Consider a decision maker who is comfortable with an investment decision that has a 50 percent chance of earning $25,000 and a 50 percent chance of losing $12,500, 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.
b. Plot the exponential utility function for this decision maker for x values between 220,000 and 35,000. Is this decision maker risk seeking, risk neutral, or risk averse?
c. Suppose the decision maker decides that she would actually be willing to make an investment that has a 50 percent chance of earning $30,000 and a 50 percent chance of losing $15,000. Plot the exponential function that approximates this utility function and compare it to the utility function from part b. Is the decision maker becoming more risk seeking or more risk averse?