1. (20 pts) You and a classmate (let's call him Dave) discover that your economics teacher has been secretly talking about notions such as "love." "fairness," and "decency." Desperate to preserve his reputation in the community of economists, he tries to buy your silence in the following way."You two sit silently at a table. I'll put down a hundred-dollar bill. You can take the bill, or pass the decision to Dave. Before Dave decides, I'll put another hundred-dollar bill on the table. If he passes, I'll add yet another bill to the table and you can have another turn. The game will end when someone takes the money, or when the $500 in my wallet is gone, whichever comes first." You both agree to keep quiet about your instructor's transgressions for the chance to play the game, and as your teacher indicated, you get the first turn. a) Suppose that each of you has passed twice, and your instructor has just put the last $100 bill on the table. It is your turn: What should you do? b) Suppose that you have passed twice, and Dave has passed once. Your instructor has just put the fourth $100 bill on the table. What should Dave do: Take the money or pass? Why? c) Suppose that you and Dave have each passed once. Your instructor has just put the third $100 bill on the table. What should you do: Take the money or pass? Why? d) Suppose that you have passed once. Your instructor has just put the second $100 bill on the table. What should Dave do: Take the money or pass? Why? e) Your instructor has just laid the first $100 bill on the table. It is your turn. Should you take the money or pass? Why? f) What is the likely outcome of this game? Does your instructor pay the entire $500 for your silence