Dual price and quantity aggregation

In his seminal 1959 paper (in Econometrica), Gorman developed conditions for price aggregation in the context of income-constrained utility maximization. Price aggregation is defined as the existence of group income allocation functions with price indices and income as arguments. This paper develops and proves propositions about quantity aggregation that are dual to the Gorman results. These dual structures contain interesting asymmetries. The quantity aggregation concepts should be useful in the study of organizational structures characterized by decentralized shadow price (demand price) determination.