3. (35) Herds. Consider the herding model of Bikhchandani, Hirshleifer and Welch (1992). In the economy, there is a unique investment opportunity. The cost of the investment C' is equal to 1/2. The return of the investment V is equal to 1 with probability a and is equal to 0 with probability 1 - A, / C [1/2, 1]. Agent t = 1,2, .... does not observe the value of V. However, he observes the investment decision of agents j = 1, 2...1-1 and a private signal of. If V = 1, the signal is equal to H with probability o and to L with probability 1 - o, where o e (1/2, 1). If V = 0, the signal is equal to # with probability 1 - a and equal to L with probability o. a. What probability does agent 1 assign to the event V = 1 before observing the signal? b. What probability does agent 1 assign to the event V = 1 if he receives the signal of = H? c. What probability does agent 1 assign to the event V = 1 if he receives the signal of = L? d. What is the investment strategy of agent 1? e. Under what condition on the precision of the private signal o, is the strategy of agent 1 independent of his private signal? f. Under the conditions you derived in part (e), what is the investment strategy of agents 2, 3, 4