6. Do NOT do this question if you have done question #5 above! (20 pts total) 1 Castor (C) and Pollux (P), two twins, have identical preferences over two goods described by the utility function: 1 U(X1, X2) = UC(X1, X2) = UP(X1, X2) = /3In(X1) + 3/3In(x2) 91 where In() is the natural log function and x1 and x2 are the quantities consumed of goods 1 and 2. Suppose Castor's initial endowment of the two goods are (e1(, ez() = (20, 10) whereas Pollux's initial endowment is (e1, ex.) = (10, 20).1 Given the twins starting endowments and their utility functions, 1 (a) (12 points) Would the allocation (x1(, x2() = (15, 15) and (X1), X2 ) = (15, 15) be a Pareto efficient allocation? Provide analysis and explanation. 1 (b) (8 points) Would the twins be willing to trade to get the allocation in (a), where they each get 15 units of both goods? If "yes" by how much would Pollux's utility increase? If "no", why not? 1