Consider the following social welfare function for a small community of five people. SW = Ua(Na, Ca, C~a, Pa) + Ub(Nb, Cb, C~b, Pb) + Uc(Nc, Cc, C~c, Pc) + Ud(Nd, Cd, C~d, Pd) + Ue(Ne, Ce, C~e, Pe) where: N = noncompetitive goods C = competitive goods P = pollution a,b,c,d,e = people ~a = all people besides a let Cb be a new mansion on Cape Cod. Let P be the environmental costs of building the mansion. Finally, let C~a, C~c, C~d, and C~e be the status impact on folks who are not Ms. b arising from the new mansion. Assume that the positive increment to individual utility for Ms. b of a one-unit increase in Cb equals $10,000 in consumer surplus and that the negative status increment to other people is -$2,000. Assume also that a one-unit increase in Cb produces one unit of P, which decreases everyone’s consumer surplus by $500. 3. What are the private benefits to Ms. b of consuming one more unit of Cb? 4. What are the environmental costs to Ms. b consuming one more unit of Cb? 5. What are the status costs to others to Ms. b consuming one more unit of Cb? 6. Will social welfare increase if Ms. b builds her mansion.