Abstract

Purpose: The purpose of this research is to explore the macroeconomic model through both static and dynamic equations. The primary objective of this study is to investigate the variations in the elasticity of substitution across changing economic variables within the framework of the Allen-Uzawa production functions. Research, design, data and methodology: The data were drawn from the World Bank's annual central statistical office database from 2010 to 2021 in the United States of America. The level of expenditures and of the public finance sector, macroeconomic data like output, inflation rates, and labor are examined. Results: This study demonstrates the interaction of two equations, clarifying that the macroeconomic model is practical to determining the stability of both static and dynamic equation systems analytically. The Allen-Uzawa equations allow for the verification of macroeconomic model properties, and study results demonstrate an increase in the range of capital uses as a form of mechanization. A constant elasticity of substitution function is derived from the macroeconomic variables. Conclusion: The macroeconomic model, though the analysis of the static and dynamic Allen - Uzawa model, not only facilitates the examination of long-term trends in crucial endogenous variables but also overcomes challenges commonly associated with other mathematical methods. Overall, the analysis promotes economic growth, investment, and employment. The levels of expenditures and the public finance sector, along with macroeconomic data such as output, inflation rates, and labor, are examined.