Final answer:
A discontinuous preference relation in a utility function refers to a preference relation that is not continuous, and it is when there are abrupt changes in preference at certain levels.
Step-by-step explanation:
A discontinuous preference relation in a utility function refers to a preference relation that is not continuous.
Continuity is an important assumption in utility theory because it guarantees that small changes in the attributes of a good will result in small changes in the level of utility. However, there are situations where preferences are not continuous, such as when there are abrupt changes in preference at certain levels.
For example, let's say a person prefers to buy clothes from a particular brand. However, their preference suddenly changes if the price of the clothes exceeds a certain threshold. This would result in a discontinuous preference relation in their utility function.