There are two states of nature, 9' and 93. 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 3 politician has the following payoff function: if the state is 9 and the policy chosen by the politician is i E {21, B}, her utility lunction is given by 1+5 if3=9,andR=l; 1 ifs=s..de=o; a Hamming; 0 ifaga.andn=o. mums): where R is the decision of the voters to re-elect the politician {R = 1 means yes, R = 0 means no. (Notice: 6' = 9\" means 9 = 9,; it the policy chosen is i = A and 9 = 93 if the policy chosen is 8. Similarly for 9 a at A type b politician always chooses alternative A it the state is 93 and alternative B if the state is 9A. 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 9 = 9,1 equals \"4 and that the probability that a politician is of type 3 equals U3. FIRST QUESTION: Suppose that the voters expect that a type 3 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 .4? (round to three decimal points]. E SECOND QUESTION: Assume r5 :- 1. If voters reelect the politician if and only if she chooses A, what would a type 3 politician do? Select one: Q a. Choose the alternative that matches the stateI i.e.I i E {11, B} such that 6' = 9;. O b. She is indifferent between choosing alternative A and B. O c. Choose alternative A. 0 cl. Choose alternative B O a. Choose the alternative opposite to the one matching the state, i E {A, B} such that I9 = 3p} 9': i. THIRD QUESTION: Assume that there is an equilibrium where a type g politician always chooses i E { A, B). What is the logical conclusion for the voters if they observe alternative j # i being chosen? Select one: O a. That the politician is of type g with probability 2/5. O b. That the politician is of type b with probability 1. O c. That the politician is of type g with probability 1/4. O d. That the politician is of type g with probability 1. O e. That the politician is of type g with probability 1/3.FOURTH (AND LAST) QUESTION: If 6 > 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