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Exercises · Q22

Q.Consider the demand for a good. At price Rs 4, the demand for the good is 25 units. Suppose price of the good increases to Rs 5, and as a result, the demand for the good falls to 20 units. Calculate the price elasticity.

Yanam CbseNCERTSubjective· 3mImportance★★★★★
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Price elasticity of demand measures the responsiveness of quantity demanded to a price change. Here, a 25% price rise causes a 20% fall in quantity, yielding an elasticity of –0.8 (inelastic demand).

Price elasticity of demand tells us how sensitive consumers are to a change in price. When price rises, quantity demanded typically falls—but by how much? A large response means demand is elastic (consumers are price-sensitive); a small response means demand is inelastic (consumers will buy roughly the same amount even if price changes). The elasticity coefficient captures this relationship as a ratio: the percentage change in quantity demanded divided by the percentage change in price.

The formula is:

ed=Percentage change in quantity demandedPercentage change in price=ΔQ/QΔP/Pe_d = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} = \frac{\Delta Q / Q}{\Delta P / P}

Because price and quantity move in opposite directions along a demand curve, elasticity is negative. We often report the absolute value for convenience, but the sign matters economically—it reflects the law of demand.

Now let's calculate step by step.

Step 1. Identify the initial and new values.

  • Initial price P1=4P_1 = 4, initial quantity Q1=25Q_1 = 25
  • New price P2=5P_2 = 5, new quantity Q2=20Q_2 = 20

Step 2. Compute the change in quantity and the change in price.

ΔQ=Q2−Q1=20−25=−5\Delta Q = Q_2 - Q_1 = 20 - 25 = -5

ΔP=P2−P1=5−4=1\Delta P = P_2 - P_1 = 5 - 4 = 1

Step 3. Calculate the percentage change in quantity demanded.

ΔQQ1=−525=−0.2=−20%\frac{\Delta Q}{Q_1} = \frac{-5}{25} = -0.2 = -20\%

Step 4. Calculate the percentage change in price.

ΔPP1=14=0.25=25%\frac{\Delta P}{P_1} = \frac{1}{4} = 0.25 = 25\%

Step 5. Divide the percentage change in quantity by the percentage change in price.

ed=−0.20.25=−0.8e_d = \frac{-0.2}{0.25} = -0.8 …

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