A company faces a price elasticity of demand of -2.5 for its product and is currently selling 10,000 units per month. If it wants to increase the quantity sold by 6 per cent, by approximately what percentage must it reduce its price, assuming the price elasticity of demand remains constant?

Introduction / Context:
Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is widely used by firms when deciding how much to alter prices in order to achieve a target change in sales volume. This question presents a numerical application of the elasticity formula, asking you to calculate the approximate percentage price reduction needed to increase quantity demanded by a given percentage when elasticity is known.

Given Data / Assumptions:

• Price elasticity of demand (E) for the product is -2.5.
• The company currently sells 10,000 units per month (this helps set context, but the calculation focuses on percentages).
• The firm wants to increase quantity sold by 6 per cent, so percentage change in quantity demanded (ΔQ%) is +6%.
• Price elasticity is assumed to remain constant over the small change in price.
• We use the standard formula: E = (percentage change in quantity demanded) / (percentage change in price).

Concept / Approach:
Price elasticity of demand is defined as E = (ΔQ% / ΔP%), where ΔQ% is the percentage change in quantity demanded and ΔP% is the percentage change in price. Because demand curves typically slope downward, E is negative, reflecting that quantity demanded and price move in opposite directions. If we know E and the desired ΔQ%, we can rearrange the formula to find ΔP% as ΔP% = ΔQ% / E. Here, the company wants to increase quantity demanded by 6 per cent, and elasticity is -2.5, so we can compute the required price change.

Step-by-Step Solution:
Step 1: Write down the elasticity formula: E = ΔQ% / ΔP%.Step 2: Substitute the known values: E = -2.5 and ΔQ% = +6% (since the company wants a 6 per cent increase in quantity demanded).Step 3: Rearrange the formula to solve for ΔP%: ΔP% = ΔQ% / E.Step 4: Substitute the numbers: ΔP% = 6 / (-2.5).Step 5: Compute 6 divided by 2.5: 6 / 2.5 = 2.4. Because E is negative, ΔP% = -2.4%.Step 6: The negative sign indicates that price must be reduced by approximately 2.4 per cent to achieve a 6 per cent increase in quantity demanded.Step 7: Among the given options, 2.40% matches this required price reduction.

Verification / Alternative check:
We can verify the calculation by checking the implied elasticity using our result. If price falls by 2.4 per cent and quantity demanded increases by 6 per cent, then E = 6 / (-2.4) = -2.5, which matches the given elasticity. This confirms that our computed price change is consistent with the defined elasticity. The exact initial price or quantity does not matter because the elasticity formula uses percentage changes.

Why Other Options Are Wrong:
3.50%: If price fell by 3.5 per cent and quantity increased by 6 per cent, elasticity would be 6 / (-3.5) ≈ -1.71, which does not match the given elasticity of -2.5.

15.00%: A 15 per cent price cut would be far too large. With elasticity -2.5, this would imply quantity increasing by about 37.5 per cent, which is much more than the desired 6 per cent.

2.50%: Using 2.5 per cent, elasticity would be 6 / (-2.5) = -2.4, which is close but not exactly the given -2.5; the question expects more precise alignment with -2.5 via 2.4 per cent.

1.50%: A 1.5 per cent reduction would yield elasticity 6 / (-1.5) = -4, which is very different from -2.5.

Common Pitfalls:
One common error is to invert the formula incorrectly, using ΔP% / ΔQ% instead of ΔQ% / ΔP%. Another is to ignore the negative sign on elasticity and forget that a rise in quantity demanded typically requires a fall in price. Students may also guess a round number like 2.5 per cent without carefully dividing 6 by 2.5. To avoid such mistakes, always start from the correct elasticity formula, rearrange it algebraically, and pay attention to the sign of the elasticity.

Final Answer:
To increase quantity sold by 6 per cent, the company must reduce its price by approximately 2.40 per cent.