what is the meaning of arc elasticity of demand and how to measure it
The correct answer and explanation is :
Arc Elasticity of Demand:
Arc elasticity of demand refers to the method of calculating elasticity over a range of prices, rather than at a specific point. It is particularly useful when there is a significant change in price, and it helps to measure the average responsiveness of quantity demanded to changes in price over a given price range. Unlike point elasticity, which evaluates elasticity at a specific price point, arc elasticity allows for a more accurate measure of elasticity when both the initial and final prices and quantities are considered.
Formula for Arc Elasticity of Demand:
The formula to calculate the arc elasticity of demand is:
[
E_d = \frac{\left( \frac{Q_2 – Q_1}{Q_2 + Q_1} \right)}{\left( \frac{P_2 – P_1}{P_2 + P_1} \right)}
]
Where:
- ( E_d ) = Arc elasticity of demand
- ( Q_1 ) = Initial quantity demanded
- ( Q_2 ) = Final quantity demanded
- ( P_1 ) = Initial price
- ( P_2 ) = Final price
This formula is derived from the midpoint method and is often referred to as the “midpoint formula” for elasticity. The reason for using the average values of price and quantity in both the numerator and denominator is to avoid bias in the measurement that could arise from using either the initial or final values exclusively.
Explanation:
- Elasticity measures how much the quantity demanded changes in response to a change in price. If demand is elastic (i.e., elasticity > 1), consumers are highly responsive to price changes. If demand is inelastic (i.e., elasticity < 1), consumers are less responsive to price changes. If demand is unitary (i.e., elasticity = 1), the percentage change in quantity demanded equals the percentage change in price.
- Why use Arc Elasticity? Arc elasticity is particularly useful when analyzing large changes in price and quantity. Point elasticity can be difficult to apply in such cases because it assumes that small changes occur, but arc elasticity accounts for large, discrete changes.
- Practical Application: Arc elasticity is applied when businesses or policymakers want to understand the average responsiveness of demand over a range of prices. For instance, if a company plans to change its price significantly, arc elasticity can help predict how demand will adjust, allowing for more informed pricing decisions.