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text 6. (20 points) Let X = 14. Let _ be a preference relation on X. In Le

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text 6. (20 points) Let X = 14. Let _ be a preference relation on X. In Lecture notes-2
(see Lecture 2, page 7, Definition 9) we have encountered the definition of additiveity
property of a preference relation.
(a) (10 points) Suppose that the preference relation _ is represented by the utility
function u(21, 12) where,
u(21, $2) = 071 + 3×2
where o, 3 > 0. Verify that the preference relation _ satisfies addivity and strict
monotonicity.
2
(b) (10 points) Consider now the lexicographic preference ~{ on X = R?. Prove or
disprove the following statement : "The Lexicographic preference relation EL also
satisfies additiveity and strict monotonicity".

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