Person A smokes but his roommate B hates smoking. Their utility functions are as follows: A = __ 2. a = ._ U 100 + 102 0'12 ' U 100 102; where z is the number of cigarettes smoked by A. Determine The number of cigarettes smoked by A when the external effect on B is ignored. 9"?\" The socially optimal level of cigarettes that should be smoked by A. P The optimal Pigouvian tax needed to decentralize the social optimum. p. The outcome with Coasian Bargaining when the property right is assigned to the smoker. e. The outcome with Coasian Bargaining when the property right is assigned to the non- smoker