An Order Theoretic Approach to Net Substitution Effects

We revisit the analysis of discrete comparative statics effects in the classical consumer expenditure minimization framework, using techniques that exploit the order and lattice properties of the problem, without reference to topological properties. It is shown that these comparative statics effects give rise to classes of partial orders, which in turn induce lattice structures that define the critical points of comparability (for the behavior of the utility function), meets and joins, which are used to derive sufficient conditions, from the quasi-supermodular class of properties, for a good(s) to be a net substitute or complement of another. Examples demonstrate the analysis.