information value

You are considering whether to buy a stock or not. The value of the stock tomorrow is represented by a binary random variable 5 = (0, 1 p; 100,p), where p is the probability of high value (D = 100) while 1 p the probability of low value (D = 0). It costs 50 to buy the stock. a. What is the distribution of profits attached to each of the two states? [5%] b. Draw the expected profit attached to each decision as a function of p and characterize the optimal expected profit. Show that it is convex in p. [10%] c. Assume a signal which perfectly reveals the true state of the world. Which is, the signal is good (G) whenever the future value is D=100, or bad (G) whenever the future value is D=0. Calculate the maximum price you are willing to pay for such information, when p = 0.1, p = 0.3, and p = 0.7, respectively. [20%] d. Draw the value of info as function of p. [7%] e. Explain in your own word when information might have negative value. [8%]