In microeconomics, what is the formula for calculating the price elasticity of demand using the percentage (midpoint) method?

• A. $E{d}_p=\frac{\frac{Q_2-Q_1}{\frac{Q_1+Q_2}{2}}}{\frac{P_2-P_1}{\frac{P_1+P_2}{2}}}$
• B. $E{d}_p=\frac{Q_2+Q_1}{P_2+P_1}$
• C. $E{d}_p=\frac{\frac{P_2-P_1}{\frac{P_1+P_2}{2}}}{\frac{Q_2-Q_1}{\frac{Q_1+Q_2}{2}}}$
• D. $E{d}_p=\frac{Q_2-Q_1}{P_2-P_1}$

Answer: (A)

Verified step by step guidance

1. Identify the initial and new quantities demanded, denoted as \(Q_1\) and \(Q_2\), respectively, and the initial and new prices, denoted as \(P_1\) and \(P_2\), respectively.
2. Calculate the percentage change in quantity demanded using the midpoint formula: compute the difference \(Q_2 - Q_1\) and divide it by the average quantity \(\frac{Q_1 + Q_2}{2}\), so the percentage change in quantity is \(\frac{Q_2 - Q_1}{\frac{Q_1 + Q_2}{2}}\).
3. Calculate the percentage change in price similarly by finding the difference \(P_2 - P_1\) and dividing it by the average price \(\frac{P_1 + P_2}{2}\), so the percentage change in price is \(\frac{P_2 - P_1}{\frac{P_1 + P_2}{2}}\).
4. Form the price elasticity of demand by dividing the percentage change in quantity demanded by the percentage change in price, which gives the formula: \(E_{dp} = \frac{\frac{Q_2 - Q_1}{\frac{Q_1 + Q_2}{2}}}{\frac{P_2 - P_1}{\frac{P_1 + P_2}{2}}}\)
5. Interpret the result: the elasticity measures how responsive quantity demanded is to a change in price, using the midpoint method to avoid bias depending on the direction of change.