Consider the following two-person (1 and 2) two-good (X and Y) economy.

The utility of person i is given by

=b_ix_i^1/2y_i^1/2

where x_i and y_i denote respectively person i's the consumption amount of good X and good Y, i=1, 2.

The value of parameter b_i is b₁ = 4 for person 1 and b₂ = 1 for person 2.

Person 1's income is M₁ = 1050 and person 2's income is M₂ = 1830 dollars.

The price of good X and price of good Y are given respectively by p_x =10 and p_y = 10.

Suppose the government takes T dollars 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"(if 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 free-market 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.