Suppose that Beyonc and Madonna have utility functionsxJ+Jln (g)whereJ=Bfor Beyonc andJ=Mfor Madonna.xJis a private good andgis a public good.B= 2andM= 4. Each of them has10units 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:

Allocation1:g=0,xB=xM=10

Allocation2:g=2,xB=xM=9

Allocation 3:g= 6,xB= 10,xM= 4

Allocation 4:g= 2,xB= 8,xM= 10

1.(a)Is allocation 1 Pareto efficient?

2.(b)Which allocation maximizes the sum of utilities?

(c) Which is Beyonc's preferred allocation? Does this mean that Beyonc is a Utilitarian?

(d) Now suppose that Kanye who has utility functionxK+ 2 ln(g)joins with Beyonc and Madonna to form a community of three people. He has an endowment of ten units ofxand 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?