The market as a self-controlled inert dynamic systemwith time-lag under balanced strategy of the goods delivery

dynamic system with time-lag under balanced strategy of the goods delivery to the market. Thisstrategy defines the volume of an order goods for delivery it to the market depending on relationof the demand volume and available goods from storehouse at every current moment of discretetime. Such strategy is directed into economical satisfaction of the purchase requirement when thecontrol by the price of goods is providing maximum of the seller profit. The seller profit turns outto be by the unceasing function of the vector of the prices under such strategies at consequentmoments of discrete time. This function is differentiated in vector space of the prices nearlyaround, excluding the points of the dog-leg, defined by relation between demand for goods andcash by spare of goods in storehouse. The market inertia, limiting velocity of the change of theprice of the goods, is prototyped or by means of square-law penalty function for velocity of theprice change ("soft" inertia restrictions), or by limitation of the interval of possible values of thevelocity of the price change ("hard" inertia restrictions). For decision of the problem of maximizationsof the seller total profit for a certain time interval at condition of those two types of the inertiarestrictions, as well as restrictions onto minimum and maximum values of the price of thegoods, 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 allvariables, defining the optimal (from the viewpoint of the maximum seller profit) behavior of themarket at consequent moments of discrete time is explored. This concerns the price of goods, velocitiesof the price changes, purchase requirement, volume of the order goods, volume of thespare of goods in the storehouse, volume of the sales and the current seller profit under constantprices of the goods buying and of the goods storage at storehouse. It is shown that after output ofthe market from the balance state (for instance, by means of instant increasing of the price of thegoods) the aperiodic (at absence of time-lag of deliveries of the ordered goods for the market) orthe fading periodic (at presence of time-lag) transitional process appears, gradually again bringingthe market into the balance state. The temper of the transitional process for all variables of thestate of the market under the different time delays and under the "soft" and "hard" restrictions ofthe market inertia is investigated. It is given the profound interpreting of the oscillatory temper ofthe transitional process.

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