The midpoint method for calculating price elasticity of demand provides a consistent approach to determine how quantity demanded responds to price changes, regardless of whether the price is increased or decreased. The formula for price elasticity of demand using this method is still based on the percentage change in quantity demanded divided by the percentage change in price, but it modifies how these percentage changes are calculated.
To compute the percentage changes, instead of using the original values, the midpoint method utilizes the average of the two quantities and the average of the two prices. This adjustment helps avoid discrepancies that can arise from using different starting points for the calculations. The formula can be expressed as:
\[E_d = \frac{\left( \frac{Q_2 - Q_1}{\frac{Q_1 + Q_2}{2}} \right)}{\left( \frac{P_2 - P_1}{\frac{P_1 + P_2}{2}} \right)}\]
Where \(E_d\) is the price elasticity of demand, \(Q_1\) and \(Q_2\) are the initial and new quantities demanded, and \(P_1\) and \(P_2\) are the initial and new prices.
To illustrate this method, consider a pizza company that raises its lunch special price from $5 to $6, resulting in a decrease in quantity demanded from 2,000 to 1,400 specials. The steps to calculate the elasticity of demand are as follows:
1. **Calculate the changes**: Subtract the two quantities to find the change in quantity demanded (600) and the change in price (1).
2. **Sum the quantities and prices**: Add the two quantities (3,400) and the two prices (11).
3. **Find the averages**: Divide the sums from step 2 by 2 to get the average quantity (1,700) and average price (5.50).
4. **Calculate the percentage changes**: Divide the change in quantity (600) by the average quantity (1,700) to get a percentage change in quantity demanded of approximately 0.353 (or 35.3%). Similarly, divide the change in price (1) by the average price (5.50) to get a percentage change in price of approximately 0.182 (or 18.2%).
Finally, substitute these values into the elasticity formula:
\[E_d = \frac{0.353}{0.182} \approx 1.934\]
This result indicates that the demand is elastic since the elasticity value is greater than 1. This means that the quantity demanded is quite sensitive to price changes, confirming that a small price increase leads to a relatively larger decrease in quantity demanded.
By following these steps, the midpoint method simplifies the calculation of elasticity, ensuring accuracy and consistency in determining how demand reacts to price fluctuations.
