In microeconomics, in which of the following cases does the law of demand fail to hold in its usual form, so that quantity demanded may rise when price rises?

Introduction / Context:
The law of demand states that, other things being equal, when the price of a good rises, the quantity demanded usually falls, and when the price falls, quantity demanded usually rises. However, there are rare exceptions where this relationship can be reversed. One of the most famous exceptions in microeconomics is the case of Giffen goods, which this question focuses on.

Given Data / Assumptions:

• The law of demand refers to an inverse relation between price and quantity demanded.
• We are asked when this law fails in its normal form.
• Options include Giffen goods, normal goods, inferior goods in general, and a combination.
• Ceteris paribus assumptions such as constant income and tastes are in the background.

Concept / Approach:
Giffen goods are a special category of inferior goods where the negative income effect of a price rise is so strong that it outweighs the usual substitution effect. As a result, when the price of such a staple good rises, very poor consumers may actually buy more of it because they can no longer afford better alternatives. This creates a positively sloped demand curve, contradicting the usual law of demand. Not all inferior goods behave this way, only specific ones with very particular conditions.

Step-by-Step Solution:
Step 1: Recall that normal goods always follow the law of demand, with higher price leading to lower quantity demanded.Step 2: Recognise that inferior goods usually still obey the law of demand even though demand falls when income rises.Step 3: Giffen goods are a rare type of inferior good where a price rise may cause quantity demanded to increase.Step 4: This behaviour means the law of demand fails in its typical form for Giffen goods.Step 5: Therefore, the correct choice is Giffen goods, not all inferior goods.

Verification / Alternative Check:
Textbooks frequently present Giffen goods as the classic exception to the law of demand. Diagrams show an upward sloping demand curve for such goods, with the positive relationship between price and quantity demanded. They also emphasise that Giffen goods are theoretically possible and were named after the economist Robert Giffen. Normal and most inferior goods retain a downward sloping demand curve, confirming that only Giffen goods break the usual law.

Why Other Options Are Wrong:
Normal goods by definition show higher demand when income rises and follow the typical inverse relation between price and quantity, so the law of demand holds. Inferior goods in general are not exceptions to the law of demand; they differ only in how demand responds to income changes. Option D, which groups Giffen goods with all inferior goods, is wrong because only some very special inferior goods are Giffen goods. Hence, only option A is correct.

Common Pitfalls:
Students often confuse inferior goods and Giffen goods, assuming all inferior goods violate the law of demand. The important distinction is that inferior goods are defined by income response, not by price behaviour, and most still have downward sloping demand curves. Another pitfall is to think that luxury goods or normal goods could show a positive price demand relation due to prestige effects, but such goods are usually discussed separately as Veblen goods, not as standard exceptions in exam level microeconomics.

Final Answer:
The law of demand fails in its usual inverse form primarily in the case of Giffen goods.