Order-Preserving and Order-Reversing Mappings between Consumption Bundles and Utilities

Chunhua Jin,Eulalia Mart Nez

doi:10.1155/2021/9934743

Abstract

Economics and management believe that income and price play decisive roles in consumer demand for commodities. However, there is no analysis of the order-preserving or order-reversing mapping between consumer demand and utility when income and price are not constrained. Customer utility is always determined by the amount of commodities in real life. This research analyzes the mapping relationship between the amount of commodities and utility. The set which consists of consumption bundles with a binary relation is a poset. The set of utility values with the binary relation is a chain. Furthermore, the relationship between consumption bundles and utilities is illustrated by figures. If the increasing directions of utility and the amount of commodities are consistent, the utility function is order-preserving. If they are opposite, the utility function is order-reversing. Finally, examples are included to illustrate the mapping relationship between consumption bundles and utilities.

Highlights

Customer preference is an important market information which is a useful guideline during decision-making
Management and economics believe that income and price play decisive roles in consumer
There is no analysis of the relationship between consumer demand and utility when income and price are not constrained

Summary

Introduction

Customer preference is an important market information which is a useful guideline during decision-making. The use value of commodities is obtained, and a kind of consumption desire is satisfied. If the amount of commodities in the consumption bundle is greater, the utility value of the customer is greater, the utility function is order-preserving. If the amount of commodities is smaller, the utility value of the customer is greater, the utility function is order-reversing. In this case, if the relationship between utility and the amount of commodities is known, customer preferences can be directly reflected by the amount of commodities, and it is more beneficial to make decisions for enterprises. E remainder of the paper is as follows: in Section 2, consumer preference and chain are introduced.

Preliminaries

Mapping between Consumption Bundle and Utility

Illustrated Examples

Conclusions