riskI do not know the specific felicity function, so let it be a general form of u(x).
Ok, so absolute risk aversion = - $u_x$$_x$ / $u_x$
How can I show that this is decreasing over x?
Let $r=-u_{xx}/u_{x}$. You need to show that this is decreasing in $x$, or that $\frac{dr}{dx}<0$. Since $r$ is a function of $u$, this can be further solved out in terms of $u$ by using the chain rule on the expression for $r$.
Of course, not every utility function exhibits decreasing absolute risk aversion, so you’ll need to know something more about the utility function to show that $\frac{dr}{dx}<0$ is true.
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