I pull out a six-sided die, and offer you the following gamble for a price of $X: you owe me $100 if I roll a 1, I owe you $200 if I roll a 2, you owe me $300 if I roll a 3, I owe you $400 if I roll a 4, you owe me $500 if I roll a 5, and I owe you $600 if I roll a 6.
a. If I charge an actuarially fair price for this gamble, what is $X? Show me.
b. suppose I set $X at $30, your utility over wealth is (where W is your wealth), and you currently have $10,000 to your name. Would you take this gamble? Show me how you know.