The use of functional differential equations in the model of the meat market with supply delay

Veronika Novotna

Abstract


Purpose: The authors have focused on modelling relationships on the meat market in the Czech Republic. The work aims to analyse the behaviour of the model from the viewpoint of change to input parameters, and in particular from the viewpoint of the effect of delay in supply lasting various lengths of time, and to demonstrate the use of functional differential equations with delay in economics

Methodology: In economic applications, relationships between individual quantities must be expected to be of a variable nature over time. One way of incorporating the dynamics of processes into a model is to describe them by means of functional differential equations. The authors anticipate that a balance between supply and demand can be expressed successfully with the use of a model described by differential equations even in a situation in which the supply of goods takes place with a certain delay. The economic theory that forms the essential basis to such models is adequately explained in the introductory section of the paper and serves as a basis for the drawing up of the model. Also used are methods of analysis, synthesis, dynamic modelling and functional differential equations.

Results: The question of the oscillatoricity of the solution and a situation involving price movement in the case of delay in supply – both the situation of constant delay in delivery and the situation of non-constant delay in delivery – is considered. The equation is solved by means of modern theory and the effect of individual model parameters on its solution is studied. Theoretical results are accompanied by an illustrative example presenting readers with specific results in graphic form. The solution is presented with the help of a computer simulation and the Maple system is used for depiction in graphic form.

The theoretical contribution: The authors come to the conclusion that delay in supply may cause price oscillation. On the other hand, it is also possible to define conditions under which the solution is monotone. This phenomenon cannot be observed when the model is drawn up with ordinary differential equations.

Practical implications (if applicable): The authors have shown, with the use of a practical example, that the original model can be expanded successfully and that significantly more precise information on the behaviour of the examined model can thereby be obtained. An attractive aspect to the modern solution method used is that, if suitable computer software is available, significantly greater possibilities to problem analysis may be obtained in problems of this kind that may help in further research.


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