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Worked Examples · Example 3

Q.A shopkeeper finds that when he charges ₹50 per unit he sells 200 units (total sales value ₹10,000), and when he lowers the price to ₹40 he sells 260 units (total sales value ₹10,400). Using the total-outlay method, state the nature of demand, and verify with the percentage method.

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Total-outlay reasoning. Total expenditure (= seller's total revenue) was ₹10,000 at ₹50 and became ₹10,400 at ₹40. Price fell and total expenditure rose — by the total-outlay rule this signals elastic demand (Ep>1E_p>1). The price cut more than paid for itself through higher volume.

Verification by the percentage method. Base P=₹50P = ₹50, Q=200Q = 200; ΔQ=260−200=+60\Delta Q = 260-200 = +60; ΔP=40−50=−₹10\Delta P = 40-50 = -₹10.

Ep=ΔQΔP×PQ=60−10×50200=−6×0.25=−1.5E_p = \frac{\Delta Q}{\Delta P}\times\frac{P}{Q} = \frac{60}{-10}\times\frac{50}{200} = -6\times0.25 = -1.5

Numerical value Ep=1.5>1E_p = 1.5 > 1, which agrees with the total-outlay verdict. …

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