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Math Help - characterizing slope of an implicit function

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    characterizing slope of an implicit function

    I have been working on the following problem for a long time, and got stuck. I really appreciate if someone can help.

    Let u be a twice differentiable, strictly increasing and concave function
    defined over positive real numbers ( u^{\prime }>0, and u^{\prime \prime}<0). Moreover, -\frac{u^{\prime \prime}(x)}{u^{\prime<br />
}(x)} is decreasing in x. I need to characterize the slope
    of an implicit function, y(x) , which solves the following equation:

    u(x+y) -u(x+b) =\alpha \int_{y}[u(x+x^{\prime}) -u( x+y)] dG(x^{\prime })

    where b is positive constant, and G is a continuous cumulative distribution function.

    I need to show that y^{\prime }(x) <1.

    So far I can show y^{\prime }(x) >0:
    Last edited by bkguler; December 2nd 2010 at 10:36 AM.
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