Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

CHAP. 14] GENERAL EQUILIBRIUM AND WELFARE ECONOMICS 331
and Y). The aim of society is to choose among this infinity of Pareto optimum points along the grand utilitypossibility
frontier, the one point that leads to the maximum social welfare.
14.18 Suppose that three social welfare functions from the social welfare map of the economy of Problem
14.17 are given by the figures in Table 14.3. (a) Plot these social welfare functions; what do they
show? (b) What assumption must we make in order to construct a social welfare function? How can
a society gets its social welfare map?
Table 14.3
W 1 W 2 W 3
u A u B u A u B u A u B
75 900 150 900 225 975
225 525 300 600 375 675
450 375 525 450 600 525
900 225 900 375 900 450
(a)
(b)
A social welfare function or social indifference curve shows the various combinations of u A and u B that give
society the same level of satisfaction or welfare. For example, point S and D 0 on W 2 result in the same social
welfare. However, at point S, individual B is better off than at point D 0 , while individual A is better off at point
D 0 than at point S. On the other hand, points on a higher social welfare function involve a greater social
welfare than points on a lower social welfare function. For example, u A and u B are both greater at point
D 0 than at point D, while u A and u B at point D 0 are both smaller than at point D 00 .
In order to construct a social welfare function, society must make value or ethical judgments (interpersonal
comparisons of utility). That is, since a movement along a social welfare curve makes one individual better off
while the other worse off, in order to get a social welfare function, society must compare the two individuals
in “deservingness”. A social welfare function may be constructed by (and thus reflect the value judgment of) a
dictator, if one exists. In a democracy, a social welfare function could be developed by voting, but only under
certain circumstances. In any event, the construction of a social welfare function is very difficult. What we do
here is simply assume that social welfare functions exist for our society and are given by W 1 ,W 2 , and W 3 in
Fig. 14-16.
Fig. 14-16 Fig. 14-17