Problem 13-31 (Algorithmic) Consider a decision maker who is comfortable with an investment decision that has a 50 percent chance of earning $35,000 and a 50 percent chance of losing $17,500, 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. (i) (ii) 2+ 2- 1.5+ 1.5- 1+ 1+ 0.5+ 0.5+ ++ ++ +X +X -30000-20000-10000 10000 20000 30000 40000 -30000-20000-10000 10000 20000 30000 40000 -0.5+ -0.5+ -1+ -1.5+ -1.5+ -2+ -1+ (iii) 2+ 1.5+ 1+ 0.5+ X -30000-20000-10000 10000 20000 30000 40000 -1.5+ -2+ Is this decision maker risk seeking, risk neutral, or risk averse? The decision maker is -0.5+ -1+ (iv) -30000-20000-10000 2+ 1.5+ 1+ 0.5+ -0.5+ -1+ -1.5+ -2+ X 10000 20000 30000 40000 c. Suppose the decision maker decides that she would actually be willing to make an investment that has a 50 percent chance of earning $40,000 and a 50 percent chance of losing $20,000. 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). (i) (ii) 2- 2+ 1.5+ 1.5+ 1+ 1+ 0.5+ 0.5- X X -30000-20000-10000 10000 20000 30000 40000 -30000-20000-10000 10000 20000 30000 40000 -0.5+ -0.5- -1+ -1.5- -1.5+ -24 -1+ (iii) 2 | 1.5+ -30000-20000-10000 1+ 0.5+ -0.5+ -1+ -1.5+ -2- The decision maker is becoming + * (iv) 10000 20000 30000 40000 than in part (b). 1.5+ 1+ 0.5+ -30000-200000000 -0.5+ -1+ -1.5+ -2- + * 10000 20000 30000 40000