Graduate student A smokes, but his office mate B hates smoking. A and B have the following utility functions: UA=100+ 10z -0.1z2 and UB = 100-10z, where z is the number of cigarettes smoked by A (and UA includes the cost of cigarettes). Determine: a. The number of cigarettes smoked by A when the external effect on B is ignored. b. The socially optimal level of cigarettes that should be smoked by A. c. The optimal Pigouvian tax needed to decentralize the social optimum. d. 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 nonsmoker.