Suppose there are two people in an economy whose utility functions are: U' (X ] , Z1 ) = 4 1 x, + In z, U'(X2,Z2) = 41 X2 + In Z2 where x1 and x2 denote conumption of a pure private good for person 1 and 2, respectively. Suppose the equation for the economy's production possibility frontier (PPF) is X = 160 - Z where X = X1 + x2 and z1 = Z2 = Z. a. Show that in this economy there is one efficient level of the public good and many efficient allocations. [9 marks] b. Now suppose that the person 2 has a strong (weak) taste for the public (private) good relative to person 1 as captured by this new utility function: U2(X 2, 2:2) = Inx1 + 41 22 Maintaining the utility function for person I and the other details given in part 4(a), show that in this modified two person economy there are many efficient levels of the public good and many efficient allocations. [12 marks]