A manufacturer faces a price elasticity of demand of minus 2 for its product. If it lowers the price by 5 per cent, by what percentage will the quantity sold increase?

Introduction / Context:
Price elasticity of demand is a central concept in microeconomics. It measures how sensitive the quantity demanded of a good is to changes in its price. Many quantitative questions in exams use the elasticity formula to link percentage change in quantity demanded with percentage change in price. This question focuses on applying the basic elasticity formula when elasticity and percentage change in price are given, and asks for the percentage change in quantity sold under a specific scenario.

Given Data / Assumptions:
• Price elasticity of demand (Ed) for the product is minus 2. • The manufacturer reduces price by 5 per cent. • We assume the elasticity remains constant in this range of price change. • We must find the resulting percentage increase in quantity sold.

Concept / Approach:
The basic formula for price elasticity of demand is Ed = percentage change in quantity demanded divided by percentage change in price. The sign is usually negative because quantity demanded moves in the opposite direction to price. Rearranging this formula allows us to compute the unknown percentage change in quantity when elasticity and price change are known. Here the given elasticity is minus 2, and the price change is a reduction of 5 per cent, so the percentage change in quantity demanded will be equal to Ed multiplied by the percentage change in price.

Step-by-Step Solution:
Step 1: Write the elasticity formula: Ed = (% change in quantity demanded) / (% change in price). Step 2: Substitute the known values: Ed = minus 2 and % change in price = minus 5 (because price falls). Step 3: Let % change in quantity demanded be represented by x. Then we have minus 2 = x / minus 5. Step 4: Multiply both sides by minus 5 to solve for x. This gives x = minus 2 * minus 5. Step 5: Compute the product. Minus 2 * minus 5 equals positive 10, so x = plus 10 per cent. Step 6: Therefore quantity sold will increase by 10 per cent when price is reduced by 5 per cent with elasticity equal to minus 2.

Verification / Alternative check:
A quick mental check is to ignore the minus sign and think in absolute values. An elasticity of 2 means quantity responds twice as much as the price change in percentage terms. If the price change is 5 per cent, the quantity change must be 10 per cent. Since the price falls, quantity must rise, so we add the positive sign and get a 10 per cent increase. This reasoning confirms the formal calculation and avoids possible sign errors.

Why Other Options Are Wrong:
3 per cent is lower than the price change and would correspond to elasticity in absolute value less than one, which contradicts the given elasticity of 2.
2.5 per cent would suggest that the quantity response is only half of the price change, which again conflicts with the idea of a highly elastic demand with magnitude 2.
7 per cent is not equal to twice the given price change and does not match the direct proportional relationship implied by the formula Ed = 2 in absolute value.

Common Pitfalls:
Many learners forget the negative sign in elasticity and become confused about whether quantity increases or decreases. Others mix up the formula and divide the price change by elasticity instead of multiplying. Another common mistake is to write 5 multiplied by 2 as 15 by accident in haste. Careful attention to signs and a calm check that a price fall should lead to a quantity increase when the elasticity magnitude is greater than one will avoid these errors in similar questions.

Final Answer:
If the manufacturer lowers the price by 5 per cent with a price elasticity of demand of minus 2, the quantity sold will increase by 10 per cent.