On measuring changes in welfare when changes in consumption bundles are small

The paper examines three extensively used propositions regarding changes in utility and social welfare attributable to small changes in consumption bundles. It is shown that, though these propositions are valid when the changes in consumption bundles are ``infinitesimally small,''' none of the propositions can be sustained when we have finite changes in consumption bundles, even when such finite changes are arbitrarily small. This drastically reduces the usefulness of the propositions for any practical purpose. The paper discusses the underlying formal structure of the problem and identifies the reason why the propositions run into difficulties in the case of finite changes.