INTRODUCTION

In any static optimization problem, the objective function and the constraint functions will contain certain parameters and the optimal solution will depend on the values taken by these parameters. Thus, if any particular parameter value is altered, then we should expect the optimal choice of control variables and the maximum value of the objective function to change. The determination of the effects of parameter variations on the optimal choice of control variables and the maximum value of the objective function is referred to in the economics literature as comparative statics analysis. Section 4.2 is devoted to comparative statics analysis.

Closely related to comparative statics analysis is the theory of duality. At the heart of duality theory in economics is the notion of ‘equivalent representations’. Following Epstein (1981) we may say that:

Thus, in economics, duality refers to the existence of ‘dual functions’ which, under appropriate regularity conditions, embody the same information on preferences or technology as the more familiar ‘primal functions’ such as the utility or production function. Dual functions describe the results of optimizing responses to input and output prices and constraints rather than global responses to input and output quantities as in the corresponding primal functions.