Question 3 Consider an economy where households consume a single private good, X, and a public good G. In this economy all resources of production are exhausted, ie we are on the boundary of the production possibilities frontier. Households are homogeneous with utility defined by 1- U(Xi, G) = G X-a (4) Note that with homogenous utility we have 1 MRS; = n x MRS. It follows that the marginal utilities are and MUxi = au axi = (1 - a)GaX-a-1 = (1 - a)GaX-a MUG = au JG aGa-1X1-a 1- (5) (6) Defining X, as the numeraire good, we also have the following conditions over production OF OF 1 & = C, axi G where C is a constant. (7) 3a. Express the Samuelson Condition for the efficient level of G. 3b. Show your steps and simplify. Rearrange your expression so that G is on the left hand side by itself. Is G increasing, or decreasing in a? 3c. Is it possible to have a > 1? Explain, showing how the utility function is affected with a > 1, and what that means for the level of G provided.