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The hysteresis nature of demand, depending on the price ratio and purchasing power, is well-known, but mathematical models that describe this relationship have not been developed so far. This article provides a dynamic model of optimal production within price hysteretic behaviour. Unlike the standard description methods, the proposed cobweb model provides for qualitative description of the solution to the equation at the slowly changing control. The article also describes the production model enable to determine the adjustment dynamics of product quantity from the manufacturer and the consumer. The solution is described by standard methods of optimal control theory.

Dynamic Model of Optimal Production Control in a Hysteretic Behaviour of Economic Agents