The midpoint method is a technique used to calculate the price elasticity of demand, providing a consistent measure regardless of whether the price is increased or decreased. The formula for price elasticity of demand using this method remains the same: it is the percentage change in quantity demanded divided by the percentage change in price. However, the calculation of these percentage changes is adjusted to use averages rather than original values.

To calculate the percentage change in quantity demanded and price, the midpoint method employs the average of the two quantities and the average of the two prices. This approach helps avoid discrepancies that can arise from using original values, ensuring that the elasticity calculation is symmetrical. The formula can be expressed as:

Elasticity of Demand (E_d) = \(\frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}\)

Where:

Percentage Change in Quantity Demanded = \(\frac{Q_2 - Q_1}{\frac{Q_1 + Q_2}{2}}\)

Percentage Change in Price = \(\frac{P_2 - P_1}{\frac{P_1 + P_2}{2}}\)

To illustrate this, consider a pizza company that raises its lunch special price from $5 to $6, resulting in a drop in weekly demand from 2,000 to 1,400 lunch specials. To find the price elasticity of demand, follow these steps:

Step 1: Calculate the changes in quantity and price:

Change in Quantity = \(1,400 - 2,000 = -600\) (absolute value is 600)

Change in Price = \(6 - 5 = 1\)

Step 2: Calculate the sums of the quantities and prices:

Sum of Quantities = \(2,000 + 1,400 = 3,400\)

Sum of Prices = \(5 + 6 = 11\)

Step 3: Divide the sums by 2 to find the averages:

Average Quantity = \(\frac{3,400}{2} = 1,700\)

Average Price = \(\frac{11}{2} = 5.5\)

Step 4: Calculate the percentage changes:

Percentage Change in Quantity Demanded = \(\frac{600}{1,700} \approx 0.353\) (or 35.3%)

Percentage Change in Price = \(\frac{1}{5.5} \approx 0.182\) (or 18.2%)

Finally, substitute these values into the elasticity formula:

Elasticity of Demand = \(\frac{0.353}{0.182} \approx 1.934\)

Since the elasticity of demand is greater than 1, this indicates that the demand is elastic, meaning that quantity demanded is highly responsive to price changes. This method simplifies the calculation process and ensures accuracy, making it a valuable tool for analyzing demand sensitivity.