Consider the following social welfare function: SW=U a (X nc a , X c a , X c ~a
ID: 1194538 • 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)+...
where:
X=consumption bundle
P=pollution
nc=non-competitive
c=competitive
a, b, d = people
~a, ~b, ~d = all other people besides a, b, d.
(2 points) Place positive and negative signs above all the terms in the function, illustrating whether they increase or decrease each individual’s utility.
(2 points) Will an overall increase in the level of non-competitive consumption always increase social welfare? Why or why not?
Explanation / Answer
a) the signs of all terms are placed in the given function below:
SW=Ua(+Xnca, +Xca, -Xc~a, -Pa)+Ub(+Xncb, +Xcb, -Xc~b, -Pb)+ Ud(+Xncd, +Xcd, -Xc~d,-Pd)
non-competitive consumption and competetive consumption of each individual would increase the respective individual's utility where as consumption by other people and population would reduce the same.
b) Yes an overall increase in the level of non-competitive consumption always increase social welfare because here in the function as we can see the signs of non competitive consumption is positive and inceases the welfare without having any opportunity loss of another one.