The market as a self-controlled inert dynamic system with time-lag under balanced strategy of the goods delivery
dynamic system with time-lag under balanced strategy of the goods delivery to the market. This strategy defines the volume of an order goods for delivery it to the market depending on relation of the demand volume and available goods from storehouse at every current moment of discrete time. Such strategy is directed into economical satisfaction of the purchase requirement when the control by the price of goods is providing maximum of the seller profit. The seller profit turns out to be by the unceasing function of the vector of the prices under such strategies at consequent moments of discrete time. This function is differentiated in vector space of the prices nearly around, excluding the points of the dog-leg, defined by relation between demand for goods and cash by spare of goods in storehouse. The market inertia, limiting velocity of the change of the price of the goods, is prototyped or by means of square-law penalty function for velocity of the price change ("soft" inertia restrictions), or by limitation of the interval of possible values of the velocity of the price change ("hard" inertia restrictions). For decision of the problem of maximizations of the seller total profit for a certain time interval at condition of those two types of the inertia restrictions, as well as restrictions onto minimum and maximum values of the price of the goods, the quasi-Newton algorithm with approximation of the Hessian by the Broyden, Fletcher, Goldfarb, Shanno's formula (BFGS) is used. By means of this algorithm the track records of all variables, defining the optimal (from the viewpoint of the maximum seller profit) behavior of the market at consequent moments of discrete time is explored. This concerns the price of goods, velocities of the price changes, purchase requirement, volume of the order goods, volume of the spare of goods in the storehouse, volume of the sales and the current seller profit under constant prices of the goods buying and of the goods storage at storehouse. It is shown that after output of the market from the balance state (for instance, by means of instant increasing of the price of the goods) the aperiodic (at absence of time-lag of deliveries of the ordered goods for the market) or the fading periodic (at presence of time-lag) transitional process appears, gradually again bringing the market into the balance state. The temper of the transitional process for all variables of the state of the market under the different time delays and under the "soft" and "hard" restrictions of the market inertia is investigated. It is given the profound interpreting of the oscillatory temper of the transitional process.