The following is the model you should study in the following 4 questions: There are two states of nature, DA and OB. Voters cannot observe the state. There is an incumbent politician who knows the true state. The politician can be of two types: g or b. A type s politician has the following payoff function: if the state is 0 and the policy chosen by the politician is i E (A, B) , her utility function is given by 1 +6 ife = 0; and R = 1; " (1, R | 0 ) if 0 = 0; and R = 0; if 0 + 0; and R = 1; if 0 # 0, and R = 0. where R is the decision of the voters to re-elect the politician (R = 1 means yes, R = 0 means no. (Notice: 0 = 0; means 0 = 0A if the policy chosen is i = A and 8 = 0g if the policy, chosen is B . Similarly for 0 # 0; ). A type b politician always chooses alternative A if the state is 0 and alternative B if the state is A. Voters cannot observe the type of the politician, but want to reelect her only if she is of type g. Assume that the probability that ? = 04 equals 1/5 and that the probability that a politician is of type g equals 1/5 points). FIRST QUESTION: Suppose that the voters expect that a type g politician always chooses A . What should the voters believe about the probability that a politician is of type g if they observe that the politician chooses alternative A ? (round to thre Continue to study the same model SECOND QUESTION: Assume > 1 . If voters reelect the politician if and only if she chooses A, what would a type g politician do? Select one: a. Choose the alternative that matches the state, i.e., i e { A, B) such that 0 = 0; . b. Choose alternative A. c. She is indifferent between choosing alternative A and B. d. Choose alternative B Choose the alternative opposite to the one matching the state, i e ( A, B) such that 0 = 0j j # i Continue to study the same model THIRD QUESTION: Assume that there is an equilibrium where a type g politician always chooses i s ( A, B) . What is the logical conclusion for the voters if they observe alternative j # i being chosen? Select one: That the politician is of type g with probability 1/3 b. That the politician is of type g with probability 1. C. That the politician is of type b with probability 1. d. That the politician is of type & with probability 1/4 . That the politician is of type g with probability 2/5 Continue to study the same model FOURTH (AND LAST) QUESTION: If 8 > 1 , is there an equilibrium where a g candidate always chooses A? Answer: YES/NO and explain the basic logic in no more than 20 words