Revisited the Constructing a Model of an Excessive Demand

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Abstract

A modification of the Kermack - McKendrick epidemic model for forecasting the development of an excessive demand is introduced. We can consider market participants do not lay in a stock the necessary goods as “healthy”, “sick” participants are struck with panic. The use of this model for description of the excessive demand and the selection of the intensity of “infection” and “recovery” allow predicting the dynamics of the "infected" (panicked) participants, but do not predict the price change. The modified model allows predicting the dynamics of price change of goods at an excessive demand. An excessive demand is possible both in the consumer market and the market of industrial products, if this market is similar to the market of perfect competition and a price regulator is the balance between supply and demand. These markets and products include lumber, pulp, cardboard, paper. To the equations of Kermack - McKendrick epidemic model one more equation reflecting the balance of supply and demand in the commodity market is added. The intensity of "disease" and "recovery" is considered as the linear functions of a price. The modified model contains five adjustable parameters (coefficients). Their determination requires, at least, five observations of change in demand. On the example of the corrugated cardboard the computational solution of the differential equation system of the modified model is given. Application of the modified model and at least five observations of change in demand allow predicting the price change.

Authors

• S.V. Ershov, Candidate of Engineering, Associate Professor,
  Northern (Arctic) Federal University named after M.V. Lomonosov,
  Naberezhnaya Severnoy Dviny, 17, Arkhangelsk, 163002, Russia;
  е-mail: svershov@gmail.com

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References

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2. Kermack W.O., McKendrick A.G. Contributions to the Mathematical Theory of Epidemies. Proc. Royal Society. London, 1927, vol. 115, 700 p.