Problem 2. (Prediction market with margin requirement) Suppose we have a prediction market betting on whether Oilers can win the Stanley cup. If Oilers wins, the payoff is $1, otherwise, 0. There are a continuum of agents participating the bet. Their beliefs are uniformly distributed in [0, 1]. The market has a margin requirement that ex-post, agents cannot suffer the loss more than the wealth that they have. (a) Suppose agents have the same wealth, determine the price of the bet that Oilers wins the cup. (b) Suppose the market maker cannot see the wealth of each individual, but he can see the quantities that each person buys and sells. On average, each seller shorts 2 shares and each buyer purchases 1 share. What is the price of the bet? Problem 2. (Prediction market with margin requirement) Suppose we have a prediction market betting on whether Oilers can win the Stanley cup. If Oilers wins, the payoff is $1, otherwise, 0. There are a continuum of agents participating the bet. Their beliefs are uniformly distributed in [0, 1]. The market has a margin requirement that ex-post, agents cannot suffer the loss more than the wealth that they have. (a) Suppose agents have the same wealth, determine the price of the bet that Oilers wins the cup. (b) Suppose the market maker cannot see the wealth of each individual, but he can see the quantities that each person buys and sells. On average, each seller shorts 2 shares and each buyer purchases 1 share. What is the price of the bet