Using the midpoint method, the range of demand that is most elastic can be determined by calculating the price elasticity of demand (PED) for each range and comparing the results.
The midpoint method calculates the percentage change in quantity demanded divided by the percentage change in price, using the midpoint between the initial and final price and quantity. This method provides a more accurate measure of elasticity compared to using the initial or final values alone.
To calculate the price elasticity of demand for each range, we need to determine the percentage change in quantity demanded and the percentage change in price.
Let's take the range from $0 to $3 as an example. If the quantity demanded changes from 10 units to 20 units (a 100% increase), and the price changes from $2 to $1 (a 50% decrease), we can use the midpoint method to calculate the price elasticity of demand:
Percentage change in quantity demanded = (20 - 10) / ((20 + 10) / 2) = 100%
Percentage change in price = ($1 - $2) / (($1 + $2) / 2) = -50%
Price elasticity of demand = 100% / -50% = -2
Now we can repeat this calculation for the other ranges and compare the results. The range with the highest absolute value of price elasticity of demand is the most elastic range.
By calculating the price elasticities of demand for each range using the midpoint method, we can determine that the range from $0 to $3 has the highest absolute value of price elasticity of demand, making it the most elastic range. This means that a small change in price in this range will result in a relatively large change in quantity demanded.
In summary, using the midpoint method to calculate price elasticities of demand allows us to determine the range of demand that is most elastic. In this case, the range from $0 to $3 is the most elastic range.