 # Arc Elasticity

The sensitivity of one variable to another between two points on a curve

## What is Arc Elasticity?

Arc elasticity is the sensitivity of one variable to another between two points on a curve. It is often used in the context of the law of demand to measure the inverse relationship between price and demand.

Arc elasticity measures the responsiveness of demand to price changes over a range of values. The magnitude of change in price and demand is divided by its midpoint to arrive at a measure of change over a curve rather than at a point.

### Summary

• Arc elasticity measures the sensitivity of demand relative to the mid-point rather than the original point. It gives the same value for price increases and decreases of equal amounts.
• If the magnitude of price change is small, it matters less whether arc elasticity or price elasticity is used for determining price increases or decreases.
• Arc elasticity is used in non-uniform pricing to measure the elasticity of demand and price products in a way that maximizes profits.

### Arc Elasticity Formula

Arc elasticity is calculated as:   ### Practical Examples

Let’s calculate the arc elasticity for an equal dollar price increase and decrease.

#### Case 1

Price increases from \$6 to \$8, quantity demanded decreases from 40 units to 20 units.

#### Case 2

Price decreases from \$8 to \$6, quantity demanded increases from 20 units to 40 units.

In both cases, arc elasticity remains at 2.3. From here, it’s evident that a price increase and decrease of \$2 indicates the same sensitivity of demand for a company’s customers.   ### Why Use Arc Elasticity?

• Arc elasticity is useful for larger price changes.
• It provides the same absolute elasticity measure when prices rise and fall.

### Applications in Pricing

Arc elasticity is an alternative approach to measure elasticity rather than using price elasticity. Based on whether elasticity is equal to, greater than, or less than one, demand is considered unit elastic, elastic, and inelastic. Elasticity of demand can be used to understand a customer’s willingness to pay and price products in a way that maximizes profits.

#### Monopoly Pricing

Elasticity measures are used in monopoly pricing. If the monopolist believes that the demand for a product is inelastic, then the demand for that product should not decrease significantly with a price increase.

So, a monopolist may set high prices to capitalize on a consumer’s willingness to pay. Profits will be maximized under the assumption that the decrease in demand is compensated by higher prices.

#### Price Discrimination

Price discriminators charge different prices for providing the same goods or services. For example, business trips are essential, and thus the business travelers’ demand is inelastic. So, an airline company can set a high price for business travelers. As a result, airfare for business travelers is typically higher than airfare for leisure travelers.

Similarly, airfare is higher for flights booked closer to the travel date compared to those booked in advance. It is estimated that people who book flights at shorter notice are in urgent need of travel and show an inelastic demand. Therefore, airline companies charge higher prices to such travelers.