CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
PROBABILISTIC MODEL OF THE DEMAND DYNAMICS WITH FIXED SUPPLY OF GOODS ON THE MARKET
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Read | Mikheev Andrey V. PROBABILISTIC MODEL OF THE DEMAND DYNAMICS WITH FIXED SUPPLY OF GOODS ON THE MARKET // Caspian journal : management and high technologies. — 2019. — №4. — pp. 110-120. |
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Mikheev Andrey V. - Cand. Sci. (Physics and Mathematics), Associate Professor, Kazan National Research Technological University, 68 Karl Marks St., Kazan, 420015, Russian Federation, veehima@gmail.com
A probabilistic model of demand for goods, the amount of which in the market is limited, was developed. The novelty of the model is that the expected values of demand and demand intensity are presented in it in the form of functionals defined on the set of probability distribution functions of economic quantities that describe the interaction of producers and consumers in the product market. It is shown that, with fixed supply, stochastic demand dynamics is determined by two random variables: the points in time of purchase of goods and the number of units of goods purchased by one consumer. It was found that the time dependence of the demand for a product is a Bernstein polynomial, the argument of which is the cumulative distribution function of the moments of time of goods purchase, i.e. the probability that the moment of purchase is less than or equal to the current point in time. The degree of a polynomial is determined by the number of consumers in the market, and Bernstein coefficients depend on the law of distribution of the quantity of goods purchased by one consumer, provided that the supply of goods is limited. An analytical expression was found for the time dependence of the intensity of demand (the function defining the curve of the product life cycle) through similar Bernstein polynomials. For particular laws of the random variables distribution, a numerical simulation of the established time dependencies was carried out. The influence of the parameters of these distribution laws on the product life cycle was investigated.
Key words: спрос, предложение, кривая жизненного цикла товара, дефицит товара, плотность распределения вероятности, функция распределения вероятности, математическое ожидание, полиномы Бернштейна, demand, supply, product life cycle curve, shortage of goods, probabil