Social welfare functions and income taxation The relationship between social welfare functions and the optimal distribution of individual tax burdens is a complex one in welfare economics. In this problem, we look at a few elements of this theory. Throughout we assume that there are m individuals in the economy and that each individual is characterized by a skill level, aj, which indicates his or her ability to earn income. Without loss of generality suppose also that individuals are ordered by increasing ability. Pretax income itself is determined by skill level and effort, ci, which may or may not be sensitive to taxation. That is, 1; = 1(aj, C). Suppose also that the utility cost of effort is given by (c), V >0,V' 0,V'