Question

If the price elasticity of demand for a commodity is -2.5% and the percentage decrease in the quantity demanded is 10%, find out the percentage change in its price.

• A. 25%
• B. -25%
• C. 4%
• D. -4%

Hint:

Remember that price elasticity of demand is usually a negative number because price and quantity demanded move in opposite directions.
If you get a positive percentage change for price, it means the price has increased.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Price elasticity of demand ($\varepsilon_d$) measures how responsive quantity demanded is to a change in price.
Key Formula or Approach:
The formula for price elasticity of demand is:
\[ \varepsilon_d = \frac{% \text{ change in quantity demanded}}{% \text{ change in price}} \]

Step 2: Detailed Explanation:
We are given the following values:
- Price elasticity of demand ($\varepsilon_d$) = $-2.5$
- Percentage change in quantity demanded = $-10%$ (since it is a decrease)
Let $X$ be the percentage change in price.
Using the elasticity formula, we write:
\[ -2.5 = \frac{-10%}{X} \] Rearranging the equation to solve for $X$:
\[ X = \frac{-10%}{-2.5} \] \[ X = 4% \] A positive value of $4%$ represents a $4%$ increase in the price of the commodity.
This is consistent with the Law of Demand: to cause a decrease in quantity demanded, the price must rise.

Step 3: Final Answer:
Therefore, the percentage change in price is $4%$.