Consider the following twoperson (1 and 2) two-good (X and Y) economy. The utility of person i is given by l l U) = bloc? y? where xi and yi denote respectively person i's the consumption amount of good X and good Y, i:1, 2. The value of parameter bi is b1 = 4 for person 1 and b2 = 1 for person 2. Person 1's income is M = 1050 and person 2's income is M2 = 1830 dollars. The price of good X and price of good Y are given respectively by pX :10 and py = 10. Suppose the government takes Tdoilars from the person with the greater income {and if their incomes are equal, takes it from person 2) and gives it to the other person. Derive the equation of the utility possibilities frontier (UPF) associated with this "redistribution scheme" (it you haven't already). Then determine the amount of good X consumed by the recipient of the T (after the redistribution) if the government chooses the T such that the utility of the recipient increases by 80 compared to her utility in the freemarket outcome, i.e., her utility in the absence of this redistribution scheme. Then enter below the amount of good X consumed by person 1 after the redistribution