Consider the following social welfare function for a small community of five peo
ID: 1213728 • Letter: C
Question
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
1. Place positive and negative signs above all the terms in the function, illustrating whether they increase or decrease each person’s utility.
2. Assume that producing all types of goods (both N and C) requires some level of pollution. Will an increase in the consumption of non-competitive goods always increase social welfare? Now, 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?
Explanation / Answer
1) non competitive goods and competitive good increaes the utityand pollution devreases the utility.
2)yes increasing in consumption of N increases the social welfare.
3)7500
4)500
5)2000
6) no