Comparative statics for the consumer problem

This paper studies comparative statics in the consumer utlity maximization problem with two goods. The analysis can be global, and it allows for indivisibilities, discrete changes, and non-binding budget constraints. It does not rely either on topological or convexity assumptions. Instead, it uses lattice programming techniques. The conditions derived are superextremal variant properties on the utility function, in appropriately constructed lattices on the consumption set. Sufficient conditions are given for one or both goods to be normal, for one to be inferior, and for some cases of price effects, using what are called value orders and lattices.