Final answer:
Complementary goods are items used together where an increase in one leads to an increase in the other, but not all goods have this relationship. Usual properties of preferences like completeness, transitivity, and non-satiation can be modeled with utility functions. Compensating variation is the monetary measure of returning to original utility after a price change.
Step-by-step explanation:
Not all goods can be complements because complementary goods are defined as items that are often used together, and an increase in consumption of one leads to an increase in consumption of the other. For example, if the price of hot dogs rises and demand for hot dog buns falls as a result, hot dogs and buns are complements. However, some goods do not have this relationship and can be consumed independently without affecting the demand for another good.
Preferences have "usual" properties that can be represented by a utility function. These include completeness, where individuals can rank their preferences; transitivity, where if a person prefers A over B and B over C, they should prefer A over C; and non-satiation, where more of a good is better. These can be modeled using utility functions to explain and predict consumer behavior.
The compensating variation is defined using the expenditure function. It measures the amount of money a consumer would need to reach their original utility after a price change, showing the consumer's willingness to pay to return to the initial welfare level.