A good whose demand is unitary elastic refers to:
A. one in which the absolute value of the percentage change in the quantity demanded exactly equals the absolute value of the corresponding percentage change in price.
B. one in which the absolute value of the percentage change in quantity exactly equals one.
C. one in which the absolute value of the percentage change in price exactly equals one.
D. one in which both the absolute value of the percentage change in quantity demanded and the absolute value of the corresponding percentage change in price equals one.
The correct answer and explanation is :
The correct answer is:
A. one in which the absolute value of the percentage change in the quantity demanded exactly equals the absolute value of the corresponding percentage change in price.
Explanation:
When we say a good has unitary elasticity of demand, we are referring to a situation in which the percentage change in quantity demanded is exactly proportional to the percentage change in price. In other words, the absolute value of the percentage change in quantity demanded is equal to the absolute value of the percentage change in price. This means that the elasticity coefficient is equal to 1.
To understand this, let’s break it down further:
- Elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price. The formula for price elasticity of demand is: $$
E_d = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}
$$ - If the absolute value of this elasticity coefficient is 1, then the percentage change in quantity demanded is exactly proportional to the percentage change in price. For example, if the price of a product rises by 10%, the quantity demanded will decrease by exactly 10%. Conversely, if the price drops by 10%, the quantity demanded will increase by 10%.
- This scenario is called unitary elasticity because the demand curve has a specific slope where the total revenue (price × quantity) remains unchanged when prices change, as the loss in revenue from a price increase is exactly offset by the reduction in quantity demanded.
Why the other options are incorrect:
- B: This refers to a specific percentage change in quantity being equal to 1, which is not a definition of unitary elasticity.
- C: This suggests a situation where the percentage change in price equals 1, which is unrelated to elasticity of demand.
- D: This is incorrect because unitary elasticity is about the relationship between price changes and quantity demanded changes in terms of percentage change, not whether they both equal 1.
In conclusion, the definition of unitary elasticity of demand is the equality of the absolute percentage changes in quantity demanded and price, which matches option A.