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

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.