Consider an agent (a) with piecewise linear utility function (u^{a}(x)=x) for (x leq x_{0}) and (u^{a}(x)=x_{0}+aleft(x-x_{0} ight)) otherwise, for some (a in(0,1)), and an agent

Consider an agent \(a\) with piecewise linear utility function \(u^{a}(x)=x\) for \(x \leq x_{0}\) and \(u^{a}(x)=x_{0}+a\left(x-x_{0}\right)\) otherwise, for some \(a \in(0,1)\), and an agent \(b\) with utility function \(u^{b}(x)=x\) for \(x \leq x_{0}\) and \(u^{b}(x)=x_{0}+b\left(x-x_{0}\right)\) otherwise, for some \(b \in(0,1)\). Show that agent \(b\) is more risk averse than agent \(a\) if and only if \(b \leq a\).