Utility maximization analysis of an emerging firm: a bordered Hessian approach

In this paper, method of Lagrange multipliers is used to investigate the utility function; subject to two constraints: budget constraint, and coupon constraint, and to verify that the utility is maximized. An economic model of an emerging firm has been developed here by considering four commodity variables. In the study, determinant of the 6×6 bordered Hessian matrix is operated to verify the utility maximization. Two Lagrangian multipliers are used here, as devices of optimization procedures, during the mathematical calculation. In this article, an attempt has been taken to achieve optimal result by the application of scientific method of optimization.