An investor has the following utility function: $=$ ln$()$ He is facing the following risky investment: Probability Payoff $($A$)0\mathrm{.}252200\mathrm{.}75110$ a$.$ What is the expected value of this investment? $(2$ marks$)$ b$.$ What is the expected utility of this investment? $(2$ marks$)$ c$.$ Is this investor risk$-$averse? Show why this is the case. $(4$ marks$)$ d$.$ Explain what the certainty equivalent is and compute it for the above risky gamble for the investor. $(4$ marks$)$ e$.$ What is the level of the risk premium if investor is asked to pay $137\mathrm{.}50$ for this investment? $(2$ marks$)$ f$.$ Define absolute risk aversion $($ARA$).$ Does this investor$$s utility function display increasing ARA? $(4$ marks$)$ g$.$ Find the relative risk aversion $($RRA$)$ of this utility function. Is it constant, increasing or decreasing? Is the RRA displaying rational economic behaviour? $(4$ marks$)$ h$.$ What do the slopes of the indifference curves of the type of investor as the one in this question depend on$?(3$ marks$)$