Tools and Tricks of the Trade, Part I:
Many policy issues in development economics cannot be addressed in a rigorous manner without building models that allow for considerable structural detail. Depending on the issue, it may be important to distinguish between agriculture and industry, between importable, exportable, and nontraded goods, between employment in high-wage vs. low-wage sectors, between domestically produced and imported capital goods, or between private and parastatal production. Unfortunately, there is a basic problem with the generally laudable strategy of including all relevant structural detail in a model: the more complicated the economic interactions, the messier the analysis and the more difficult it is to derive clean, insightful results. This is why duality theory should be part of the policy-oriented development economist's tool kit. Duality theory provides the model builder with functions based on the solutions to various static optimization problems. The functions summarize in a compact manner how demand and supply depend on preferences, technology, and optimizing behavior on the part of competitive, price-taking firms and consumers. This enables multisector general equilibrium models to be specified and manipulated with comparative ease as it is not necessary to explicitly solve the optimization problems that govern private agents' behavior. When duality theory is used to characterize demand and supply responses, general comparative statics results can be derived directly by exploiting the properties of the relevant maximum or minimum value functions.
I start by discussing the duality functions that describe production and supply. The exposition will be heuristic, with an emphasis on how to apply duality theory for the purpose of constructing and manipulating models. Readers who desire a more in-depth treatment of the subject should consult Blackorby, Primont, and Russel (1978); Diewert (1978); McFadden (1978); Chambers (1988); and Cornes (1992).