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 7 .0 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.