In consumer theory, which law states that when a consumer's demand for a good moves in the same direction as the consumer's income, this demand is inversely related to the price of the good?

Introduction / Context:
Consumer theory in microeconomics is built around several basic laws that describe how quantity demanded responds to changes in price, income, and related variables. The question highlights a situation where demand for a normal good moves in the same direction as income but is inversely related to price. This description corresponds to the core idea of the law of demand, which is one of the most important principles in introductory economics.

Given Data / Assumptions:

• The consumer is choosing a normal good, so demand rises with income.
• The demand for the good moves in the same direction as income, meaning higher income leads to higher demand.
• Demand is inversely related to price, meaning higher price leads to lower quantity demanded and vice versa.
• We assume ceteris paribus, that is other factors remain constant.

Concept / Approach:
The law of demand states that, other things being equal, there is an inverse relationship between the price of a good and the quantity demanded. As price falls, quantity demanded rises, and as price rises, quantity demanded falls. For normal goods, demand also typically increases with income. The combination of these ideas matches the description in the question. Other listed laws, such as the law of supply or law of substitution, do not directly describe the inverse price quantity relationship for consumers.

Step-by-Step Solution:
1. Recognise that the question describes a demand function where demand increases with income, typical for a normal good.2. Note that it also states demand is inversely related to price, which is the core of the law of demand.3. Recall that the law of supply describes a direct relationship between price and quantity supplied, which is different from demand behaviour.4. Understand that the law of substitution refers to substitution between goods when relative prices change, not directly to demand versus price for a single good.5. Conclude that the statement in the question corresponds most closely to the law of demand.

Verification / Alternative check:
A simple everyday example confirms this. When the price of a favourite snack decreases, consumers usually buy more of it, holding income and other factors constant. When the price increases, they buy less or switch to substitutes. If the consumer's income increases, they are able to buy more of the snack at any given price. This behaviour is perfectly captured by the law of demand combined with the idea of a normal good. No other listed law captures both the inverse relationship with price and the normal relationship with income in such a direct way.

Why Other Options Are Wrong:
Option B: The law of supply describes producers, not consumers. It states that quantity supplied and price move in the same direction, not an inverse direction.
Option C: The law of substitution focuses on the substitution effect between goods and does not directly summarise the overall relationship between price and quantity demanded for one good.
Option D: The law of optimal choice is not a standard named law in basic textbooks and does not specifically refer to demand and price.
Option E: The law of diminishing marginal utility explains why the demand curve slopes downward but does not itself state the complete inverse price quantity relationship; it is more about additional satisfaction from each unit.

Common Pitfalls:
Students sometimes confuse the law of demand with its underlying reasons such as diminishing marginal utility, income effect, and substitution effect. Remember that the law of demand is the final statement that quantity demanded varies inversely with price, holding other things constant. The other concepts are explanations for this law, not alternative laws. It is also important not to mix up the law of demand with the law of supply, since one applies to consumers and the other to producers.

Final Answer:
The situation described is explained by the law of demand.