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# What Is Arc Elasticity? Definition, Midpoint Formula, and Example

Photo: Arc Elasticity Photo: Arc Elasticity

### Arc Elasticity: What Is It?

The elasticity of a variable concerning another between two specified locations is known as arc elasticity. It is employed when a universal definition of the link between the two variables cannot be found. The elasticity between two points on a curve is another definition of arc elasticity.

Both mathematics and economics make use of the idea. The relationship between changes in the amount of commodities required and their pricing is frequently measured in economics.

Acknowledging Arc Elasticity

Arc elasticity is frequently used in economics to calculate percentage changes in the amount of commodities demanded and prices per the law of demand.

Price (or point) elasticity of demand and arc elasticity of demand are the two methods that may be used to calculate elasticity. The responsiveness of quantity demanded to a price is measured by the price elasticity of demand. It measures the demand elasticity between any two points on the demand curve or at a specific point. A point in the middle of the two points is used in arc elasticity of demand.

### How to Determine Demand’s Price Elasticity

The price elasticity of demand may be computed as follows if a product’s price drops from \$10 to \$8 and the quantity required rises from 40 to 60 units:

• Price change = (P2 – P1) / P1 = (8 – 10) / 10 = -0.2 % change in amount required = (Qd2 – Qd1) / Qd1 = (60 – 40) / 40
• PEd = 0.5/-0.2 = 2.5 as a result.
• The negative sign is disregarded since price elasticity only interests absolute values. You can conclude that this good’s price elasticity is 2.5 when it drops from \$10 to \$8.

Demand Elasticity in an Arc

One of its flaws is that the price elasticity of demand formula yields different numbers depending on whether prices rise or fall. The Ped would be the following if you used alternative start and end points in the example above—that is, if you assumed the price rose from \$8 to \$10 and the quantity requested dropped from 60 to 40:

• Demand quantity change as a percentage: (40 – 60) / 60 = -0.33
• Price change as a percentage = (10 – 8) / 8 = 0.25 PEd as a percentage = -0.33 / 0.25 = 1.32, which is much less than 2.5
• How to Determine Demand’s Arc Elasticity
• The demand arc elasticity can be employed to solve this issue. Arc elasticity of demand uses a midway between two chosen locations on

The demand curve to quantify elasticity at that moment. You may compute the arc elasticity of demand as follows:

Arc Ed is equal to (Qd2 – Qd1) / (P2 – P1) / midpoint P.
Let’s compute the arc elasticity using the previously provided example:

• Midpoint Qd is equal to (Qd1 + Qd2) / 2 (40 + 60) / 2 (50), where
% change in quantity requested = (60 – 40) / 50 = 0.4 % change in price = (8 – 10) / 9 = -0.22 Midpoint Price = (P1 + P2) / 2 = (10 + 8) / 2 = 9
Arc Ed = 0.4 / -0.22 = 1.82

Since the arc elasticity of demand produces the same number for elasticity, whether prices rise or fall, you do not need to worry about which point is the starting point and which point is the ending point when using this method.

### What Does Economic Elasticity Mean?

Elasticity is a term used in economics to describe the relationship between changes in the quantity requested for a good and changes in its price. If a product’s demand responds significantly to price changes, it is said to be elastic.

### The Law of Demand: What Is It?

One of the most basic ideas in economics is the law of demand. According to this, demand for an item or service would decline as prices rise.

What Are the Advantages of Demand Arc Elasticity?
The formula for arc elasticity of demand uses a midway between the two locations to estimate elasticity between two chosen points. Consequently, it is especially helpful when there is a significant price fluctuation.

In economics, arc elasticity is frequently used to calculate the percentage change in the relationship between the demand for an item and its price. Price elasticity of demand and arc elasticity of demand are two methods for calculating elasticity. The latter is more helpful when there is a big fluctuation in pricing.

### Conclusion

• The idea of arc elasticity involves measuring the elasticity of one variable between two specified locations.
• Both mathematics and economics make use of the idea.
• It is frequently used to gauge changes in the demand for items and their prices.
• There are two methods for calculating the elasticity of demand: price (or point) elasticity and arc elasticity.