Lattice-Theoretic Foundations of the Consumer's Problem.

This paper provides an introduction to and discussion of the application of lattice-theoretic methods to classic problems in consumer theory. General characterizations of income effects with two goods, and with an arbitrary number of goods, as well as examples of comparative statics over densities and consumer types are also presented.consumer's problem; income effects; lattice programming; super-extremal

Lattice programming, its generalization, and applications to microeconomics

制度:新 ; 報告番号:甲3353号 ; 学位の種類:博士(経済学) ; 授与年月日:2011/3/15 ; 早大学位記番号:新567

Comparative Statics with Concave and Supermodular Functions

Certain problems in comparative statics, including (but not exclusively) certain problems in consumer theory, cannot be easily addressed by the methods of lattice programming. One reason for this is that there is no order on the choice space which orders choices in a way which conforms with the comparison desired, and which also orders constraint sets in the strong set order it induces. The objective of this paper is to show how lattice programming theory can be extended to deal with situations like these. We show that the interaction of concavity and supermodularity in objective or constraint functions yield a structure that is very useful for comparative statics.

A generalization of monotone comparative statics

In this paper, we generalize the lattice theoretical comparative statics by Li Calzi and Veinott, and Milgrom and Shannon. While their theorem is constructed on lattices, particularly on partially ordered sets, we do not require the antisymmetry on a binary relation defined on the set. On the basis of this result, we can deal with the comparative statics of constrained optimization problems, including the cases with nonlinear constraints, in a very intuitive, but considerably general fashion. Specifically, we can extend the Âgvalue order methodsÂh proposed by Antoniadou and Mirman and Ruble in the context of consumer problems with linear constraints. It is also worth noting that our results on the value order can be applicable for any comparative criterion as long as it is a complete preorder on the domain of the objective function.

Taxes and labour supply under interdependent preferences

In this paper we identify how changes in the income tax rate affect the labour supply under interdependent utility functions. To reach that aim we create a model of the economy in which households choosing their optimal labour supply take into account not only their income, tax rate and individual consumption but also so called relative consumption level (Garbicz 1997). Taking into account the last issue we significantly modify the well known Becker model (1965). We conduct a comparative statics exercise using na lattice and supermodular game theory. Thanks to which we show sufficient and necessary conditions for a labour supply to be monotonic function of the income tax rate. We analyze the economic behaviour under static and dynamic setup. Under quite general assumptions concerning the household utility function we show that the higher the tax rate the lower the macroeconomic labour supply. Additionally we show the possibility of multiple equilibria in the economy that offers the explanation of differences in the working time between e.g. European countries and the US as well as discrepancies between micro and macroeconomic elasticity of labour supply (see Alesina, Glaeser, and Sacerdote 2005).supermodularity; lattice programming; multiplicity; interdependent preferences; labour supply;