Maria is a contestant on a game show and has selected the pr

Maria 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 worthless to Maria, who is allergic to goats). Before the door is opened, someone in the audience shouts, \"I\'ll give you the option of selling me what is behind the door for $8,000 if you will pay me $4,500 for the option.\" If Maria only cares about the expected value of various outcomes, will she buy this option? Show me mathematically how you know. If Maria has no starting wealth, and her utility of wealth is U = W^0 8, would she benefit from taking this option? Again, show me how you know.

Solution

The expected return from the door is = (0.5*15000)+(0.5*0)=$7500

If she buys the option and she wants to use the option the return is :

Assuming she got goat then only she uses options

return= 8000-4500=$3,500

If she does not use option meaning she own prize

return =15000-4500= $11,500

For both the above the expected return = (0.5*3500)+(0.5*11500)= $7500

She will buy the option because the return of option is $3500 or $11500 but if she does not buy option then she get 15000 or 0.

As first case is better as she gains something she will buy option

b)No idea how to solve this