On the commutativity of expansion and substitution effects

The reversibility of sequential economic choices concerning production and consumption is addressed. A geometric approach to substitution effects and output/income effects is set forth in terms of vector fields on bundle space. By means of suitable fixing relations the 0-homogeneity of such problems can be circumvented, so as to define global parametrizations of effects, for which Lie brackets measure the departure from commutativity. A couple of propositions are established, assessing the benchmark relevance of homothetic models. Application to Farrell decompositions, as tailored by Bogetoft et al. (Eur J Oper Res 168:450–462, <CitationRef CitationID="CR4">2006</CitationRef>), results in complete agreement with the results found by such Authors. The theoretical relevance of the approach is thoroughly discussed. Copyright Springer-Verlag Wien 2013