Arc Elasticity refers to a specific form of economic elasticity, which is a measure of the sensitivity or responsiveness of a particular economic variable, such as demand for a particular good or service, to changes in another variable. Generally, arc elasticity is used to measure the change in demand with respect to a change in price in a certain range, on a specific point of the demand curve. Arc elasticity differs from point elasticity in that point elasticity is used to measure changes in demand with respect to a change in price at a given point; while arc elasticity captures changes in demand with respect to a change in price, over a specific range.

Arc elasticity is applied when making decisions about prices, production, and decisions made in order to optimize profits. This form of elasticity is an important concept to measure as it can help businesses understand how their prices in the range of a given value might affect demand for their goods or services.

Arc elasticity allows businesses to understand, for example, how price cuts and increases can impact demand in the short-term and long-term, as well as how changing a price in the middle will affect demand. Businesses may also use arc elasticity to determine the best strategy for pricing goods and services in order to maximize profits.

In economics and mathematics, the formula for calculating arc elasticity is:

Arc Elasticity = (d(Q2-Q1))/((Q2+Q1)/2)*((P2-P1)/((P2+P1)/2))

Where Q1 and Q2 are the quantities demanded at two different points, and P1 and P2 are the corresponding price.

It is important to note that, because arc elasticity measures average changes between two points, it may not necessarily reflect the level of elasticity of demand at a particular point. Therefore, to accurately measure elasticity of demand, it is necessary to consider both arc elasticity and point elasticity, as it is the combination that provides the most complete picture.

Overall, the concept of arc elasticity is an important measure in economics and can help businesses determine the best pricing strategies to capture the largest demand and maximize profits.