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 ( , and ). Moreover, is decreasing in x. I need to characterize the slope

of an implicit function, y(x) , which solves the following equation:

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

I need to show that .

So far I can show :