Mathematical models for developing interactive components of distance education systems

Abstract

A formalized mathematical model of a dynamic economic system with regulated parameters is proposed to analyze economic equilibrium under the interaction of a producer, an aggregate consumer, and a price-regulating authority. The model accounts for production constraints, consumer utility, pricing dynamics, and the closed nature of the economic environment. It investigates supply–demand imbalances, identifies the conditions for restoring equilibrium through price adjustments, and examines the effects of unrealized stock and deferred demand. The dynamic framework enables the analysis of successive system states, evaluation of pricing strategies, and identification of critical operating regimes. Designed as the basis for an interactive simulator integrated into a distance learning environment, the model supports flexible parameter adjustment, enhances the realism of economic process simulation, and fosters analytical thinking and practical skills in economic modeling.