Efficiency and Equilibrium: Numerical Optimization in Economic Theory: Optimizing Economic Efficiency through Numerical Optimization (Journal of Advances and Scholarly Researches in Allied Education, 2022)
Numerical optimization techniques play a pivotal role in advancing economic theory byproviding actionable insights into complex economic scenarios. This paper explores the application ofnumerical optimization methods in two distinct yet interconnected case studies optimizing tax policiesfor efficiency enhancement and analysing Nash equilibrium in game theory.In Case Study 4.1, we investigate the optimal tax rates that strike a balance between revenue generationand labour supply efficiency. Employing gradient descent algorithms, we identify tax rates tailored todifferent income groups, fostering progressive taxation policies. Case Study 4.2 delves into equilibriumanalysis within a duopoly scenario, employing the Newton-Raphson method to identify stable Nashequilibrium prices. These equilibrium points offer a lens into market dynamics, guiding policymakers inensuring fair competition and market stability.Through these case studies, we unveil the power of numerical optimization in generating policyrecommendations that align economic efficiency with equilibrium attainment. The study emphasizes theimportance of this synergy in fostering informed decision-making and shaping more effective economicpolicies.