Inferior Good | an individual allocates his or her entire budget between two goods, food and clothing

Suppose that an individual allocates his or her entire budget between two goods, food and clothing. Can both goods be inferior? Explain.

ANSWER

No, the goods cannot both be inferior; at least one must be a normal good. Here’s why. If an individual consumes only food and clothing, then any increase in income must be spent on either food or clothing or both (recall, we assume there are no savings and more of any good is preferred to less, even if the good is an inferior good). If food is an inferior good, then as income increases, consumption of food falls. With constant prices, the extra income not spent on food must be spent on clothing. Therefore as income increases, more is spent on clothing, i.e., clothing is a normal good.