In microeconomics, demand for a good is said to be inelastic when which relationship between percentage change in demand and percentage change in price holds?

Introduction / Context:
Price elasticity of demand is a key concept in microeconomics, marketing and business strategy. It measures how sensitive quantity demanded is to changes in price. Knowing when demand is elastic, inelastic or unit elastic helps firms set prices, predict revenue changes and understand consumer behaviour. Inelastic demand, in particular, describes situations where quantity demanded does not respond strongly to price changes.

Given Data / Assumptions:

• We are analysing the percentage change in quantity demanded relative to the percentage change in price.
• Price elasticity of demand is defined as percentage change in quantity demanded divided by percentage change in price.
• We are concerned with the magnitude of elasticity, not the sign (which is usually negative for normal goods).
• Demand can be classified as elastic, inelastic or unit elastic based on this magnitude.

Concept / Approach:
If the absolute value of price elasticity of demand is less than 1, demand is inelastic. This means that the percentage change in quantity demanded is smaller than the percentage change in price. For example, a 10 percent increase in price might cause only a 5 percent decrease in quantity demanded. When elasticity is greater than 1, demand is elastic, and quantity demanded responds strongly to price changes. When elasticity equals 1 in absolute value, demand is unit elastic, with proportional changes in price and quantity demanded.

Step-by-Step Solution:
Step 1: Recall the formula for price elasticity of demand as elasticity = (% change in quantity demanded) / (% change in price). Step 2: Define inelastic demand as the case where the absolute value of elasticity is less than 1. Step 3: Translate this into percentages: if price changes by a certain percentage, quantity demanded changes by a smaller percentage. Step 4: Recognise that in the options, the phrase “less than the percentage change in price of the good” corresponds to an elasticity magnitude below 1. Step 5: Choose the option that correctly captures this relationship, which is option A.

Verification / Alternative check:
Suppose the price of a necessity such as salt increases by 20 percent. Because consumers still need roughly the same amount, quantity demanded might fall by only 4 percent. Elasticity in this case is 4 / 20 = 0.2 in absolute value, which is less than 1, so demand is inelastic. This example matches the definition in option A: percentage change in quantity demanded is less than the percentage change in price. For luxury goods, the opposite often holds: a small price increase might cause a large drop in demand, indicating elastic demand, which is not the case here.

Why Other Options Are Wrong:
Option B describes a situation where percentage change in demand is greater than the percentage change in price, which corresponds to elastic demand, not inelastic demand. Option C describes unit elastic demand, where percentage changes are equal. Option D is incorrect because elasticity is specifically defined using percentage changes. Option E suggests no change in demand regardless of price, which would represent perfectly inelastic demand, a special extreme case, and is not the general definition given in standard economics. Only option A accurately captures the usual meaning of inelastic demand.

Common Pitfalls:
Students sometimes confuse inelastic with elastic because of everyday language, where “elastic” simply means stretchable. In economics, you must pay attention to whether quantity changes more or less than price in percentage terms. Another mistake is to ignore the absolute value and focus on the negative sign of elasticity. In exams, clearly state that inelastic demand means the absolute value of elasticity is less than 1 and that quantity demanded responds proportionally less than price changes. This precise understanding will help you answer related questions confidently.

Final Answer:
Demand is said to be inelastic when the percentage change in quantity demanded is less than the percentage change in the price of the good.