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Tobin and Houthakker's work on consumer behavior under quantity rationing has been extended by many authors, especially through the use of duality theory. This paper uses duality theory to extend the work on demand theory under rationing to the case of producer behavior under quotas. These results permit estimation of otherwise unobservable market supply and demand structures The structure of the farm economy operating under a tobacco quota system is estimated, and the theory is utilized to infer that the supply elasticity of tobacco would be about 70 if the quotas were removed. Estimates such as this are not normally attainable without the theory outlined here, even though they are essential for the evaluation of policy changes.
There has recently been a revival of interest in the implications of rationing, or more generally of quantity constraints, in a number of different branches of economic theory. Much of the earlier work on rationing was done during and immediately after World War II. The principal results establishing locally valid relationships between demand curve slopes under rationed and unrationed conditions were derived by Tobin and Houthakker (1950-51). Related works were surveyed by Tobin (1952), the results were later restated by Pollak (1969), and were extended by Howard (1977), Latham (1980), Neary and Roberts (1980), and Deaton (1981). In particular, the last two authors illustrate how duality theory can be used to generate empirically estimable demand functions under rationing in the same way that it can do so in the unrationed case.
In this paper we extend the work on demand theory under rationing to explore the implications of quantity constraints in the context of production theory. Because of the presence of short-run adjustment costs leading to short-run input fixity or because of regulatory or institutional constraints, quantity rationing often influences production decisions. Import licensing and quotas and the rationing of intermediate inputs are widespread in the developing world. In many developing countries, agricultural input, output and credit markets are often targets of government intervention that results in dual markets. In Canada, in the European Community, and in the United States, production quotas have been implemented for dairy products, tobacco, peanuts and poultry. Mandatory sales of agricultural output at below free market prices have been features of India, Indonesia, China, and many African nations. Quantity restrictions became widely used in international trade as substitute tariffs after the Tokyo round of GATT negotiations. All of these cases have a common attribute, kink points in the iso-cost sets of firms. These kink points arise from binding constraints on inputs or outputs or other types of restrictions that result in kink points in the interior (as opposed to the vertices) of iso-cost sets, the extreme case being a quantity constraint.