Problem 1: Consider your consumption level this weekend and suppose that you have $1,000 available. On Friday night, the UofT is playing Western in a women's basketball tournament, and you have the opportunity to bet an amount $X 3 $1,000 on the game. If you bet $X, you will only have ($1,000 $X) if you lose the bet, but you will have ($1,000 + $X) if you win. Suppose that you believe that each team has a 50% chance of winning (and that, if a game is tied, it goes into overtime until the tie is broken.) a) Suppose your utility over money is given by 320'5. I offer you an opportunity to place a bet of X = 500 on either team. Will you take it? b) Suppose you placed the bet on the UoiT and now want to back out. The game is currently tied and going into overtime to decide on a winner. How much would you pay me to get out of the bet? c) Suppose the UoiT is on a winning streak and you changes your estimated probability of them winning to 5 > 0.5.For what values of 6 will you want to still stay in the bet? (:1) Suppose now that your utility over money is given by 3:2. we go back to each team being equally likely to win. How much would you bet on either team? e) Suppose your states of the world are "UoiT winning" and " W. winning". Write down an expected utility function in terms of 33U0T (on the xaxis) and my. What is the MRS? For what value of 6 is a $500 bet on the UofT optimal? Keep 11(3) 2 1:0'5