Arc elasticity is a measure of the responsiveness of the quantity demanded of a good or service to a change in its price, calculated as the ratio of the percentage change in quantity demanded to the percentage change in price over a finite interval, rather than at a single point on the demand curve.
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Arc elasticity is used to measure the responsiveness of quantity demanded to a change in price over a finite interval, rather than at a single point on the demand curve.
Arc elasticity is calculated as the ratio of the percentage change in quantity demanded to the percentage change in price over the finite interval.
Arc elasticity provides a more accurate measure of the responsiveness of quantity demanded to price changes than point elasticity, particularly when the price change is large.
Arc elasticity is useful for analyzing the impact of price changes on revenue and for making pricing decisions, as it takes into account the change in quantity demanded over the entire interval.
The formula for arc elasticity is: Arc Elasticity = (Δ Quantity / Average Quantity) / (Δ Price / Average Price).
Review Questions
Explain how arc elasticity differs from point elasticity in measuring the responsiveness of quantity demanded to price changes.
Arc elasticity measures the responsiveness of quantity demanded to a change in price over a finite interval, while point elasticity measures the responsiveness at a single point on the demand curve. Arc elasticity provides a more accurate measure of the overall change in quantity demanded, particularly when the price change is large, as it takes into account the change in quantity over the entire interval. In contrast, point elasticity only considers the change in quantity at a specific point, which may not be representative of the overall response to the price change.
Describe how arc elasticity can be used to analyze the impact of price changes on revenue.
Arc elasticity can be used to analyze the impact of price changes on revenue because it measures the responsiveness of quantity demanded to a change in price. If the arc elasticity is greater than 1 (in absolute value), it indicates that the percentage change in quantity demanded is greater than the percentage change in price, meaning that a price increase will lead to a decrease in total revenue. Conversely, if the arc elasticity is less than 1 (in absolute value), it indicates that the percentage change in quantity demanded is less than the percentage change in price, meaning that a price increase will lead to an increase in total revenue. This information can be used to make pricing decisions that optimize revenue.
Analyze how the formula for arc elasticity, $$ Arc Elasticity = (Δ Quantity / Average Quantity) / (Δ Price / Average Price) $$, can be used to understand the relationship between price changes and quantity demanded.
The formula for arc elasticity shows that the responsiveness of quantity demanded to a price change is determined by the relative magnitudes of the percentage change in quantity and the percentage change in price. If the percentage change in quantity is greater than the percentage change in price, the arc elasticity will be greater than 1 (in absolute value), indicating that demand is elastic and quantity demanded is highly responsive to price changes. Conversely, if the percentage change in quantity is less than the percentage change in price, the arc elasticity will be less than 1 (in absolute value), indicating that demand is inelastic and quantity demanded is less responsive to price changes. Understanding this relationship is crucial for making pricing decisions and analyzing the impact of price changes on revenue.
Point elasticity is the responsiveness of quantity demanded to a change in price at a specific point on the demand curve, calculated as the ratio of the percentage change in quantity demanded to the percentage change in price.
The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded, showing how the quantity demanded changes as the price changes.
Percentage Change: Percentage change is the relative change in a variable, expressed as a percentage of the original value, and is calculated as the change in the variable divided by the original value.