On a Notion of Similarity with Endowments in Public Economics

We establish that a novel notion of similarity with endowments by Shitovitz and Spiegel (1998) amounts to severe functional form restrictions, and these restrictions on utility functions can be determined by functional equation methods. The resulting functional forms are related to the familiar Cobb-Douglas and quasi-linear forms, as well as the classical result of Bergstrom and Cornes (1983) on the independence of allocative efficiency from distribution in the theory of public goods.