Modeling Cost Functions in Computerized Business Simulation: An Application of Duality Theory and Sheppard’s Lemma

Abstract

The paper develops an algorithm to model jointly, cost and production functions in computerized business simulations. The algorithm utilizes the concepts of duality theory to derive a generalized cost function, where costs depend both on the level of input prices and the production rate. Sheppard’s Lemma is applied to derive the cost minimizing input demand levels based on the characteristics of the cost function. The application of Sheppard’s Lemma is shown to help avoid inconsistencies between the cost structure and production technology of the firm. A recommended set of equations is presented and discussed to simulate the cost function of the firm. A numerical example is given to illustrate how the function may be used to demonstrate the stability of the system.