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A mathematical model of goods production and sale for production supervision and planning. (Russian. English summary) Zbl 1019.37051
A dynamical model of the input/output process is presented. The model is given by the following system of differential equations. \begin{aligned} \dot z &= u-n(c)(Y-v)z-k_1z,\\ \dot v &= n(c)(Y-v)z-k_2v,\\ \dot w &= cn(c)(Y-v)z-k_3z, \end{aligned} here $$u$$ is the quantity of units of goods produced in the unit of time; $$z$$ is the quantity of goods at the market; $$v$$ is the quantity of goods having by people; $$w$$ is yield (the difference between obtained and spend money); $$Y$$ is potential demand; $$c$$ are the costs of goods ($$c>1$$ since it is assumed that self-costs are equal to 1); $$k_1$$ is the coefficient of goods damage by lying at the market; $$k_2$$ is the coefficient of input of bought goods in the unity of time; $$k_3$$ are the costs of staying of a unity of uncelled goods in the unity of time; $$n(c)$$ is the coefficient of velocity of celling process. The basic properties of this model are investigated. It is shown how to modify this model to the different economical situation, including rush and market saturation. The advantages of this model in comparison with some well-known statistical models are discussed.

MSC:
 37N40 Dynamical systems in optimization and economics 90B30 Production models 91B38 Production theory, theory of the firm 37H10 Generation, random and stochastic difference and differential equations