A main objective of economics analysis consists in the derivation of demand and supply functions for the purpose of establishing market equilibria and predicting their response in relation to the displacement of some parameters (either prices or quantities). Such a variation of parameters corresponds to a comparative statics analysis common to theoretical investigations. When the available information allows it, the derivation of demand and supply functions can be obtained by econometric methods. In that case, the appropriate methodology consists of two phases: estimation and prediction. The estimation phase corresponds to a calibration of the econometric model and includes hypothesis testing. The prediction phase analyzes the behavior of the model outside the sample information and provides a measure of response induced by parameter variations.

When the available information is insufficient for a proper application of econometric procedures, mathematical programming admits the exploitation of limited information and a complete analysis of the given scenario. Problems of environmental economics, natural resources, economic development, and many others often defy econometric analysis because the necessary time series of information are too short for a meaningful employment of those procedures.

The outline of this chapter is articulated in various sections. The first development deals with the relations of comparative statics proper of the theory of the firm operating in conditions of certainty. Such conditions are known as the Hicksian relations of the competitive firm. The second section discusses the parametric programming of a general LP model.