Output Maximization Subject to a Nonlinear Constraint

Using method of Lagrange multipliers and applying first-order necessary conditions as well as second-order sufficient conditions for maximization, an attempt has been made to maximize an output of an agency subject to a nonlinear budget constraint by assuming that the agency gets price discounts for purchasing larger quantity of an input. Such quantity discounts alter the linear budget constraint and result in a nonlinear (convex type) budget constraint. Using comparative static analysis, we study behaviour of the agency when prices of inputs undergo change, besides providing an interpretation of the Lagrange multipliers in this specific case.