A general theory of price and quantity aggregation and welfare measurement

The paper presents a general theory of the aggregation of prices and quantities that unifies the field and relates topics that in the past have been treated separately and unsatisfactorily, or not at all. The theory does without the common but unrealistic assumptions of homotheticity, or representative agents and is valid with or without an explicit utility maximization assumption. Two different derivations are given, one in continuous time, using Divisia integrals, and one employing more traditional discrete arguments. The unifying concept is the money metric, which is interpreted as a partial welfare indicator, rather than as a comprehensive welfare measure. On this basis, a consistent set of chained price and quantity indexes for a set of additive time series, such as those in the national income and product accounts, is derived. All variants of the theory lead to Törnqvist indexes defined on the appropriate data set. A numerical example confirms that in the non-homothetic case, these indexes are superior both to Fisher's 'ideal' index and to the consumer surplus approximation.