Supply and Demand Modelling in a Local Market

Abstract: With simulations and analysing method, the paper demonstrates how both liner and differential model can effectively capture the behaviour of local markets, offering valuable tools for the small-scalar a producer. The results highlight the importances of the mathematical modelling in predicting market outcomes, understanding economic forces, and guidelines of the subject level. This paper presents a mathematical modelling approach to analyse the supply and demand interactions within a local market, incorporating both linear models and differential equations. The study begins with classical static models where supply and demand are represented as liner functions of price. These functions are used to determine equilibrium price and quantity, providing insights into local producers and consumers respond to changes in pricing, subsides or external shocks.

To understand bitterly the dynamic behaviour of the market over time, the paper extends to analysis by the introducing a system of first-order differential equations that model how prices adjust based on excess demand or supply. This model simulates gives the real-world market price and other adjustments where price changes are not means changing of price instantaneous but it evolves which means prisents in response to market imbalances. Stable analysis is performed to the determine under what conditions the market converges to equilibrium or experiences the oscillations.

Assuming liner supply and demand functions, we simulate market behaviour over a series of scenarios including price shocks and demands surges. The model highlights and gives the nonlinear impacts of even modest parameter changes and this will demonstrates with example the importances of the accurate forecasting. It has (Theoretical background) Liner supply and Demand Models, Market Equilibrium, Dynamic Adjustment via Differential Equations. (Model Construction and Assumption) like assumptions, Model Parameters, Equilibrium Calculations

Keywords: Market Equilibrium, Dynamic Modelling, Supply and Demand Analysis