A canonical utility function. Consider the utility function "(c) - mo -1 1-o 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 c>0 (because "negative consumption" is an ill-defined concept). The parameter o is treated as a constant. a. Plot the utility function for o = 0. Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? b. Plot the utility function for o = 1 / 2. Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? C. 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? Determine the value of o (if any value exists at all) that makes the general utility d. function presented above collapse to the natural-log utility function in part c. (Hint: Examine the derivatives of the two functions.)