Output Maximization Subject to a Nonlinear Constraint
Jamal Nazrul Islam
Haradhan Kumar Mohajan
Pahlaj Moolio
Abstract
The main aim of this paper is to derive the mathematical
formulation to device an optimal purchasing policy for
the service providing agency. An attempt has been made
to maximize the output function of an agency subject to
a nonlinear budget constraint by assuming that the
agency gets price discounts for purchasing larger
quantities of other inputs. Such quantity discounts
alter the linear budget constraint and result in a
nonlinear (convex type) budget constraint. We use the
method of Lagrange multipliers and apply the first-order
necessary conditions as well as the second-order
sufficient conditions for maximization. We also use
comparative static analysis and study the behavior of
the agency when prices of inputs undergo change, besides
providing useful interpretation of the Lagrange
multipliers in this specific case. Illustrating an
explicit example, we show that the optimization problems
play an important role in the real world.
JEL. Classification: C51; C65; C61; D24
Keywords: Maximization, Nonlinear Constraint, Interpretation of Lagrange Multiplier
