Rawlsian Welfare Function:

Thus, social welfare  is  a hnction of the  levels of utility of members in  the society. Alternatively, the social welfare  function can  be  expressed  as  a function  of other variables relevant  to  welfare, such  as  income  or  life expectancy. The form of the social welfare function can be seen as expressing a statement of the objectives of a society. For example, take a social welfare function:  

where W is social welfare and Y,  is the income of each of the X^th  individual in a  society.  In  this case, maximising the  social  welfare function means maximising the total  income  of the  people  in  the  society, without regard to how incomes are ,distributed in  the society. Alternatively, consider the Max- Min utility function:

Here,  the social welfare of the society  is taken to be related  to the  income of the  poorest  person in  the society,  and  maximising  welfare  would mean maximising the  income of the poorest person without regard for the  incomes of the others.
These two social welfare  functions express very  different views about how a society would need  to be organised in order to maximise welfare. While the first  emphasises  the  total  incomes,  the  second considers the needs of  the poorest.

However,  often  choice of  such  a function  is  considered part  of  political economy. Choosing between two such functions may be a matter of tolerances versus preferences, or some broader political or ethical issue that  cannot be resolved  by  economics at  all. A related  problta  is  the  need  of  individual capital  for  rest  and  recreation,  which  prevents  anyone  from  actually maximising  the  total  income. This  is  at  the  root  of many  of  the  balanced growth assumptions  of  macroeconomics: Unless  a  uniform  social welfare function is chosen across an entire society, growth is not balanced. Due in part to  this  concern, more  direct  means  of  measuring well-being  than  "total incomes" or GDP  are  required  by  modem human  development  theory. Amartya Sen makes the point more directly: "What is the relation between our wealth, and  our  ability  to  live  as we  would  like?"  Without  answering this question, income and welfare are only indirectly related.