Cost and Profit Functions

In the preceding chapters, we first developed the production function as a technological envelope, demonstrating how inputs can be mapped into outputs. Next, we showed how these functions could be used to derive input demand, cost, and profit functions based on these functions and optimizing behavior. In this development, we stated that economists had little to say about the characteristics of the production function. We were only interested in these functions in the constraints that they imposed on optimizing behavior. Thus, the insight added by the “dual” approach is the fact that we could simply work with the resulting optimizing behavior. In some cases, this optimizing behavior can then be used to infer facts about the technology underlying it. According to Gorman (1976): “Duality is about the choice of the independent variables in terms of which one defines a theory.” Similarly, Chambers (1988, p. 49) states: “The essence of the dual approach is that technology (or in the case of the consumer problem, preferences) constrains the optimizing behavior of individuals. One should therefore be able to use an accurate representation of optimizing behavior to study the technology.”