3. Consider the following lottery: to (b) (C) (d) (f) P=(l.p1:2.p2;3..033 Jack is an expected utility maximizer and his utility function is u(1) = 1, u(2) = 2, u(3) = 3. In the prob- ability (Marchak-Machina) triangle with m on the horizontal and 193 on the vertical axis, sketch a indifference curve for Jack. What is the slope of this curve? Alice is an expected utility maximizer and her utility function is u(1) = 1, 11(2) 2 4, 14(3) 2 6. Does Alice prefer receiving 2 for sure or a 50 : 50 gamble between 1 and 3? In the same probability triangle sketch an indifference curve for Alice. What is the slope of this curve? Bob is also an expected utility maximizer and his utility function is u(1) = 9, u(2) = 12, u(3) = 18. Does Bob prefer receiving 2 for sure or a 50 : 50 gamble between 1 and 3? In the same probability triangle sketch an indifference curve for Bob. What is the slope of this curve? Infer a general principle from your ndings in (a)-(e) above. Instead of the numbers for consequences and utilities, use general symbols x1