Y5

2. Seojeong considers an idea of investing in a start-up. He has 200 Won, and he chooses either invest all of his money (I) or not invest (NI). If he invests, then the outcome depends on an unknown state WE {WH, WL} = 2. If w = WH, then he will obtain 500 Won; if w = WL, he receives nothing. If he does not invest, he will keep his 200 Won in any state. Seojeong is an expected utility maximizer with a risk-neutral Bernoulli utility function u(c) = c. (a) Suppose that Pr(w = WH) = 7. Write Seojeong's optimal choice correspondence a* (7 ) as a function of T. (b) Now suppose that 7 = 0.2, and that there exists some information about the start-up that Seo- jeong can access. The information is a binary signal of Good and Bad, with Pr(Good w = WH) = q and Pr(Bad|w = WL) = q for some q E (0.5, 1]. Using the Bayes' rule, calculate Seojeong's posterior belief after observing each signal (that is, Pr(w = WH |Good) and Pr(w = WH| Bad)). (c) Find the range of q for which the value of information { Good, Bad} is strictly positive