The Arc Elasticity Calculator measures how demand responds to changes in price over a range of prices. It calculates the arc elasticity of demand, which considers the average price and quantity rather than specific points. This makes it useful for analyzing real-world scenarios where prices and quantities vary.
Formula of Arc Elasticity Calculator
Arc elasticity measures how demand responds to changes in price over a range of prices. The formula is:
where:
- Q1 and Q2 are the initial and final quantities demanded.
- P1 and P2 are the initial and final prices.
This formula provides a more accurate measure of elasticity over a range of values, making it practical for real-world applications.
Pre-calculated Values Table
To make it easier, here is a table of pre-calculated arc elasticity values for common scenarios:
| Initial Price (P1) | Final Price (P2) | Initial Quantity (Q1) | Final Quantity (Q2) | Arc Elasticity |
|---|---|---|---|---|
| 10 | 12 | 100 | 90 | -0.22 |
| 15 | 18 | 200 | 180 | -0.18 |
| 20 | 25 | 300 | 250 | -0.24 |
| 30 | 35 | 400 | 350 | -0.14 |
This table helps you quickly reference elasticity values without needing to calculate each time.
Example of Arc Elasticity Calculator
Let's go through an example to see how the arc elasticity formula works.
Suppose the price of a product increases from $10 to $12, and the quantity demanded decreases from 100 units to 90 units. Using the formula:
Arc Elasticity of Demand = ((90 - 100) / (90 + 100)) / ((12 - 10) / (12 + 10)) = (-10 / 190) / (2 / 22) = -0.0526 / 0.0909 = -0.578
The arc elasticity of demand is -0.578, indicating that the demand is inelastic since the absolute value is less than 1.
Most Common FAQs
Arc elasticity measures elasticity over a range of prices, while point elasticity measures elasticity at a specific point on the demand curve. Arc elasticity is useful for broader analysis, whereas point elasticity is precise for small changes.
Arc elasticity provides a more accurate representation of how demand responds to price changes in real-world scenarios, where prices and quantities are not constant. It helps businesses and policymakers make better decisions based on average changes.
To use the Arc Elasticity Calculator, input the initial and final prices and quantities. The calculator will apply the arc elasticity formula and provide the elasticity value, helping you understand the relationship between price changes and demand.