MODIFICATION OF THE COBWEB MODEL INTO GENERALIZED LOGISTIC EQUATION FOR THE WHEAT PRICE ANALYSIS

Jelena Stanojević; Nemanja Vuksanović; Katarina Kukić; Vesna Jablanović

doi:10.59267/ekoPolj23041025S

Authors

Jelena Stanojević University of Belgrade - Faculty of Economics and Business, Kamenička 6, Belgarde 11000, Serbia https://orcid.org/0000-0001-5668-5297
Nemanja Vuksanović University of Belgrade - Faculty of Economics and Business, Kamenička 6, Belgarde 11000, Serbia https://orcid.org/0000-0002-8522-7022
Katarina Kukić University of Belgrade - Faculty of Transport and Traffic Engineering, Vojvode Stepe 305, Belgrade 11000, Serbia https://orcid.org/0000-0001-7369-2456
Vesna Jablanović University of Belgrade - Faculty of Agriculture, Nemanjina 6, Belgarde 11080-Zemun, Serbia https://orcid.org/0000-0001-7021-992X

DOI:

https://doi.org/10.59267/ekoPolj23041025S

Keywords:

cobweb theorem, wheat price, growth model, generalized logistic equation

Abstract

In the paper we constructed the new wheat growth model, based on the generalized logistic equation. Starting from the theoretical framework of the cobweb model, we adapted generalized logistic equation to better fit the real data of wheat prices, according to the presented wheat growth model. The aim of the paper is to present how logistic and generalized logistic equations can be used for both prediction of wheat prices and for the wheat price stability analysis. Data analysis showed better performances of the generalized logistic map in comparation with the conventional logistic map as a main result of this paper. For estimated parameters of the model the bifurcation diagrams also have been presented to show stability of wheat price over time. The conclusion is that the proposed model can be useful in predicting future wheat prices in the short-run period, as well as for the analysis of stability in conditions of uncertainty, which is also a recommendation for the application of the model in the future research.

Downloads

Download data is not yet available.

References

Akhmet, M., Akhmetova, Z. & Onur Fen, M. (2014). Chaos in economic models with exogenous shocks. Journal of Economic Behavior and Organization, Vol. 106, 95-108.

Ausloos, M. & Miskiewicz, J. (2006). Influence of information flow in the formation of economic cycle. In: The logistic map and the Rout to Chaos. Berlin: Springer-Verlang, 223-238.

Chiarella, C. (1988). The cobweb model: Its instability and the onset of chaos. Economic modelling, 5(4), 377-384.

Day, R. H. (1994). Complex economic dynamics-vol. 1: An introduction to dynamical systems and market mechanisms. MIT Press Books, 1.

Dieci, R., & Westerhoff, F. (2009). Stability analysis of a cobweb model with market interactions. Applied Mathematics and Computation, 215(6), 2011-2023.

El-Moneam, M. A., & Alamoudy, S. O. (2014). On study of the asymptotic behavior of some rational difference equations. DCDIS Series A: Mathematical Analysis, 21, 89-109.

Elsayed, E. M. (2014). Solution for systems of difference equations of rational form of order two. Computational and Applied Mathematics, 33(3), 751-765.

Elsayed, E. M., & Ahmed, A. M. (2016). Dynamics of a three‐dimensional systems of rational difference equations. Mathematical Methods in the Applied Sciences, 5(39), 1026-1038.

Evans, G. W., & McGough, B. (2020). Equilibrium stability in a nonlinear cobweb model. Economics Letters, 193, 109-130.

FAOSTAT. (2023). Retrieved from https://www.fao.org/faostat/en/#data/ (May 10, 2023)

FAO (2022). FMPA Bulletin. Food price monitoring and analysis. Retrieved from https://www.fao.org/3/cc0908en/cc0908en.pdf (May 8, 2023)

Goeree, J. K., & Hommes, C. H. (2000). Heterogeneous beliefs and the non-linear cobweb model. Journal of Economic Dynamics and Control, 24(5-7), 761-798.

Halim, Y. A. C. I. N. E. (2015). Global character of systems of rational difference equations. Electronic Journal of Mathematical Analysis and Applications, 3(1), 204-214.

Hommes, C. H. (1998). On the consistency of backward-looking expectations: The case of the cobweb. Journal of Economic Behavior & Organization, 33(3-4), 333-362.

Hommes, C. H. (1991). Adaptive learning and roads to chaos: The case of the cobweb. Economics Letters, 36(2), 127-132.

Ibrahim, T. F. (2014). Periodicity and Global Attractivity of Difference Equation of Higher Order. Journal of Computational Analysis & Applications, 16(1), 552-564.

Kaldor, N. (1934). The equilibrium of the firm. The economic journal, 44(173), 60-76.

Li, T. Y., & Yorke, J. A. (2004). Period three implies chaos. In The theory of chaotic attractors (pp. 77-84). Springer, New York.

López-Ruiz, R., & Fournier-Prunaret, D. (2004). Complex behaviour in a discrete coupled logistic model for the symbiotic interaction of two species. arXiv preprint nlin/0401045.

Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Sciences, 20, 130-148.

May, R. M. (1972). Will a large complex system be stable? Nature, 238(5364), 413-414.

Milovanovic, M. (2011). Microeconomic analysis. Faculty of Economics, University of Belgrade.

Mitra, S., & Boussard, J. M. (2008). A nonlinear cobweb model of agricultural commodity price fluctuations. Department of Economics, Fordham University.

Radwan, A. G. (2013). On some generalized discrete logistic maps. Journal of advanced research, 4(2), 163-171.

Rak, R., & Rak, E. (2015). Route to chaos in generalized logistic map. arXiv preprint arXiv:1502.00248.

Ricker, W. E. (1954). Stock and recruitment. Journal of the Fisheries Board of Canada, 11(5), 559-623.

Rosser, J. B. (2000). Chaos theory and complex macroeconomic dynamics. In From Catastrophe to Chaos: A General Theory of Economic Discontinuities (pp. 175-205). Springer, Dordrecht.

Spiess, A. N., & Neumeyer, N. (2010). An evaluation of as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach. BMC pharmacology, 10(1), 1-11.

Stanojević, J., & Kukić, K. (2018, January). Dynamical systems in economics. In AIP Conference Proceedings (Vol. 1926, No. 1, p. 020043). AIP Publishing LLC.