Consider a two state decision problem with two actions $a,b$ with the

following state dependent payoffs:

$u(a,{}_1)=3$;$u(a,{}_2)=1$

$u(b,{}_1)=0$;$u(b,{}_2)=2$

$(a)$ Draw the figure illustrating the expected utility $of$ both actions $as$

a function $of$ the belief $p_1$ that the state $is{}_1.$

$(b)$ Draw and compute maximized $EU$ for all levels $of{p}_1,as$ defined

$by$ the upper envelope $in$ the figure.

$(c)$ Use the figure $to$ illustrate the value $of$ updating the probability

$of$ state ${}_1$ from prior ${}_1=0\mathrm{.}4to$ the pair $of$ posteriors ${}_1^L=$

$0\mathrm{.}2,{}_1^H=0\mathrm{.}8.[No$ computations needed.$]$