Arc elasticity of demand is a measure of the responsiveness of the quantity demanded of a good or service to a change in its price. It is calculated using the formula:
Arc elasticity of demand = (ΔQ/Q)/(ΔP/P)
Where ΔQ is the change in quantity demanded, Q is the original quantity demanded, ΔP is the change in price, and P is the original price.
To calculate arc elasticity of demand, you will need to gather data on the quantity demanded of the good or service at two different prices. For example, let's say you want to calculate the arc elasticity of demand for a particular brand of coffee. You might gather data on the quantity of coffee sold at a price of $10 per pound, and then compare that to the quantity of coffee sold at a price of $12 per pound.
To calculate the arc elasticity of demand, you would first need to determine the change in quantity demanded, which is the difference between the quantity of coffee sold at the two different prices. In this example, let's say that 500 pounds of coffee were sold at a price of $10 per pound, and 400 pounds of coffee were sold at a price of $12 per pound. The change in quantity demanded would be 500 - 400 = 100 pounds.
Next, you would need to determine the change in price, which is the difference between the two prices. In this example, the change in price would be $12 - $10 = $2.
Finally, you can use the formula to calculate the arc elasticity of demand:
Arc elasticity of demand = (ΔQ/Q)/(ΔP/P) = (100/500)/(2/10) = 0.2
This means that the demand for this particular brand of coffee is relatively inelastic, as a small change in price (in this case, a 20% increase) resulted in only a small change in quantity demanded (a 20% decrease).
It's important to note that arc elasticity of demand only measures the responsiveness of demand to a change in price over a specific range of prices. If the price of the good or service were to change significantly, the arc elasticity of demand could change as well.
In conclusion, calculating arc elasticity of demand can help you understand how changes in price will affect the demand for a particular good or service. By gathering data on the quantity demanded at different prices and using the formula provided, you can determine the elasticity of demand and make informed decisions about pricing and quantity.