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This is an advanced microeconomics question. Let p' be a probability distribution giving prizes $10 and $20 with probabilities 2/3 and 1/3, respectively, and p be a probability distribution giving prizes $5, $15, and $30 with probabilities 1/3, 5/9 and 1/9, respectively. Show that any risk averse expected utility maximizer will (weakly) prefer p' to p ( Contructo as a compound lottery). Can you supply a general statement of the principle at work in this specific example?2. (25 points) Consider Rubinstein's sequential bargaining game where players have differ- ent discount factors: of for player 1 and 62 for player 2. (a) Consider the three-period version of the game in which player 1 proposes first. Represent the game in extensive form. (b) Solve for the backward-induction outcome and the subgame-perfect Nash equilib rium. (c) Solve for the backward-induction outcome in the infinite horizon