Consider the following social welfare function: SW=U a (X nc a , X c a , X c ~a
ID: 1194539 • Letter: C
Question
Consider the following social welfare function:
SW=Ua(Xnca, Xca, Xc~a, Pa)+Ub(Xncb, Xcb, Xc~b, Pb)+ Ud(Xncd, Xcd, Xc~d, Pd)+...
c. (4 points) Let Xcb be a new house overlooking a canyon. Let P be the reduction in scenic beauty experienced by the community. Finally, let Xc~b be the status impact on folks who are not b arising from the new mansion. Assume that the positive increase in individual utility for individual b of a one unit increase in Xcb equals $10,000 in consumer surplus; and that the negative status reduction in utility to other people is -$500. Assume also that a one unit increase in Xcb produces one unit of “P”, which further causes a -$1000 unit impact on utility for everyone exposed. In a world of 5 people (including Mr. b), what are the private benefits to Mr. b of consuming one more unit of Xcb? What are the external costs of a one unit increase in Xcb if everyone is exposed to P? What will be the net increase in SW of a one unit increase in Xcb?
Explanation / Answer
We have the following social welfare function:
SW=Ua(Xnca, Xca, Xc~a, Pa)+Ub(Xncb, Xcb, Xc~b, Pb)+ Ud(Xncd, Xcd, Xc~d, Pd)+...
c) Private benefit for Mr. b is calculated as below:
= (the positive increase in individual utility for individual b of a one unit increase in Xcb - reduction in utility to other people - Impact on others utility because of a one unit increase in Xcb produces one unit of “P”) * 2
=($10,000 $500 $1,000) × 2 = $17,000
External Cost is calculated as follows:
= (reduction in utility to other people + Impact on others utility because of a one unit increase in Xcb produces one unit of “P”) * 2 * number of people
= (-$1,000 $500) × 5 × 2 = -$15,000
SW net increase:
= Private benefit for Mr. b - External cost
= $17,000 $15,000 = $2,000