Unformatted text preview: { x  f ( x ) ≥ f ( y ) } is convex. Obviously, if a preference relation is represented by a utility function, then it is convex iff the utility function is quasiconcave. However, the convexity of % does not imply that a utility function representing % is concave. (Recall that u is concave if for all x , y , and λ ∈ [ 0, 1 ] , we have u (λ x + ( 1 − λ) y ) ≥ λ u ( x ) + ( 1 − λ) u ( y ) .) Special Classes of Preferences Often in economics, we limit our discussion of consumer preferences to a class of preferences possessing some additional special properties. ±ollowing are some examples of “popular” classes of preference relations discussed in the literature....
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 Fall '10
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