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Worked Examples · Example 5

Q.The demand function for a good is Qd=100−2PQ_d = 100 - 2P. Find the price elasticity of demand at price P=₹20P = ₹20 using the point method.

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Step 1 — find QQ at P=20P = 20. Qd=100−2(20)=100−40=60Q_d = 100 - 2(20) = 100 - 40 = 60 units.

Step 2 — find the slope coefficient. In Qd=100−2PQ_d = 100 - 2P, the coefficient of PP is −2-2, so ΔQΔP=−2\dfrac{\Delta Q}{\Delta P} = -2.

Step 3 — apply the point-elasticity formula.

Ep=ΔQΔP×PQ=−2×2060=−4060=−0.67E_p = \frac{\Delta Q}{\Delta P}\times\frac{P}{Q} = -2\times\frac{20}{60} = -\frac{40}{60} = -0.67

Numerical value Ep=0.67E_p = 0.67.

Step 4 — classify. Since Ep<1E_p < 1, demand is inelastic at this price. …

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