Consider the Diamond$-$Dybvig banking model. Assume, as in the notes, that u$($c$)=($c $^(1-$ a$))/(1-$ a$)$ and that a $=0\mathrm{.}5$ Assume that r $=0\mathrm{.}05$ and t $=0\mathrm{.}5$ using the Excel spreadsheet, find the optimal banking contract. Find c and c$.$ Compare these to the case above when a $=2$ Economically, how do these banking contracts differ? Why do you think this is the case $($hint: think about risk$-$aversion$)?$ Explain your answers carefully.