2. Consider the case of two people, A and B, with incomes 1A and ls, and suppose that they enter a risk sharing contract so that A's income is als + Blg + y, with B receiving the balance. The total risk premium for this arrangernent is given by Equation 7.1 in the chapter. (a) Expand this equation into one expressed in terms of Varla); Varls), and Cowly, 13). (Hint: Your answer should be a quadratic function of a and B.) (b) To find the values of a, b, and y that minimize this expression, take the derivatives of the expression with respect to a and B and set the derivatives equal to zero. Show that the solution of these three equations has a = B = pulpa + PB), where Pa = 1/7A and De = 1/Tg are the two risk tolerances. (c) Use mathematical induction and the results of this and the preceding problem to show that regardless of the number of people, person l's share of each risk should be the same as his or her share of the total risk tolerance of the group. 2. Consider the case of two people, A and B, with incomes 1A and ls, and suppose that they enter a risk sharing contract so that A's income is als + Blg + y, with B receiving the balance. The total risk premium for this arrangernent is given by Equation 7.1 in the chapter. (a) Expand this equation into one expressed in terms of Varla); Varls), and Cowly, 13). (Hint: Your answer should be a quadratic function of a and B.) (b) To find the values of a, b, and y that minimize this expression, take the derivatives of the expression with respect to a and B and set the derivatives equal to zero. Show that the solution of these three equations has a = B = pulpa + PB), where Pa = 1/7A and De = 1/Tg are the two risk tolerances. (c) Use mathematical induction and the results of this and the preceding problem to show that regardless of the number of people, person l's share of each risk should be the same as his or her share of the total risk tolerance of the group