Step 1: Understanding the Concept:
A demand curve parallel to the y-axis is a vertical straight line. This graphical representation shows that the quantity demanded of a commodity remains constant, regardless of any change in its price.
Step 2: Key Formula or Approach:
The formula for price elasticity of demand (\(E_d\)) is:
\[ E_d = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} = \frac{%\Delta Q_d}{%\Delta P} \]
Step 3: Detailed Explanation:
For a demand curve parallel to the y-axis, the quantity demanded does not change at all as the price changes. This means the change in quantity demanded (\(\Delta Q_d\)) is zero.
Substituting this into the formula:
\[ E_d = \frac{0}{%\Delta P} = 0 \]
This situation is known as perfectly inelastic demand. It typically applies to absolute necessities like life-saving drugs, where consumers will buy the same quantity irrespective of the price.
Step 4: Final Answer:
When the demand curve is parallel to the y-axis, the elasticity of demand is zero. Thus, option (A) is the correct answer.