Understanding Non-Convex Preferences in Consumer Theory: f(u)=x+y

This article explores the utility function f(u)=x+y, which signifies that the consumer's preferences are not strictly convex. This implies that the consumer doesn't necessarily favor a balanced combination of x and y. Instead, they might have a preference for either x or y, or a combination of x and y that isn't equally balanced.

For instance, if x represents the amount of food consumed and y represents the amount of leisure time, the consumer might prefer more leisure time than food, or vice versa. Alternatively, they could favor a combination of food and leisure time that is uneven, such as having a lot of food and very little leisure time, or vice versa.

In conclusion, the utility function f(u)=x+y illustrates that the consumer's preferences are not strictly convex, and they might have a preference for specific combinations of x and y that aren't equally balanced.