In case the price (P), quantity (Q), and changes (∆) are represented by the respective symbols given in the brackets, the price elasticity of demand (Ed) is measured by:
Ed = $\frac{(∆Q/Q)}{(∆P/P)}$
Price elasticity of demand measures the responsiveness of the quantity demanded to a change in price, and it is defined as a ratio of proportional (percentage) changes, not of absolute changes.
By definition, price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. Writing the percentage change in quantity as ∆Q/Q and the percentage change in price as ∆P/P, this gives Ed = (∆Q/Q) ÷ (∆P/P). That is exactly option (B).
The other options are wrong because they use the wrong quantities. ∆Q/∆P and ∆P/∆Q are ratios of absolute changes (essentially slopes), not of percentage changes, so they are not unit-free and are not elasticity. And (∆P/P)/(∆Q/Q) inverts the ratio, giving the reciprocal of elasticity rather than elasticity itself.
Because elasticity must be a pure, unit-free number comparing proportional changes, only the ratio of the two percentage changes qualifies.
Hence the price elasticity of demand is measured by Ed = (∆Q/Q)/(∆P/P).
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