3. Consider a general equilibrium model where there are two persons, A and B, and two goods, 1 and 2 (good 2 is the numeraire," i.e., its price can be normalized to unit once you find the equilibrium price ratio). Person A has 6 units of good 1 and 3 units of good 2 while person B has 4 units of good 1 and 5 units of good 2. Person A's utility is represented by UA- 3In (x4 ) +21n (x2) and person B's utility is given by Us= 2 In (x; ) +3 In (x, ). The corresponding Marshallian demands are given byxc^ = (3/5) (m^/p, ), x4 = (2/5) (m^/P2), xi = (2/5) (m /p1), and x5 - (3/5) (m /p2), where m' is the income of personj = A, B. (a) Find the marginal rates of substitution for both persons. Examine if the following three allocations are feasible and (for feasible allocations only) Pareto efficient: . x*- (5.4, 6.0) and x= (4.6, 3.2) . x4- (6.0, 6.0) and x= (4.0, 2.0) . x*= (6.0, 3.2) and x"= (4.0, 4.8)