There are two types of people in the world: brave and wimpy. Brave people incur a disutility of 200 from bungee jumping, while wimps incur a disutility of 300. 70% of people are wimps. Bungee jumping creates no social value. Kelly has a partner Sam, and is trying to determine how assertive to be in the relationship. Let a be the degree of Kelly's assertiveness, which can be any nonnegative number. Kelly's utility is -a if Sam is brave, and -(a-1) if Sam is a wimp. Suppose that Sam incurs disutility 400a, where a is Kelly's assertiveness. Therefore, Sam's overall utility is u(a,e) = -400a-200e if brave and u(a,e)=-400a-300e if wimpy, where e=1 if Sam bungee jumps and e=0 otherwise. Also assume that Kelly and Sam love each other so much that both would incur infinite disutility from breaking up. a) Find Kelly's optimal assertiveness if Sam is wimpy with probability p. b) Does there exist an equilibrium where Kelly can determine Sam's type with certainty by giving Sam the choice of bungee jumping or not? Explain. c) Does there exist an equilibrium where Kelly gains no information from whether Sam bungee jumps? If so, find all such equilibria. If not, explain. d) Does there exist an equilibrium where Kelly gains some information from whether Sam bungee jumps? If so, find all such equilibria. If not, explain. e) In which equilibrium is Kelly best off? Brave Sam? Wimpy Sam?