Application of the Techniques of Determinants to Utility Maximization for a 4-Period Age-Specific Inter-Temporal Budget Constraint

Abstract

In the modern economics, one has to choose financial strategies for investment and expenditure to optimize the expected utility over the subsequent lifetimes. In this article, the Lagrange multiplier method was used to derive a mathematical formulation to work out an optimal solution for a 4-period overlapping generation model with autonomous consumption to maximize a lifetime utility for households subject to age-specific inter-temporal budget constraints. Also, the Cramer's rule is used in finding the critical point where utility is maximized. Further test for sufficient conditions has been carried out using the Hessian determinants to check if there is a local maximum in the critical point C, where the utility is maximized. The inter-temporal marginal rate of substitution was implored to show the future growth path of utility maximization, and analytical argument was used to support such finding.

Received: 11 August 2022 | Revised: 22 September 2022 | Accepted: 6 October 2022

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Author Contribution Statement

Nelson Pandi Sabo: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing – original draft, Writing – review & editing, Visualization, Project administration. Emmanuel Torsen: Conceptualization, Validation, Formal analysis, Resources, Writing – review & editing, Supervision. Danladi Martins: Conceptualization, Methodology, Validation, Formal analysis, Data curation, Writing – review & editing, Visualization, Project administration. Umar Muhammad Modibbo: Conceptualization, Software, Validation, Resources, Writing – review & editing, Supervision, Project administration.