Arc Elasticity

Published Aug 1, 2023

Definition of Arc Elasticity

Arc elasticity is a measure of the responsiveness of demand or supply to a change in price by comparing the percentage change in quantity to the percentage change in price. This measure is called the arc elasticity of demand because it calculates the elasticity of demand along an arc of the demand curve between two points. It is sometimes also referred to as the midpoint method. The formula for arc elasticity is as follows:

Arc Elasticity = (Q₂ – Q₁) / ((Q₂ + Q₁) / 2) / (P₂ – P₁) / ((P₂ + P₁) / 2)

Where Q₂ is the quantity demanded or supplied after the price change, Q₁ is the quantity before the price change, P₂ is the new price, and P₁ is the original price.

Example

Let’s say we have a business that sells coffee. Currently, they sell 100 cups of coffee per day at a price of $2 per cup. Due to an increase in the cost of coffee beans, the business decides to raise the price of a cup of coffee to $2.50. After the price increase, the business observes that they are selling 80 cups of coffee per day.

Using the formula for arc elasticity, we can calculate the elasticity of demand for the coffee:

Arc Elasticity = (80 – 100) / ((80 + 100) / 2) / (2.50 – 2) / ((2.50 + 2) / 2)

Arc Elasticity = -0.44

This result means that the demand for coffee is inelastic, meaning that a 1% increase in price results in less than a 1% decrease in the quantity demanded.

Why Arc Elasticity Matters

Arc Elasticity is an essential concept in microeconomics since it allows us to understand how buyers and sellers will react to price changes. If demand is elastic, then a small change in price will result in a large change in quantity demanded, and vice versa. On the other hand, if demand is inelastic, then price changes will have a minimal impact on the quantity demanded by buyers.

By knowing the arc elasticity of demand or supply, firms can adjust their prices and output to maximize profits. Policymakers can also use arc elasticity to design effective policies, such as taxation or price controls, to achieve specific social goals.