price-elasticity-of-demand/).”