Suppose that Beyonce and Madonna have utility functions ry + 0 In (g) where J = B for Beyonce and J = M for Madonna. my is a private good and g is a public good. 0g = 2 and Oy = 4. Each of them has 10 units of the private good that can be transformed into units of the public good on a one to one basis. Consider four possible allocations of these goods: Allocation 1:9 = 0, TB = CM = 10 Allocation 2: g = 2, TB = IM = 9 Allocation 3: g = 6, TB = 10, IM = 4 Allocation 4: g = 2, TB = 8, IM = 10 (a) Is allocation 1 Pareto efficient? (b) Which allocation maximizes the sum of utilities? (c) Which is Beyonce's preferred allocation? Does this mean that Beyonce is a Utilitarian? (d) Now suppose that Kanye who has utility function rx + 2 In(g) joins with Beyonce and Madonna to form a community of three people. He has an endowment of ten units of r and can propose a referendum with a majority vote over any pair of allocations. What will the outcome be? Does this mean that Kanye is a Utilitarian