Duality Theory for Variable Costs in Joint Production
将消费者需求方程的不完全系统二元性方法应用于联合生产中可变成本函数的二元结构，识别出技术约束和成本约束，使条件要素需求可表示为投入价格、固定投入和成本的函数，从而利用可观测数据研究事前条件需求。
Abstract Duality methods for incomplete systems of consumer demand equations are adapted to the dual structure of variable cost functions in joint production. This allows identification of necessary and sufficient restrictions on technology and cost so that conditional factor demands can be written as functions of input prices, fixed inputs, and cost. These are observable when variable inputs are chosen and committed to production, hence the identified restrictions allow ex ante conditional demands to be studied using observable data. This class of production technologies is consistent with all von Neumann–Morgenstern utility functions when ex post production and/or output prices are uncertain.