Ted is considering an investment project that will give him a wealth of W $=50$ if the plan is successful and a wealth of $25$ if it fails. The local bank will sell him a certificate of deposit $($CD$)$ that will give him a wealth of $40$ without any risk.

$1.$ What is Ted$$s expected wealth if each outcome occurs with an equal probability: $($a$)50$; $($b$)25$; $($c$)40$; $($d$)37\mathrm{.}5$;

$2.$ What probability for the good outcome would make Ted$$s project have the same expected return as

the CD $($a$)0\mathrm{.}2$; $($b$)0\mathrm{.}6$; $($c$)0\mathrm{.}8$; $($d$)0\mathrm{.}3$;

Assume that Ted$$s utility is given by U $=$

$3.$ What is Ted$$s expected utility using the probabilities you found in $2$: $($a$)5\mathrm{.}55$; $($b$)6\mathrm{.}24$; $($c$)7\mathrm{.}23$; $($d$)$

$8\mathrm{.}29$;

$4.$ What is the coefficient of absolute risk aversion at W $=50$: $($a$)0\mathrm{.}07$; $($b$)-0\mathrm{.}0001$; $($c$)1\mathrm{.}07$; $($d$)0\mathrm{.}01$;