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    June 06

    How to prove indifference curve is convex function (under the conditions of U’(w)>0 and U’’(w)<0)?

    某大学金融系.某副教授答案:

    Initial set up:

    clip_image002[2]

    Indifference curve is represented by:

    clip_image004[2]

    clip_image006

    clip_image008

    clip_image010

    clip_image012

    For the following equation hold,
    clip_image008[1]

    the following inequality must satisfy:

    clip_image014

    clip_image016

    clip_image018

    Which means indifference curve is convex function.