Sophia is a contestant on a game show and has selected the prize that lies behind door number 3. The show’s host tells her that there is a 50 percent chance that there is a $15,000 diamond ring behind the door and a 50 percent chance that there is a goat behind the door (which is worth nothing to Sophia, who is allergic to goats). Before the door is opened, someone in the audience shouts, “I will give you the option of selling me what is behind the door for $8,000 if you will pay me $4,500 for this option.”

a. If Sophia cares only about the expected dollar values of various outcomes, will she buy this option?

b. Explain why Sophia’s degree of risk aversion might affect her willingness to buy this option.