What Is Arc Elasticity?

What Is Arc Elasticity?

Let me explain arc elasticity to you directly: it's the elasticity of one variable in relation to another between two specific points. You use it when there's no straightforward way to define the relationship between those variables. Essentially, arc elasticity is the elasticity measured between two points on a curve.

This concept applies in both economics and mathematics. In economics, I often see it used to measure changes between the quantity of goods demanded and their prices.

Key Takeaways

Here's what you need to grasp about arc elasticity: it measures the elasticity of one variable against another between two given points. You'll find it in economics and mathematics alike. It's frequently applied to track changes in quantity demanded versus prices. Remember, price elasticity of demand and arc elasticity of demand are two distinct methods for calculating elasticity.

Understanding Arc Elasticity

In economics, arc elasticity ties closely to the law of demand, where you measure percentage changes between quantity demanded and prices.

You have two main ways to calculate elasticity: price elasticity of demand and arc elasticity of demand. Price elasticity looks at how quantity demanded responds to price at a specific point or between points on the demand curve. Arc elasticity, however, uses the midpoint between those two points.

Formula for Price (Point) Elasticity of Demand

The formula for price elasticity of demand is straightforward: PE_d = (% Change in Quantity) / (% Change in Price). That's how you compute it.

How to Calculate the Price Elasticity of Demand

Take this example: if a product's price drops from $10 to $8, and quantity demanded rises from 40 to 60 units, you calculate it like this. Percent change in quantity demanded is (60 – 40) / 40 = 0.5. Percent change in price is (8 – 10) / 10 = -0.2. So, PE_d = 0.5 / -0.2 = 2.5.

We ignore the negative sign for absolute value in elasticity, so you conclude the price elasticity is 2.5 for this price decrease.

Arc Elasticity of Demand

One issue with the price elasticity formula is it gives different results depending on if price goes up or down. Using the same example but reversing it—price from $8 to $10, quantity from 60 to 40—you get percent change in quantity = (40 – 60) / 60 = -0.33, percent change in price = (10 – 8) / 8 = 0.25, so PE_d = -0.33 / 0.25 = -1.32, which differs from 2.5.

How to Calculate the Arc Elasticity of Demand

To fix that inconsistency, use arc elasticity, which measures at the midpoint between points. The formula is Arc E_d = [(Q_d2 – Q_d1) / midpoint Q_d] ÷ [(P2 – P1) / midpoint P].

Applying the example: Midpoint Q_d = (40 + 60) / 2 = 50. Midpoint Price = (10 + 8) / 2 = 9. Percent change in quantity = (60 – 40) / 50 = 0.4. Percent change in price = (8 – 10) / 9 = -0.22. So, Arc E_d = 0.4 / -0.22 = 1.82.

With arc elasticity, you don't worry about starting or ending points; it gives the same value whether prices rise or fall.

Important Note

Arc elasticity of demand proves more useful than price elasticity when there's a considerable price change.

What Is Elasticity in Economics?

In economics, elasticity measures how much quantity demanded changes in response to price movements. If demand shifts a lot with price changes, the product is elastic.

What Is the Law of Demand?

The law of demand is basic: when prices go up, demand for the good or service goes down.

What Are the Benefits of Arc Elasticity of Demand?

The arc elasticity formula uses the midpoint between two points, making it ideal for substantial price changes.

The Bottom Line

Arc elasticity helps determine percentage changes between demand for goods and their prices in economics. You can calculate elasticity via price elasticity or arc elasticity, with the latter being better for big price shifts.