Your wealth at the begining of the period under consideration is $100. You have an opportunity to invest $3: in a risky asset, D g a: 3 100. There is a probability p that the rate of return on the asset will be 0.2 (in which case investing $3: yields back $1.2 a: at the end of the period) and a probability 1 3) that the rate of return will be {).1 (in which case investing $3: yields back $0.9 You are an expected utility maximizer. Your utility function is My) 2 ln(y), where 3; denotes your wealth at the end of the period. (a) What is the minimal value of the probability p for which your optimal investment as" is positive? (b) Derive the formula describing how your optimal investment 22* varies with p. (c) If your wealth increases, does your optimal investment 33* increase? Explain