Samuelson's 'Curious Case" Revisited: It Turns out to be Normal - Indeed Generic

Samuelson (1974) noticed what he called a 'curious case' in which a redistribution of endowments, of the sort usually considered in connection with the Second Welfare Theorem, would not necessarily achieve a desired distribution of utilities. Samuelson's observation raises important questions for common interpretations of the Second Welfare Theorem. It also raises the interesting question of the sorts of redistributions that are needed to actually achieve a desired distribution of utilities. Motivated by Samuelson's work, this paper aims to do three things. Firstly, to explain why common interpretations of the Second Welfare Theorem are in jeopardy in the situation considered by Samuelson (1974). Secondly, to point out that far from being a 'curious case', the situation identified by Samuelson (1974) is normal (indeed generic). Thirdly to characterise an 'appropriate' redistribution of endowments to achieve a desired distribution of utilities when equilibrium is not unique.