1. Jack has a utility function U (I) = I a where I is the money he could get from a game, with a > 0. In this game, Jack is facing two choices. Each choice is a decision chosen between Option A and Option B, which is as below. Choice 1 Option A: 50% chance of getting $1000 and 50% chance of getting $0 Option B: 100% chance of getting $125 Choice 2 Option A: 50% chance of getting $1000 and 50% chance of getting $0 Option B: 100% chance of getting $250 Suppose Jack chose Option A in Choice 1, and Jack chose Option B in Choice 2. (a) Suppose J ack's preference satisfy completeness, transitivity, continuity, and independence. Which will Jack choose in Choice 3, option A or option B? Please write down which assumptions you'll use for this justication. Choice 3 Option A: 50% chance of getting $1000 and 50% chance of getting $0 Option B: 100% chance of getting $500 (b) Please nd Jack's expected utility for each option by using the VNM expected utility function