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

The utility of person i is given by

Ui=bix^1/2y^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 = 5 for person 1 and b₂ = 1 for person 2.

Person 1's income is M₁ = 1100 and person 2's income is M₂ = 1950 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 enter the value of the slope of the UPF, dU₂/dU₁ below