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 ) +2 In (x4 ) and person B's utility is given by UB= 2 In (xB) +3In (x?). The corresponding Marshallian demands are given by x4 = (3/5) (m^ /p,), x4 = (2/5) (m^ /P2). xP = (2/5) (mB/P, ), and x? = (3/5) (mB/P2), where m' is the income of person j = 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: . x4- (5.4, 6.0) and xB= (4.6, 3.2) A= (6.0, 6.0) and xB= (4.0, 2.0) . x4= (6.0, 3.2) and x= (4.0, 4.8) (b) Identify the income of each of the consumers and derive their gross demand functions. Derive their individual excess demand functions for both goods. (c) Derive the aggregate excess demands both goods. State Walras Law and use your findings to verify it. (d) Find the general equilibrium (i.e., the equilibrium price ratio). (e) Given the price ratio you found in part, find the final allocation of goods (Hint: you might want to normalize the "numerire" price before you proceed). Round your numbers to the third decimal place. Confirm that this allocation is Pareto efficient