For exam ular p mple transit tivity implies that a

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Unformatted text preview: if e ry economic ag gents aren' assumed to display 't trans sitive prefer rences. The assumption that the preference r n relation is complete and tra ansitive (i.e. nal mplications for the stric preferenc and ct ce ration preferences) has important im indiff ference rela ations If 1) (1 and , and ~. is rational (comple and tran ete nsitive) then n: is both irrefl s lexive (x x never holds) and transitive ( x d (if y z, then we must have x z). y (2 2) ~ is reflexive (x ~ x for alll x), transitive (if x ~ y and y ~ z then x ~ x z, s en z), and symmetric (if x ~ y, the y ~ x). 333 (3 If x 3) y z, z then x z. What does it all mean? Well, the first st , tatement sa that if w have a p ays we preference r relation that is ration then th strict preference rela nal, he ation will be irreflexive and transi e e itive. This simp means th I can ra my pref ply hat ank ference for cantaloupe at least as good as e s canta aloupe but I cannot rank my prefe erence for c cantaloupe as strictly preferred to e o 6 canta aloupe . The t transitive property of t first stat p the tement say that if I st ys trictly prefer steak to cat fo and I strictly prefe cat food t cantaloupe, then I m ood s er to must strictly prefer y steak to cantalo k oupe. This is sensible. The second sta atement is s simply point ting out that the indiffe erence relat tion is reflex xive, transit tive, and sy ymmetric. R Reflexivity m means that I am indiffe t erent betw ween one ca antaloupe a another cantaloupe AND I ca switch th order and r an heir and s remain indifferent. The trans still . sitivity prope says th if I am in erty hat ndifferent betw ween mango and apples and I am indifferen between apples and cherries, os m nt d then I must be indifferent b between ma angos and cherries. F Finally, the symmetric property says th I can sw hat witch goods around in this indiffer s rence ranking. For exam mple: Waterme elon ~ Lem mons can be equ uivalently st tated as Lemons ~ Waterm melon third conse equence of g s ve-like property that The t being rational is a transitiv holds for the str p...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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