Differential Demand Systems: A Further Look at Barten's Synthesis

Barten's synthetic model is attractive to applied researchers since it is useful for testing the adequacy of the competing functional forms of differential demand systems including the popular Rotterdam and almost ideal demand systems. This article shows that the synthetic model is not a mere artificial composite of the known differential demand systems as it has been considered, but rather viewed as a model in its own right. It is demonstrated that, at the individual consumer level, Barten's model has the same marginal budget shares as generated by specific forms of Engel curves formulated by the Box-Cox transformation.