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Question 31 of 35

Q.If the price of a commodity rises by 10% and its quantity demanded falls from 40 units to 30 units, calculate coefficient of price elasticity of demand. Comment on the nature of price elasticity of demand.

(OR)
Explain the effect of the increase in the level of air pollution, on the market demand for 'Air Purifiers'. (Use diagram)
CBSECBSE Class XII Board 2019Subjective· 4mImportance★★★★★
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Part (a): A 10% price rise cutting quantity from 40 to 30 units gives Ed=−2.5E_d = -2.5; demand is elastic.

Part (b): Higher air pollution increases the demand for air purifiers (rightward shift), raising both equilibrium price and equilibrium quantity.

Part (a)

Price elasticity of demand measures how responsive quantity demanded is to a price change:

Ed=% ΔQ% ΔPE_d = \frac{\%\,\Delta Q}{\%\,\Delta P}

Step 1 — percentage change in quantity demanded. Initial Q1=40Q_1 = 40, final Q2=30Q_2 = 30:

% ΔQ=Q2−Q1Q1×100=30−4040×100=−25%\%\,\Delta Q = \frac{Q_2 - Q_1}{Q_1}\times 100 = \frac{30 - 40}{40}\times 100 = -25\%

Step 2 — percentage change in price = +10%+10\% (given).

Step 3 — coefficient of elasticity:

Ed=−25%+10%=−2.5E_d = \frac{-25\%}{+10\%} = -2.5

Nature. The negative sign reflects the inverse price–quantity relationship (law of demand). The magnitude ∣Ed∣=2.5>1|E_d| = 2.5 > 1, so demand is elastic: a 1% rise in price causes a 2.5% fall in quantity demanded — a more-than-proportionate response. …

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