On the commutativity of expansion and substitution effects

Lerner Index, Productive Efficiency and Homotheticity

“…In such respects, Mantovi (2013) [6] tailors a differential geometric approach to the commutativity of (suitably defined) expansion and substitution effects, which are isomorphic to technical and allocative (in)efficiency measures for a single output production function, in terms of Lie brackets. Such a geometric approach to overall productive efficiency (and its reflection on the Lerner index) may shed light on the "second order" allocative inefficiency defined by Bogetoft et al (2006) [5], and, in turn, on the dynamics of efficient input allocations (see for instance Choi et al, 2006 [13] and references therein) and construction of index numbers (Cross and Färe, 2015 [14] assume homotheticity in their construction of the Fisher index).…”

“…Correspondingly, exploiting the well known isomorphism between the microeconomic problems of the producer and of the consumer, Mantovi (2013) [6] tailors a parallel between such a result and the commutativity of suitably defined finite expansion and substitution effects (recall, the infinitesimal expansion and substitution effects represented in Slutsky decompositions do commute by definition) in terms of the flows of vector fields on consumption space, with the generator of homotheties playing the key role (Tyson, 2013 [10] employs vector fields on consumption space in order to characterize the symmetries of preferences).…”

On luxury and Equilibrium

“…2 According to Chambers and Mitchell (2001), "Homotheticity may be the most common functional restriction employed in economics." See Mantovi (2013aMantovi ( , 2013b for a differential geometric approach to the benchmark scale invariance of homothetic problems. Scale invariance lies at the basis, for instance, of the invariance problem of index numbers, for which Samuelson and Swamy (1974) set forth a landmark analysis.…”

Taxes, subsidies, regulation in dynamic models

“…The author establishes that symmetry vector fields commute for additive and joint separability, and provides a characterizaztion of symmetry vector fields in terms of their action on the distance function. A basic pillar of the approach used in this paper is the expansion vector field, introduced by Mantovi (2013) for homothetic models, and given a general stance by Mantovi (2016). Homothetic models embody in many respects the fundamental symmetry of consumers' and producers' problems-one can think e.g.…”