Abstract
In recent times, the consensus has emerged that a profound understanding of mathematics is essential to excel as an economist, leading to a rapid increase in the number of articles incorporating mathematical methodologies within the field of economics. This study explores the dynamic aspects of economic modeling by focusing on the budget constraint equation of a group, treating it as a partial differential equation. The budget constraint problem is a common economic challenge where individuals or entities face limitations on consumption choices due to financial constraints. We introduce an alternative method for solving this equation, employing a matrix-based approach grounded in collocation points and Taylor polynomials. This technique streamlines the resolution process, transforming the solution of the group's budget constraint differential equation into a system of matrix equations featuring unknown Taylor coefficients. The paper contributes to the ongoing discourse on mathematical models in economics by presenting an innovative methodology that enhances economists' analytical toolkit for understanding and navigating the intricate dynamics of economic systems. The proposed method is then applied to the budget constraint equation of the group, providing a systematic and efficient approach to obtain numerical solutions. The study includes a numerical example to illustrate the application of the technique, demonstrating its efficiency, precision, and ability to yield highly accurate approximations for the budget constraint equation. The results highlight the versatility and effectiveness of the Taylor matrix-collocation techniques in solving economic problems.