1. Graduate student A smokes, but his office mate B hates smoking. A and B have the following utility functions: U4 =100+ 10z 0.1z%2 and U4 = 100 10z, where z=number of cigarettes smoked by A (and U4 includes the cost of cigarettes). Determine: a. The number of cigarettes smoked by A when the external factor on B is ignored. b. The socially optimal level of cigarettes that should be smoked by A