Cost Minimization of a Competitive Firm

Abstract

One of the economists’ missions is to predict the behavioral responses of consumers or firms on the assumption that optimizing continues. Once this capability is developed, economists try to manage “today” to optimize future economic return of the inputs. Techniques to predict future performance vary from an educated guess based on an appropriate analogy to very complex analytical and numerical calculations and approximations. However, what they all have in common is that they analyze performance in past to say something to obtain constrained optimal output in future. Considering Lagrange multiplier technique applied to a firm’s cost minimization problem subject to production function as an output constraint, an attempt has been made in this paper to apply necessary and sufficient conditions for optimal values. We gave interpretation of Lagrange multiplier and showed that its value is positive. Examining the behavior of the firm; that is, if the cost of a particular input increases, the firm needs to consider decreasing level of that particular input; at the same time, there is no effect on the level of other inputs; also that when the demand of product increases, the firm should consider increasing its level of inputs: capital, labour and other inputs, have been derived.Lagrange Multiplier, Optimization, Cost Minimization, Cobb-Douglas Production Function.