A MODEL ON MARKET EQUILIBRIUM USING A DIFFERENTIAL EQUATION WITH TIME DELAYS

  • Jalina Widjaja Departemen of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0009-0002-3442-5544
  • Naufal Zidan Putra Irawan Departemen of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0009-0003-4811-068X
  • Yudi Soeharyadi Departemen of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0000-0001-6113-1416
  • Dumaria R. Tampubolon Departemen of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0000-0001-9918-4599
DOI: https://doi.org/10.30598/barekengvol19iss3pp1893-1904
Keywords: Delay, Demand, Equilibrium, Price, Supply

Abstract

In this paper, a model on market equilibrium is proposed using a delay differential equation with discrete delays as a modified version of the one proposed by Kobayashi (1996). The price of a commodity is determined using the equation involving weighted supply and demand functions. Both supply and demand functions are considered at the current time and sometimes in the past. The delays are chosen by considering the seasonal behavior of the market.  We use data on some main commodities in Indonesia from 2018 to 2024 to validate the model. We found that the implementation of our modified Kobayashi model improves the estimation given by the original one. The implementation of the method also shows some characteristics of delay equations, that is longer delay time may include more dynamics, and more fluctuation, although that means it is more prone to instabilities. However, the problem of optimal delay time is yet to be resolved.

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Published
2025-07-01
How to Cite
[1]
J. Widjaja, N. Z. Putra Irawan, Y. Soeharyadi, and D. R. Tampubolon, “A MODEL ON MARKET EQUILIBRIUM USING A DIFFERENTIAL EQUATION WITH TIME DELAYS”, BAREKENG: J. Math. & App., vol. 19, no. 3, pp. 1893-1904, Jul. 2025.
Issue
Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2025 Jalina Widjaja, Naufal Zidan Putra Irawan, Yudi Soeharyadi, Dumaria R. Tampubolon

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