Unformatted text preview: X is the set of all conceivable basketball players, and V ( x ) is the height of player x . Note that the statement x % y if V ( x ) ≥ V ( y ) always deFnes a pref-erence relation since the relation ≥ on < satisFes completeness and transitivity. Even when the description of a preference relation does not in-volve a numerical evaluation, we are interested in an equivalent nu-merical representation. We say that the function U : X → < represents the preference % if for all x and y ∈ X , x % y if and only if U ( x ) ≥ U ( y ) . If the function U represents the preference relation % , we refer to it as a utility function and we say that % has a utility representation . It is possible to avoid the notion of a utility representation and to “do economics” with the notion of preferences. Nevertheless, we usually use utility functions rather than preferences as a means of de-scribing an economic agent’s attitude toward alternatives, probably...
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- Fall '10
- Utility, preference relation, taller basketball player