A preference function therefore assigns values to the ranking of a set of choices. This is useful as it allows us to see consumer behaviour as a maximisation problem: faced with a set of options and a budget constraint, we will choose what satisfies us most. Utility functions are often expressed as U(x1,x2,x3…) which means that U, our utility, is a function of the quantities of x1, x2 and so on. If A is a basket of goods, and , then U(A)>U(B). That is, if we prefer A to B it is because we derive greater utility from it.
Utility functions follow the same code of conduct, the same axioms, as preferences, because they are simply numerical representations of them. That is, they are transitive, complete, continuous and convex, for the same reasons. Being continuous allows us to differentiate them, and being insatiable allows us to say that:
This means that the more, the better, which is the same as saying that utility functions grow with quantity.
The most important thing to point out is perhaps the fact that utility functions do not assign a numerical value to our preferences. They simply indicate order and magnitude of preference, that is, what we like more and by how much.
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