Constant resource shares and Samuelson’s Shibboleth

Abstract

Suppose each individual in a community is given some fixed constant fraction of total available expenditures to spend. Samuelson (1948, 1954, 1956) argued that this would be a shibboleth (i.e., a procedure that does not have meaning) because such a procedure cannot generally be rationalized by any social welfare function defined over the utilities of individuals. For modern collective household models, Samuelson’s shibboleth has been taken to imply that household resource shares (the fraction of a household’s budget allocated to each household member) cannot be constants. We show Samuelson’s claim depends on an assumption that is inappropriate for collective household models, and when that assumption is dropped, there is no shibboleth: resource shares can be any regular functions, including fixed constant fractions.