Economic Situations of Lagrange Multiplier When Costs of Various Inputs Increase for Nonlinear Budget Constraint

Abstract

An industry always expects to survive in profit maximization atmosphere. To develop profit maximization strategy, it must follow scientific methods in every step of production and distribution. Only proper decisions can propel the industry smoothly in sustainable way. This study attempts to discuss economic effects of Lagrange multiplier when per unit costs of various inputs increase. In this paper the method of Lagrange multiplier is applied to represent higher dimensional unconstrained problem from the lower dimensional constrained problem. Cobb-Douglas production function, 6×6 bordered Hessian matrix, and 6×6 Jacobian are operated here to provide economic predictions appropriately. In the study profit maximization is considered with subject to the nonlinear budget constraint.