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    quasi-concavity

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    How to apply matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions?

    © BrainMass Inc. brainmass.com October 9, 2019, 3:43 pm ad1c9bdddf
    https://brainmass.com/economics/principles-of-mathematical-economics/jacobian-quasi-concavity-hessian-kuhn-tucker-conditions-11406

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    1. (a) Prove that quasi-concavity does not imply concavity.

    The function f(x,y) defined by:

    is quasi-concave, but not concave.

    Here's the graph in two dimensions:

    (b) Let ƒ be a C2 function on a convex subset D of R2. Assume that ƒ is strictly monotonic increasing. Prove that

    (i) if the bordered Hessian determinant of ƒ is positive (negative) for all x Є D, then ƒ is quasi-concave (quasi-convex) on D; and

    The bordered Hessian matrix for the function is
    | f_11 f_12 ... f_1n f_1 |
    | f_21 f_22 ... f_2n f_2 |
    H = | ...

    Solution Summary

    The expert prove that quasi-concavity does not imply concavity.

    $2.19