Modeling Short-Run Cost and Production Functions Using Sheppherd’s Lemma in Computerized Business Simulations

Abstract

The paper develops an algorithm to model short-run cost and production functions using Sheppard’s lemma in computerized business simulations. The algorithm is derived utilizing duality theory to maintain consistency between the production technology and cost relationships of the firm. The short-run cost function is shown to depend on: variable factor prices, the production rate, and the level of the fixed factors. Sheppard’s Lemma is applied to derive the cost minimizing input demand levels based on the characteristics of the short-run cost function. A recommended system of equations is presented and discussed to simulate the theoretical model of the firm. A numerical example is given to illustrate how the parameters of the equation set can be estimated and how the functions behave. The system is shown to be flexible and may be applied to model a wide array of cost structures.