Українська
Voronin, A., Lebedeva, I., & Lebedev, S.
(2022).
Dynamics of formation of transitional prices on the chain of sequential markets: Analytical model.
Economics of Development,
21(1),
25-35.
https://doi.org/10.57111/econ.21(1).2022.25-35
English
Article
Dynamics of formation of transitional prices on the chain of sequential markets: Analytical model
Received 13.01.2022, Revised 23.02.2022, Accepted 21.03.2022
Abstract
Although the problem of formation of market prices, determination of equilibrium prices within the model “Demand – Supply” is quite known and a great number of both theoretical works and works that summarize the results of observations are devoted to its research, this problem remains relevant, especially as to the dynamics of pricing processes and the stability of equilibrium prices in relation to changes in parameters that characterize the state of the system. Most studies addressing these issues focus on either a particular local market or the global market for some products in general. The purpose of this work is to build a mathematical model that would allow us to analyze general issues related to the formation of transitional prices in the finite N-dimensional chain of sequential markets in accordance with the scheme of market equilibrium. An analytical model is proposed that makes it possible to study the dynamics of prices in adjacent markets. Within this model, which is based on the determination of processes using a system of integral equations, it was assumed that the impact on the chain of sequential markets and the response to this impact are continuous over time. The dynamic aspect of the proposed pricing model in the vertical sequence of markets is the existence of an “after-effect”, which is described in an integral form by the delay distributed over time. The issues of adequacy of the model were examined, its internal coherence was studied, the correctness of the transition from the mathematical model of dynamics as a system of integral equations to the model in the form of a system of linear algebraic equations was substantiated. The conditions for the existence of the solution for this system of equations and the area of its stability are formulated. The mathematical model proposed in this paper allows for a qualitative analysis of the system states (by phase trajectories). Examples of numerical implementation of our analytical model for two and three sequential markets are given, equilibrium prices for each link of the chain of sequential markets are determined. Applying simulation modelling, the stability of the solution in relation to changes in such parameters of the model as the elasticity of demand and supply in the market under study and cross-elasticities in adjacent markets as well as the impact of these parameters on such dynamic indicators of the market system as the rate of attainment of equilibrium was examined
Keywords:
market vertical, pricing, phase trajectories, Volterra integral equations, model adequacy, simulation modelling, elasticities of supply and demand
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References
[1] Andrikopoulos, A., & Dassiou, X. (2020). Is “Three” a lucky number? Exchange-rate exposure in a “Rule of Three” model. Journal of Business Research, 121, 85-92. doi: 10.1016/j.jbusres.2020.08.008.
[2] Benignoa, P., & Faia, E. (2016). Globalization, pass-through, and inflation dynamics. International Journal of Central Banking, 12(4), 263-306.
[3] Liu, Q., Qu, X., Wang, D., Abbas, J., & Mubeen, R. (2022). Product market competition and firm performance: Business survival through innovation and entrepreneurial orientation amid COVID-19 financial crisis. Frontiers in Psychology. doi: 10.3389/fpsyg.2021.790923.
[4] Smale, S. (1998). Mathematical problems for the next century. The Mathematical Intelligencer, 20, 7-15. doi: 10.1007/BF03025291.
[5] Walras, L. (2013). Elements of pure economics. United Kingdom: Taylor and Francis.
[6] Samuelson, P. (1964). Economics. Moscow: Progress.
[7] Hicks, J.P. (1993). Value and capital. Moscow: Progress.
[8] Chen, L., Shaheer, N., Yi, J., & Li, S. (2018). The international penetration of ibusiness firms: Network effects, responsibilities of outsidership and country clout. Journal of International Business Studies, 50, 172-192. doi: 10.1057/s41267-018-0176-2.
[9] Jansen, M., Jallab, M.S., & Smeets, M. (Eds.) (2014). Connecting to global markets. Challenges and opportunities: Case studies presented by WTO chairpersons-holders. Switzerland: World Trade Organization.
[10] MacKay, A., & Miller, N.H. (2018). Estimating models of supply and demand: Instruments and covariance restrictions. Harvard Business School Working Paper, 19(51), 1-44. doi: 10.2139/ssrn.3025845.
[11] Lorig, M., Zhou, Z., & Zou, B. (2019). A mathematical analysis of technical analysis. Applied Mathematical Finance, 26(1), 1-29. doi: 10.1080/1350486X.2019.1588136.
[12] Meadows, D., Randers, J., & Meadows, D. (2006). Limits to growth. The 30-year update. London: Sterling, VA: Earthscan.
[13] Turner, G. (2008). A comparison of the limits to growth with thirty years of reality. Global Environmental Change, 18(3), 397-411. doi: 10.1016/j.gloenvcha.2008.05.001.
[14] Raki, M., & Mehrara, M. (2021). Modeling the market dynamics from a behavioral perspective. Iranian Economic Review, 25(1), 21-31. doi: 10.22059/ier.2021.81477.
[15] Dufeu, I. (2004). Market size and vertical equilibrium in the context of successive Cournot oligopolies. The B.E. Journal of Theoretical Economics, 4(1), article number 10220215345981122. doi: 10.2202/1534-598X.1122.
[16] Strange, R., & Humphrey, J. (2019). What lies between market and hierarchy? Insights from internalization theory and global value chain theory. Journal of International Business Studies, 50, 1401-1413. doi: 10.1057/s41267-018-0186-0.
[17] Porter, M.E. (1980). Competitive strategy: Techniques for analyzing industries and competitors. New York: Free Press.
[18] Cohen, L., & Galleani, L. (2004). Nonlinear transformation of differential equations into phase space. EURASIP Journal on Applied Signal Processing, 12, 1770-1777. doi: 10.1155/S1110865704402224.
[19] Grigorkiv, V.S., & Skrashchuk, P.V. (2012). Differential models in economics. Chernihiv: Druk Art.
[20] Tsoularis, A. (2021). On some important ordinary differential equations of dynamic economics. In B. Carpentieri (Ed.), Recent developments in the solution of nonlinear differential equations (pp. 147-153). London: IntechOpen. doi:10.5772/intechopen.97130.
[21] Jonnalagadda, J.M. (2018). Discrete state space systems of fractional order. International Journal of Dynamical Systems and Differential Equations, 8(3), 228-241. doi: 10.1504/IJDSDE.2018.092676.
[22] Voronin, A.V., Gunko, O.V., & Afanasieva, L.M. (2019). The volatility of price movements when changing the export-import balance. Business Inform, 4, 205-211. doi: 10.32983/2222-4459-2019-4-205-211.
[23] Acaya, W., Basa, E., & Abdeljawadb, T. (2020). Fractional economic models based on market equilibrium in the frame of different type kernels. Chaos, Solitons, & Fractals, 130, article number 109438. doi: 10.1016/j.chaos.2019.109438.
[24] Jan, F., Shah, I., & Ali, S. (2022). Short-term electricity prices forecasting using functional time series analysis. Energies, 15, article number 3423. doi: 10.3390/en15093423.
[25] Ganesan, S., & Uthayakumar, R. (2021). Inventory control techniques in a two-echelon supply chain model with fuzzy demand and learning effect. International Journal of Dynamical Systems and Differential Equations, 11(5/6), 473-496. doi: 10.1504/IJDSDE.2021.120044.
[26] Marshall, A. (1920). Principles of economics (8th ed.). London: Macmillan and Co.
[27] Brunner, H. (2017). Volterra integral equations: An introduction to theory and applications. Cambridge: Cambridge University Press.
[28] Lyulyov, O.V., & Pimonenko, T.V. (2017). Lotka-Volterra model as an instrument of the investment and innovative processes stability analysis. Marketing and Management of Innovations, 1, 159-169. doi: 10.21272/mmi.2017.1-14.
[29] Polianyn, A.D., & Manzhyrov, A.V. (2003). Handbook of integral equations. Moscow: Fizmatlit.
[30] Prasolov, V.V. (2015). Problems and theorems of linear algebra. Moscow: MTsNMO.
[31] Kulkarni, D., Schmidt, D, & Tsai, S.-K. (1999). Eigenvalues of tridiagonal pseudo-Toeplitz matrices. Linear Algebra and Its Applications, 297, 63-80. doi: 10.1016/S0024-3795(99)00114-7.
[32] Mallic, R.K. (2001). The inverse of a tridiagonal matrix. Linear Algebra and Its Applications, 325(1-3), 109-139. doi: 10.1016/S0024-3795(00)00262-7.
[33] Amelio, A., Giardino-Karlinger, L., & Valletti, T. (2020). Exclusionary pricing in two-sided markets. International Journal of Industrial Organization, 73, article number 102592. doi: 10.1016/j.ijindorg.2020.102592.
[34] Fedulova, I., Makarchuk, I., & Hanushevych, V. (2022). Attributes of formalisation risk culture and its typification in the enterprise. Scientific Bulletin of Mukachevo State University. Series “Economics”, 9(2), 18-30. doi: 10.52566/msuecon.9(2).2022.18-30.
[35] Alam, M.J., & Jha, R. (2021). Vertical price transmission in wheat and flour markets in Bangladesh: An application of asymmetric threshold model. Journal of the Asia Pacific Economy, 26(3), 574-596. doi: 10.1080/13547860.2020.1790146.
[36] Chenavaz, R., Paraschiv, C., & Turinici, G. (2020). Dynamic pricing of new products in competitive markets: A meaning-field game approach. Dynamic Games and Applications, 11(3), 463-490. doi: 10.1007/s13235-020-00369-6.
[37] Voloshyna, N., Voloshyn, O., Sushko, D., Dubinskyi, D., & Karpenko, Yu. (2022). Ecological mechanisms of sus scrofa population regulation in modern conditions. Scientific Horizons, 25(2), 65-75. doi: 10.48077/ scihor.25(2).2022.65-75.
[38] Strapchuk, S., & Mykolenko, O. (2022). Algorithm for selecting alternative strategies for sustainable intensification of agricultural enterprises. Scientific Bulletin of Mukachevo State University. Series “Economics”, 9(2), 9-17. doi: 10.52566/msu-econ.9(2).2022.9-17.
[39] Mishenin, Ye., Koblianska, I., Yarova, I., Kovalova, O., & Klochko, T. (2022). Operationalizing the sustainable fertilizer management global initiative at national level: A conceptual framework. Scientific Horizons, 25(2), 76-88. doi: 10.48077/scihor.25(2).2022.76-88.