If demand is inelastic then:

Question

BlackTom AI · Accepted Answer

Price elasticity of demand (PED) is defined as the percentage change in quantity demanded divided by the percentage change in price: PED = (%ΔQ) / (%ΔP). For inelastic demand, the absolute value of PED is less than 1, meaning quantity demanded changes proportionally less than price. 1) Relevant knowledge points and concepts - Law of demand: price and quantity demanded move in opposite directions (price up → quantity down). - Elasticity concept: if |PED| < 1 → inelastic demand (quantity responds less than price); if |PED| > 1 → elastic demand (quantity responds more than price). 2) Step-by-step reasoning - Let %ΔP = +10% (a 10% increase in price). - For inelastic demand, |PED| < 1. Write PED = -e where 0 < e < 1 (negative sign captures inverse relationship). - Then %ΔQ = PED × %ΔP = -e × 10%. 3) Calculations with intermediate steps (example) - Choose e = 0.5 as an illustrative inelastic value: %ΔQ = -0.5 × 10% = -5%. - This shows quantity demanded falls by 5%, which is smaller than the 10% price increase. - In general, since 0 < e < 1, |%ΔQ| = e × 10% < 10%. 4) Why the correct answer is correct - Because inelastic demand means quantity demanded is less responsive than price, a 10% price rise must produce a decrease in quantity smaller than 10%. The negative sign indicates a decrease; the magnitude is less than the price change. 5) Why the other options are incorrect - Option 1 (larger than 10% decrease) describes elastic demand (|PED| > 1), not inelastic. - Options 2 and 3 confuse causality and sign: they assert a change in quantity causes a decrease in price (reverse direction) and mix up magnitudes; elasticity describes how quantity responds to price, not the other way around, and these options also get the directional relationship wrong. 6) Conclusion Therefore the correct choice is: "a 10% increase in price will cause a smaller than 10% decrease in quantity demanded," which matches the provided answer.

If demand is inelastic then:单项选择题

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