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Revealed Preference, Lattice Programming and the Dual Consumer Problem

The paper studies comparative statics in the classical consumer expenditure minimization problem, without recourse to differentiability and convexity assumptions. It extends the revealed preference approach by embedding the problem in a lattice theoretic framework. The analysis is discrete, the optimal sets may be non-singletons, there may be indivisibilities and the constraints may be non-binding. The ensuing sufficient conditions for net subsitution effects are superextremal variant properties of the utility function, on appropriately constructed lattices on the consumption set. The revealed preference implications of the problem are used to impose restrictions on appropriate partial orders, which are used to construct such lattices.