Kindly answer all questions as soon as possible. it's very urgent. Will upvote for the first.

Problem 1 (25 points) You are an investor with CRRA utility given by u(w) = 7, where w denotes your wealth = and y 2. Your current wealth is $10. You face an additive risk (lottery) whose payoff x is equal to -$1 with a probability of 50%, $2 with a probability of 30%, and $3 with a probability of 20%. (A) Is the risk of this lottery a pure risk? Explain why and justify your answer with calculations. (5 points) (B) How would you expect the absolute risk aversion to vary if wealth increases? Explain the result. (5 points) (C) How can you modify the problem (wealth and payoffs) such that the lottery becomes a zero-mean risk? (5 points) (D) Using the Arrow-Pratt approximation, compute the risk premium associated with this risk. Interpret the result. (5 points) (E) Consider another lottery whose payoff y is equal to -$1 with a probability of 30%, $2 with a probability of 30%, and $3 with a probability of 40%. Determine whether one lottery second-order stochastically dominates the other one. Justify your answer. (5 points) Problem 1 (25 points) You are an investor with CRRA utility given by u(w) = 7, where w denotes your wealth = and y 2. Your current wealth is $10. You face an additive risk (lottery) whose payoff x is equal to -$1 with a probability of 50%, $2 with a probability of 30%, and $3 with a probability of 20%. (A) Is the risk of this lottery a pure risk? Explain why and justify your answer with calculations. (5 points) (B) How would you expect the absolute risk aversion to vary if wealth increases? Explain the result. (5 points) (C) How can you modify the problem (wealth and payoffs) such that the lottery becomes a zero-mean risk? (5 points) (D) Using the Arrow-Pratt approximation, compute the risk premium associated with this risk. Interpret the result. (5 points) (E) Consider another lottery whose payoff y is equal to -$1 with a probability of 30%, $2 with a probability of 30%, and $3 with a probability of 40%. Determine whether one lottery second-order stochastically dominates the other one. Justify your answer. (5 points)