Please solve all the parts

Antton is the head of the Economics department at Hasparren university. The university is about to vote on how to allocate its budget across departments. The game is sequential: Antton is good friends with the president of the university, so he can propose to allocate an amount $s1 to the department, to which the president can either accept or refuse. If he refuses, the amount allocated to the department is the same as the previous year, $so. Hence, the decision of the president, s2 , will either be so (rejection of SI ) or s1 (acceptance of s1 ). The president's utility function is up (s2) = (s2 (1)2. Throughout the exercise, assume that the president accepts the proposal if he is indifferent between so and s1 . (a) What is the amount S? that maximizes the president's utility? What is the maximized utility up(s) equal to? (Tip: it is useful to graph the utility of the president. Put s2 on the x-axis, and pick a value for a: just for the example) (3 points) (b) Consider the last subgame, where the president either accepts 31 or rejects it, in which case so will be allocated to the department. Wha' values of SI will the president accept to allocate over so ? Use your intuition to find these values, no math is required. (your answer in (a) will be useful.Tip: it is useful to graph the utility of the president. Put s2 on the x-axis, and pick a value for a just for the example. Locate so anywhere and find what values of s1 are preferred to so by the president) (5 points) (0) Assume Antton wants to see the highest possible amount allocated i.e. his utility is uA(s2) = s2. If so 2 a, what amount s1 will Antton