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Worked Examples · Example 1

Q.When the price of a good falls from ₹10 to ₹8 per unit, the quantity demanded rises from 40 units to 55 units. Calculate the price elasticity of demand by the percentage method and state its type.

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✓ Free question

Given: original price P=₹10P = ₹10, original quantity Q=40Q = 40; new price ₹8₹8, new quantity 5555.

Step 1 — find the changes.

ΔQ=55−40=+15\Delta Q = 55 - 40 = +15 units.

ΔP=8−10=−₹2\Delta P = 8 - 10 = -₹2.

Step 2 — apply the percentage-method formula.

Ep=ΔQΔP×PQ=15−2×1040=−7.5×0.25=−1.875E_p = \frac{\Delta Q}{\Delta P}\times\frac{P}{Q} = \frac{15}{-2}\times\frac{10}{40} = -7.5\times 0.25 = -1.875

Dropping the conventional minus sign, Ep=1.875E_p = 1.875.

Step 3 — classify. Since Ep>1E_p > 1, demand is relatively elastic: quantity changed more than proportionately to price.

Independent verification (total-outlay test). Total expenditure before =10×40=₹400= 10\times40 = ₹400; after =8×55=₹440= 8\times55 = ₹440. Price fell and total expenditure rose, which independently confirms elastic demand (Ep>1E_p>1). Both methods agree.

✓Final answer

Ep=1.875E_p = 1.875; demand is relatively elastic (Ep>1E_p>1).

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