The formula for computing price elasticity of demand is:

The correct answer is Option (3) → \( \displaystyle\left(\frac{\Delta Q}{Q}\right)\times\left(\frac{P}{\Delta P}\right) \)

Price elasticity of demand (e_D) measures how strongly the demand for a good responds to a change in its price. It is the percentage change in demand divided by the percentage change in price.

    \( \displaystyle \text{Percentage change in demand} = \frac{\Delta Q}{Q}\times 100 \)

    \( \displaystyle \text{Percentage change in price} = \frac{\Delta P}{P}\times 100 \)

Dividing the first by the second, the 100s cancel:

    \( e_D = \displaystyle\frac{\Delta Q}{Q} \div \displaystyle\frac{\Delta P}{P} = \left(\displaystyle\frac{\Delta Q}{Q}\right)\times\left(\displaystyle\frac{P}{\Delta P}\right) \)

• Option (1) \( \displaystyle\left(\frac{Q}{\Delta Q}\right)\times\left(\frac{\Delta P}{P}\right) \) — Incorrect. This is the formula turned upside down: it divides the percentage change in price by the percentage change in demand.

• Option (2) \( \displaystyle\left(\frac{\Delta P}{\Delta Q}\right)\times\frac{P}{Q} \) — Incorrect. The change in quantity must be divided by the change in price, \( \Delta Q/\Delta P \). Here it is the other way round.

• Option (3) \( \displaystyle\left(\frac{\Delta Q}{Q}\right)\times\left(\frac{P}{\Delta P}\right) \) — Correct. It is the percentage change in demand divided by the percentage change in price.

• Option (4) \( \displaystyle\left(\frac{\Delta Q}{P}\right)\times\left(\frac{\Delta P}{Q}\right) \) — Incorrect. Each change must be divided by its own level: ΔQ by Q and ΔP by P. Here the levels are mixed up, and the change in price is multiplied instead of divided.

Note: A same/similar question was asked in CUET (UG) in the papers below.

* A similar question.