Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2020, Volume 26, Number 3, Pages 154–170
DOI: https://doi.org/10.21538/0134-4889-2020-26-3-154-170
(Mi timm1753)
 

On iterative methods of finding the equilibrium in the Arrow-Debreu classical model of pure exchange with multiplicative utility functions of the participants

L. D. Popovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg
References:
Abstract: For the classical Arrow–Debreu exchange models with multiplicative utility functions of the participants, new iterative schemes for setting the equilibrium prices are proposed. Each iteration of the new algorithms corresponds to one exchange cycle. During each cycle, the participants respond to current market prices and exchange goods based on their budgets and their preference systems. The only observations available to the participants are the disappearance from the market of certain products that pass into the category of scarce ones. This forces the exchange participants to adjust the prices for such goods. Namely, the prices corresponding to the goods that have become scarce grow by some relatively constant value. At the same time, other prices, including the prices of commodities remaining in excess, do not change. Because of this, the total level of prices gradually increases (which corresponds to the normal inflation observed in any market economy). The growth of prices forces a reduction in the excessive demand for scarce goods and its switching to other product groups, in accordance with the existing norms of their interchangeability. Although the growth of prices is fixed, their overall growth from iteration to iteration leads to the fact that not absolute but relative changes gradually fade, providing a generalized convergence of the iterative process. As a convergent sequence, it is possible to track the so-called normalized prices. The corresponding convergence theorems and results of numerical experiments are presented, including cases of other types of economies, up to the most extravagant.
Keywords: economic equilibrium, exchange model, multiplicative utility function, coordinate descent methods.
Funding agency Grant number
Russian Foundation for Basic Research 19-07-01243
This work was supported by the Russian Foundation for Basic Research (project no. 19-07-01243).
Received: 16.03.2020
Revised: 20.04.2020
Accepted: 18.05.2020
Bibliographic databases:
Document Type: Article
UDC: 519.658.4
MSC: 90C05, 90C46
Language: Russian
Citation: L. D. Popov, “On iterative methods of finding the equilibrium in the Arrow-Debreu classical model of pure exchange with multiplicative utility functions of the participants”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 3, 2020, 154–170
Citation in format AMSBIB
\Bibitem{Pop20}
\by L.~D.~Popov
\paper On iterative methods of finding the equilibrium in the Arrow-Debreu classical model of pure exchange with multiplicative utility functions of the participants
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2020
\vol 26
\issue 3
\pages 154--170
\mathnet{http://mi.mathnet.ru/timm1753}
\crossref{https://doi.org/10.21538/0134-4889-2020-26-3-154-170}
\elib{https://elibrary.ru/item.asp?id=43893871}
Linking options:
  • https://www.mathnet.ru/eng/timm1753
  • https://www.mathnet.ru/eng/timm/v26/i3/p154
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Statistics & downloads:
    Abstract page:91
    Full-text PDF :44
    References:21
    First page:2
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024