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Global and Local Search Methods for D.C. Constrained Problems Read chapter Read first chapter

2020 | OriginalPaper | Chapter

On Iterative Methods for Searching Equilibrium in Pure Exchange Economy with Multiplicative Utilities of Its Agents

Author : Leonid D. Popov

Published in: Mathematical Optimization Theory and Operations Research

Publisher: Springer International Publishing

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Abstract

We consider the classical Arrow–Debreu model for a pure exchange economy with multiplicative utilities of its agents. To calculate its equilibrium prices, we present a new iterative algorithm that simulates the simplest intuitive forms of the economic behavior of market agents. It converges under very weak assumptions. The algorithm relies on increasing prices for scarce products only. Moderate inflation, accompanying the computational process, plays a positive role in establishing an equilibrium between commodity supply and demand. Schemes have a meaningful economic interpretation. The convergence theorems are proved, and the results of numerical experiments are presented, including other types of economies.

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Footnotes
1
It means that the partial derivatives \( d \mathbf{E} _ {i} (p) / dp_j> 0 \) for all \( i \ne j \).
 
2
This axiom states that for any price vectors \( p ',\ p''> 0 \), such that \( \mathbf{E} (p') \ne \mathbf{E} (p'') \), the implication is true \( \big (\mathbf{E} (p '') ^{\top } p '\le 0 \big ) \Rightarrow \big (\mathbf{E} (p') ^{\top } p ''> 0 \big )\).
 
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Metadata
Title
On Iterative Methods for Searching Equilibrium in Pure Exchange Economy with Multiplicative Utilities of Its Agents
Author
Leonid D. Popov
Copyright Year
2020
Book
Mathematical Optimization Theory and Operations Research

Print ISBN: 978-3-030-49987-7

Electronic ISBN: 978-3-030-49988-4

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-49988-4_16

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