A Generalized Social Welfare Function, its Decomposition and Application

It is easy to demonstrate that Sen's SWF satisfies Pareto criteria. This paper questions the philosophy of this concept and shows that it is possible to formulate a generalized SWF, which can be non-Paretian under special circumstances. This paper also demonstrates a method of decomposition of the proposed SWF by subgroups of population using a Gini decomposition method developed by Podder. The method is applied to investigate the trend of welfare in Australia at regional level using the Household Expenditure Survey data of 1983-84 to 1993-94. It is found that the states NSW, Victoria and Queensland, with the maximum total income share, had almost 70 percent of the share of total welfare. The elasticity of welfare with respect to mean income showed a prominent increasing trend for NSW. It is also observed that the relative share of welfare decreased for NSW, Victoria, South Australia, Queensland and Australian Capital Territory and increased for Tasmania and Northern Territory.