2. Consider a society with two individuals with utility functions U = 3X^0.5 and 6X^0.5 respectively, where X = income. The total income of the society is $100. (a) Find the expressions for the marginal utility of the two individuals. Do the MU functions exhibit diminishing MU of income? (b) How would a utilitarian government distribute this income between the two individuals? Set up the maximization problem (with resource constraint) and solve for X1 and X2 (10 pts) (c) Draw the two MU functions in a diagram and show the utilitarian allocation. (Hint: think of MU functions as similar to demand functions).