Mathematical Quantification of market equilibrium and Efficiency Economic Models - Muhammad Fikri Fahrialdie (Indonesia Journal of Engineering and Education Technology (IJEET), 2025)
This study aims to develop a mathematical framework for quantifying market equilibrium and evaluating efficiency across contemporary economic models. Using a combination of differential equations, optimization theory, and welfare analysis, the research constructs a formalized approach to measure the conditions under which markets reach equilibrium and determine the extent to which these equilibria achieve allocative and productive efficiency. The study employs a comparative model analysis that integrates classical supply demand interactions, general equilibrium structures, and modern game-theoretic market representations.The findings indicate that market equilibrium can be precisely characterized through a set of mathematically derived equilibrium conditions, including stability metrics, Pareto efficiency criteria, and welfare maximization indicators. Quantitative simulations demonstrate that deviations from equilibrium caused by price distortions, market power, or externalities can be measured through efficiency loss functions, allowing the economic impacts of disequilibrium to be assessed with greater accuracy. Furthermore, the proposed mathematical quantification model provides new insights into how structural changes within markets affect overall efficiency and social welfare outcomes.In conclusion, this research contributes a rigorous mathematical toolset that enhances the analytical capability of economists in studying equilibrium and efficiency. The model strengthens theoretical predictions, improves empirical measurement, and offers a foundation for future work in optimizing policy interventions aimed at enhancing market performance. The results highlight the importance of integrating mathematical precision into economic modeling to better inform decision-making in both microeconomic and macroeconomic contexts