Convex preferences: Difference between revisions

Revision as of 20:01, 29 November 2015

Revision as of 20:04, 29 November 2015

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Comparable to the greater-than-or-equal-to [[Order theory#Partially ordered sets|ordering]] relation <math>\geq</math> for real numbers, the notation <math>\succeq</math> below can be translated as: 'is at least as good as' (in [[Preference (economics)|preference]] satisfaction).

Similarly, <math>\succ</math> can be translated as 'is strictly better than' (in preference satisfaction), and Similarly, <math>\sim</math> can be translated as 'is equivalent to' (in preference satisfaction).

== Definition ==

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3. Consider a preference relation represented by:

:<math>u(x_1,x_2) = \max(x_1,x_2)</math>

This preference relation is not convex. PROOF: let <math>x=(3,5)</math> and <math>y=(5,3)</math>. Then <math>x\equivsim y</math> andsince both have utility 5. However, the convex combination <math>0.5 x + 0.5 y = (4,4)</math> is worse than both of them since its utility is 4.

== Relation to indifference curves and utility functions ==