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Problem 5 [2'] points} Your 1wealth at the begining of the period under euuaidecratiou is $10!]. You have an opportunity to invest $1: in a risky aaaet1 l} i: :1: E III}. There is a probability F that the rate of return on the asset 1will be (L? {in which case investing $1: yields hack $1.? :1: at the end of the period} and a probability 1 p that the rate ofreturn will be El.l {in which case investing $1: yields back $3.9 You are an expected utility maniruizer. Your utility function is u{y} = log{y], where y denotes your wealth at the end of the period. {a} 'What is the minimal Tvalue of the probability p for which your optimal investment 3" is positive? {b} Derive the formula deeeribing how your optimal investment 1:" varies with p. {c} If your wealth inuecreaaiee1 does your optimal investment 3" increase? Explain