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

Abstract

The Lagrange multiplier (LM) 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. In this paper, the use of Cramer’s rule is exhibited in finding the critical point where utility is maximized and to further test for sufficient conditions using the Hessian determinants to check if there is a local maximum in the critical point C utility is maximized. The use of the inter-temporal marginal rate of substitution was implored to show the future growth path of utility maximization an 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.