A WEB-LIKE MODEL OF THE LEARNING MARKET

Abstract

The article discusses both a simpler dynamic model of a product market (referred to as the «web-like model») and a modified version of this model where sellers set the market price. These dynamic models are described using discrete first-order difference equations and systems of difference equations.
The study focuses on the importance of understanding dynamic market models for certain products, particularly the web and web-like market models with training, which are examined in the article. Based on certain assumptions (described further in the article), a Valsar interpretation of these models is provided: the market is regulated by an auctioneer who initially announces the product price, and then buyers and sellers execute agreements and communicate the results to the auctioneer in terms of supply and demand volumes. If the agreements are found to be imbalanced, the auctioneer adjusts the price in an attempt to restore market equilibrium. Final agreements are made once equilibrium is reached.
The article considers cases where the initial point coincides or does not coincide with equilibrium, and analyzes the price and production volume trends in these scenarios. A formula is derived that determines the trajectory of price changes in the «spider model», indicating that the market price will fluctuate around the equilibrium price.
Additionally, a modification of the simpler spider-like model is discussed, where sellers determine the market price by focusing on a weighted average value between demand and supply from the previous period. Similar to the web model, the equilibrium price is found. The article investigates the case when the initial point does not coincide with equilibrium and examines the trends of prices and production volumes in this scenario.
Different types of models are presented, and the properties of general solutions of difference equations and systems of difference equations that describe the web-like model and its modification are analyzed.