On a standard price–quantity diagram, a perfectly inelastic demand curve has which geometric shape?

Introduction / Context:
Elasticity of demand measures how responsive quantity demanded is to changes in price. A perfectly inelastic demand curve describes an extreme situation in which quantity demanded does not change at all, no matter how high or low the price becomes. Understanding the shape of this theoretical demand curve is important for interpreting diagrams in microeconomics and for answering conceptual questions about elasticity.

Given Data / Assumptions:

• The demand curve is drawn on a graph with price on the vertical axis and quantity demanded on the horizontal axis.
• Perfectly inelastic demand means the price elasticity of demand is equal to zero.
• When elasticity is zero, changes in price have no effect on the quantity demanded.
• The options describe various possible shapes: horizontal, vertical, steep slopes, and upward sloping lines.

Concept / Approach:
In a diagram where quantity demanded is measured along the horizontal axis, if demand is perfectly inelastic, the quantity demanded remains constant regardless of the price. This means that no matter where you move on the price axis, the quantity stays fixed at one value. The graphical representation of a constant quantity at all prices is a vertical line. In contrast, a perfectly elastic demand curve is horizontal, indicating that at a particular price, consumers are willing to buy any quantity but will buy none at any higher price. Therefore, the correct shape for a perfectly inelastic demand curve is a perfectly vertical line.

Step-by-Step Solution:
Step 1: Recall that elasticity of demand measures percentage change in quantity demanded divided by percentage change in price.Step 2: Recognise that perfectly inelastic demand means elasticity is zero, so quantity demanded does not change at all when price changes.Step 3: Visualise the demand curve on a price–quantity graph where the horizontal axis shows quantity and the vertical axis shows price.Step 4: If quantity is constant at all price levels, the curve must be a vertical line at that fixed quantity.Step 5: Compare with other possibilities: a horizontal line would represent perfectly elastic demand, and sloping lines would indicate that quantity changes when price changes.Step 6: Conclude that a perfectly vertical line correctly represents perfectly inelastic demand.

Verification / Alternative check:
Microeconomics diagrams in standard textbooks routinely show four basic types of demand curves: ordinary downward sloping, perfectly inelastic vertical, perfectly elastic horizontal, and various curved shapes for unitary elasticity or other conditions. In each case, the perfectly inelastic demand curve is depicted as a vertical line, often used as an example in the context of life saving medicines or addictive substances where demand may be relatively insensitive to price.

Why Other Options Are Wrong:
A very steep downward sloping line is highly inelastic but not perfectly inelastic because quantity still changes slightly when price changes. A perfectly horizontal line represents perfectly elastic demand, not perfectly inelastic demand. A downward sloping line at roughly forty five degrees is a generic demand curve and does not represent zero elasticity. An upward sloping line from left to right is associated with unusual cases like Giffen goods or supply curves, not with perfectly inelastic demand.

Common Pitfalls:
Students sometimes confuse the extreme cases of elasticity and mix up which shape corresponds to perfect elasticity and which corresponds to perfect inelasticity. A useful memory aid is that when demand is perfectly inelastic, quantity is fixed, so the demand curve must be vertical at one quantity value. When demand is perfectly elastic, price is fixed, so the demand curve is horizontal at one price value.

Final Answer:
A perfectly inelastic demand curve is shown by a perfectly vertical line on the price–quantity diagram.