Efficient Use of Prices and Quantity Constraints for Control and Coordination of Linear Sectoral Production Models

Podkaminer, L. (1981). Efficient Use of Prices and Quantity Constraints for Control and Coordination of Linear Sectoral Production Models. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-81-110

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Abstract

A number of complex national agricultural models with linear programming description of the sectors of farms have been developed. Intended as tools for policy analysis, these models do not clearly endognize the government's behavior. However, it is interesting to explore the consequences and possibilities of an efficient utilization of the sectoral programming models for a fully conscious governmental decision making. The topic is especially important for those centrally planned economies where the failure of the administrative (command) methods of management of agriculture has been unequivocally acknowledged and yet no consistent alternative mechanism has so far emerged.

The paper presents a scheme for the control and coordination of production plans generated by the linear aggregative (sectoral) programs. Thereby prices and, if need be, quotas and constraints on input availabilities may be set in such a way as to guarantee the satisfaction of the governmental goals while fully respecting sovereignty of the profit-motivated producers.

It has been demonstrated that prices alone, even if fully controlled by the government, need not lead to the satisfaction of the achievable government's goals. It is only with the introduction of quotas on outputs and limits on available inputs that the possibility of a reconciliation of the government's goals with the behavior of profit-motivated sectors is recovered. However, the introduction of quantity restrictions imposes additional conditions that cannot be violated for fear that this would unleash uncontrollable speculation with respect to licenses for production and inputs. The analytical framework for the consistent simultaneous determination of prices and quantity restrictions has been given. This implies solving linear programming models with some nonconcave quadratic constraints.

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