If demand is elastic then:

Question

BlackTom AI · Accepted Answer

Price elasticity of demand greater than 1 means that quantity demanded changes proportionally more than the price change, so a price decrease leads to a relatively larger increase in quantity demanded.

1) Relevant concepts
- Price elasticity of demand (E) is defined as E = %ΔQ / %ΔP.
- For most goods E is negative (price and quantity move in opposite directions), so |E| measures responsiveness. "Elastic" means |E| > 1: quantity responds more than price in percentage terms.

2) Step-by-step reasoning
- A 10% decrease in price corresponds to %ΔP = −10%.
- Write E = %ΔQ / %ΔP. For elastic demand, let E = −k where k > 1 (the negative sign captures the usual inverse relationship).
- Solve for %ΔQ: %ΔQ = E × %ΔP = (−k) × (−10%) = k × 10%.

3) Intermediate calculation examples
- If k = 2 (E = −2), then %ΔQ = 2 × 10% = +20% (quantity increases by 20%).
- If k = 1.5 (E = −1.5), then %ΔQ = 1.5 × 10% = +15% (quantity increases by 15%).
- In every case with k > 1, %ΔQ > 10% and positive (an increase).

4) Why the correct answer is correct
- Elastic demand (|E| > 1) implies the percentage increase in quantity exceeds the percentage decrease in price. Therefore a 10% price decrease causes a larger than 10% increase in quantity demanded.

5) Why the other choices are incorrect
- Choice 1 ("larger than 10% decrease in quantity demanded"): wrong sign — a price decrease cannot cause a quantity decrease for normal downward-sloping demand.
- Choice 3 ("smaller than 10% decrease in quantity"): wrong direction and magnitude.
- Choice 4 ("smaller than 10% increase in quantity"): describes inelastic demand (|E| < 1), not elastic.

6) Conclusion
This reasoning confirms the correct answer: a 10% decrease in price will cause a larger than 10% increase in quantity demanded.

If demand is elastic then:Single choice

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