Lattice Programming and Consumer Theory Part I: Method and Applications to Two Goods

This paper recasts the consumer utility maximization comparative statics problem in an order/lattice theoretic framework. It argues that it is not possible to do so while maintaining reliance on the Euclidean lattice, and shows how order/lattice structures appropriate for income and price effects can be constructed using the revealed preference restrictions implied by each comparative statics problem. The former define what are called value orders. The class of direct value orders, is used to carry out comparative statics analysis in the two good case. The results do not rely either on topological assumptions, continuity and differentiability, or on convexity assumptions. The analysis is global, and it allows for indivisibilities, discrete changes and non-binding budget constraints.