Assuming elasticity is reported in absolute value, a measured elasticity of one implies:
A. the percentage change in quantity demanded will exactly equal the percentage change in price.
B. the percentage change in quantity demanded will always exactly equal one.
C. both the percentage change in price and quantity demanded exactly equal one.
D. None of these is true.
The correct answer and explanation is :
The correct answer is:
A. The percentage change in quantity demanded will exactly equal the percentage change in price.
Explanation:
Elasticity in economics measures the responsiveness of one variable to changes in another variable. Specifically, price elasticity of demand (PED) measures how much the quantity demanded of a good responds to changes in the price of that good.
The formula for price elasticity of demand is:
$$
\text{Elasticity of Demand (E)} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}}
$$
- Elasticity greater than 1: Demand is elastic, meaning the quantity demanded is relatively responsive to price changes. A small price change leads to a large change in the quantity demanded.
- Elasticity less than 1: Demand is inelastic, meaning the quantity demanded is not very responsive to price changes.
- Elasticity equal to 1: This is referred to as unitary elasticity, where the percentage change in quantity demanded is exactly proportional to the percentage change in price.
In the case of unitary elasticity (elasticity = 1), a 1% increase in price leads to a 1% decrease in quantity demanded, or a 1% decrease in price leads to a 1% increase in quantity demanded. Therefore, the percentage changes in quantity demanded and price are exactly equal in magnitude, but opposite in direction (one increases, the other decreases).
Why the other options are incorrect:
- Option B: “The percentage change in quantity demanded will always exactly equal one” is not true because elasticity equal to 1 means the percentage change in quantity demanded equals the percentage change in price, not that the percentage change is always one.
- Option C: “Both the percentage change in price and quantity demanded exactly equal one” is incorrect because a price elasticity of 1 means the percentage changes are equal, but not necessarily equal to one. The numbers could be any percentage, as long as they are the same (e.g., a 5% increase in price would correspond with a 5% decrease in quantity demanded).
- Option D: “None of these is true” is incorrect because option A is indeed correct.
Thus, option A correctly describes the relationship in the case of unitary elasticity.