Canonical utility function. Consider the utility function c$-$o uc$)1-0($a$)$ where c denotes consumption of some arbitrary good and o $($Greek lowercase letter "sigma"$)$ is known as the "curvature parameter" because its value governs how curved the utility function is$.$ In the following, restrict your attention to the region e $>0($because "negative consumption" is an ill$-$defined concept$).$ The parameter o is treated as a constant. i$.$ Plot $($preferably with MATLAB$)$ the utility function for o $=0.$ Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? ii$.$ Plot $($preferably with MATLAB$)$ the utility function for o $=1/2.$ Does this utility function display diminishing marginal utility? $$i$.$ Consider instead the natural$-$log utility function u$($c$)=$ In$($c$).$ Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? iv$.$ Determine the value of o $($if any value exists at all$)$ that makes the general utility function presented above collapse to the natural$-$log utility function in part $($c$)($Hint: Examine the derivaives of the two functions.$)$