Question: Problem 13-31 (Algorithmic) Consider a decision maker who is comfortable with an investment decision that has a 50 percent chance of earning $40,000 and a

Problem 13-31 (Algorithmic) Consider a decision

Problem 13-31 (Algorithmic) Consider a decision maker who is comfortable with an investment decision that has a 50 percent chance of earning $40,000 and a 50 percent chance of losing $20,000, but not with any larger investments that have the same relative payoffs. a. Write the equation for the exponential function that approximates this decision maker's utility function. U(X) = b. Choose the correct plot for this decision maker for x values between -20,000 and 35,000. (ii) 21 24. 1.5 015 X -30000 -20000-10000 10000 20000 30000 40000 10000 20000 30000 10000 -30000-20000-10000 -0.5 Utility Ux) Utility, U(X) -1. -15 (iv) 21 2+ 1.5+ 1+ 0.5 -30000 20000 000 10000 20000 30000 40000 10000 20000 30000 40000 =30000-20000-10000 -0.5+ Utility. UCO) Utility, U(x) -2- is this decision maker risk seeking, risk neutral, or risk averse? The decision maker is C. Suppose the decision maker decides that she would actually be willing to make an investment that has a 50 percent chance of earning $45,000 and a 50 percent chance of losing $22,500. Choose the correct plot that approximates this utility function (function represented by the green curve) and compare it to the utility function from part (b). (ii) ) 2-1 2 + 15 03 30000-00000000 10000 20000 30000 10000 30000220000-10006 10000 20000 30000 40000 Utility UCN) -1- Utlity, U(X) 23 Ci (iv) 21 1 0.5 X 10000 20000 30000 40000 30000=20000 = 10000 10000 20000 30000 40000 30000=20000-10000 403 -0.5 17 Utility, Ux) Utility, U(X) 32 The decision maker is becoming - than in part (b)

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