Consider an economy with a risk free asset with return \(r_{f}\) and a risky asset whose random return \(\tilde{r}\) can take two possible values \(\{d, u\}\) with probabilities \(\{\pi, 1-\pi\}\), respectively. Assume that \(d

(i) \(u(x)=\sqrt{x}\);

(ii) \(u(x)=\log (x)\);

(iii) \(u(x)=x^{\gamma} / \gamma\), with \(\gamma eq 1\).