The Relationship between Consumer Theories with and without Utility Maximization

Yuhki Hosoya

AI summary · arXiv: 2404.10931v1 · econ.TH

The Relationship between Consumer Theories with and without Utility Maximization

Yuhki Hosoya

Original paper Submitted to arXiv on 16 Apr. 2024 License: CC BY 4.0

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The essentials

The study explores the relationship between consumer theories with and without the utility maximization hypothesis.
Two axioms regarding subjective exchange ratios are introduced, showing alignment with the utility maximization hypothesis.
Differential equations are used to express how consumers determine their transaction stopping point, with stability conditions reflecting the introduced axioms.
The paper is structured into sections covering necessary notation, static theory results, dynamic theory outcomes, axiom strength evaluation, and addressing the correspondence problem between subjective exchange ratios and binary relations.
Notable definitions include binary relations on consumption sets, weak orders, and utility functions representing binary relations.
Section 4 connects the discussed theory to related studies for a broader understanding of consumer behavior models.
Section 5 concludes by summarizing key findings about how assumptions like utility maximization shape consumer behavior theories.

Key points written by AI: they may contain errors, check them against the paper.

AI-generated keywords: Consumer Theories Utility Maximization Hypothesis Subjective Exchange Ratios Binary Relations Decision-Making Processes

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Original abstract

This paper delves into the relationship between consumer theories with and without the utility maximization hypothesis. The study begins by examining a mathematical representation of pre-marginal revolution consumer theory, focusing on subjective exchange ratios. Two axioms regarding subjective exchange ratios are introduced, demonstrating that these axioms are only upheld when consumer behavior aligns with the utility maximization hypothesis. Additionally, the process for a consumer to determine their transaction stopping point is expressed through differential equations, with stability conditions mirroring the introduced axioms. The paper is structured as follows: Section 2 establishes necessary notation and definitions for subsequent discussions. Subsection 3.1 presents static theory results, while Subsection 3.2 delves into dynamic theory outcomes. Evaluating axiom strength is covered in Subsection 3.3, and addressing the correspondence problem between subjective exchange ratios and binary relations is explored in Subsection 3.4. Notable definitions include the characterization of binary relations on consumption sets, weak orders, and utility functions representing binary relations. The concept of complete, transitive, continuous, locally non-satiated, monotone, and weakly convex binary relations are discussed in relation to utility functions. Furthermore, Section 4 delves into the connection between the discussed theory and related studies to provide a broader context for understanding consumer behavior models. Finally, Section 5 concludes the paper by summarizing key findings. Given the complexity of proofs within this study . This comprehensive exploration sheds light on how assumptions like utility maximization play a crucial role in shaping consumer behavior theories and decision-making processes.

Introduction:

Consumer behavior is a complex and ever-evolving field of study that seeks to understand how individuals make decisions about what goods and services to consume. One key aspect of this research is the relationship between consumer theories with and without the utility maximization hypothesis. This paper delves into this topic, examining mathematical representations and axioms to better understand the role of utility maximization in shaping consumer behavior models.

Section 2: Notation and Definitions

To begin, it is important to establish necessary notation and definitions for subsequent discussions. This includes defining terms such as subjective exchange ratios, which represent an individual's willingness to trade one good or service for another. The paper also introduces two axioms related to subjective exchange ratios, showing that they are only upheld when consumer behavior aligns with the utility maximization hypothesis.

Subsection 3.1: Static Theory Results

In this section, the focus shifts towards static theory results, which examine consumer behavior at a single point in time. The concept of transaction stopping points is introduced through differential equations, with stability conditions mirroring the previously discussed axioms regarding subjective exchange ratios.

Subsection 3.2: Dynamic Theory Outcomes

Moving beyond static theory, dynamic theory outcomes are explored in Subsection 3.2. This section looks at how consumers make decisions over time, taking into account factors such as changing preferences and budget constraints.

Subsection 3.3: Evaluating Axiom Strength

A crucial aspect of understanding consumer theories is evaluating the strength of underlying assumptions such as utility maximization. In this subsection, various methods for assessing axiom strength are discussed.

Subsection 3.4: Addressing the Correspondence Problem

One challenge in studying consumer behavior is addressing the correspondence problem between subjective exchange ratios and binary relations (representations of preferences). This subsection explores potential solutions to this issue.

Section 4: Connection to Related Studies

To provide a broader context for understanding consumer behavior models, Section 4 delves into the connection between the discussed theory and related studies. This includes examining how other researchers have approached similar topics and their findings.

Section 5: Conclusion

In conclusion, this paper has provided a comprehensive exploration of the relationship between consumer theories with and without the utility maximization hypothesis. Through mathematical representations, axioms, and definitions, we have gained a better understanding of how assumptions like utility maximization play a crucial role in shaping consumer behavior theories and decision-making processes.

Overall, this research paper highlights the importance of considering underlying assumptions when studying consumer behavior. By critically evaluating these assumptions and their impact on theoretical models, we can gain valuable insights into human decision-making processes. As our understanding of consumer behavior continues to evolve, it is essential to continue exploring these relationships to further advance our knowledge in this field.

Created on 18 Apr. 2024

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