Question $\backslash$#$4$

$(18$ marks$)$

Consider a risky project $\backslash ($ x $\backslash )$ that has the following payoff and probability distribution table:

a$.$

Compute the expected value, EV $,$ of project x$.(3$ marks$)$

b$.$

Suppose an investor, Mrs$.$ Donna Nash, has a utility function given by the function:

$\backslash [$

g$($x$)=$i $0\mathrm{.}4*$ x$^\{2\}+10$

$\backslash ]$

Compute CE$,$ the certainty equivalence of $\backslash ($ x $\backslash )$ for our investor. $(4$ marks$)$ Is Mrs$.$ Nash risk$-$neutral, risk$-$averse, or risk$-$loving? Explain $(1$ mark$)$

c$.$

Suppose another investor, Mr$.$ John Nash, has a utility function given by the function:

$\backslash [$

f$($x$)=25+10\backslash$sqrt$\{$x$\}$

$\backslash ]$

Compute CE$,$ the certainty equivalence of x for our investor. $(4$ marks$)$ Is Mr$.$ Nash risk$-$neutral, risk$-$averse, or risk$-$loving? Explain $(1$ mark$)$

d$.$

Suppose their son, Joe Nash, has a utility function given by the function:

$\backslash [$

f$($x$)=20*$ x$-10$

$\backslash ]$

Compute CE$,$ the certainty equivalence of $\backslash ($ x $\backslash )$ for our investor. $(4$ marks$)$ Is Joe Nash risk$-$neutral, risk$-$averse, or risk$-$loving? Explain $(1$ mark$)$