Continues below Question 3 a) Imagine you are considering whether to buy a stock. The value of the stock tomorrow is represented by a binary random variable , where is the probability of high value whilst is the probability of low value . It costs to buy the stock. i. Graph the optimal expected profits as a function of and show that it is convex. [25%] Assume now that there exists a signal which perfectly reveals the true state of the world. I.e., the signal is good () whenever the future value is , and bad () whenever the future value is. ii. Graph the value of this information as function of . [25%] b) In what circumstances, in general, might the value of information not be positive? Illustrate your answer with potential examples from theory the real world. [50%] or Continues below Question 3 a) Imagine you are considering whether to buy a stock. The value of the stock tomorrow is represented by a binary random variable , where is the probability of high value whilst is the probability of low value . It costs to buy the stock. i. Graph the optimal expected profits as a function of and show that it is convex. [25%] Assume now that there exists a signal which perfectly reveals the true state of the world. I.e., the signal is good () whenever the future value is , and bad () whenever the future value is. ii. Graph the value of this information as function of . [25%] b) In what circumstances, in general, might the value of information not be positive? Illustrate your answer with potential examples from theory the real world. [50%] or