This paper characterizes all utility derived demand systmes having Engel curves that are linear in both income and an arbitrary function of income. This class encompasses virtually all utility derived demand systems that have been estimated in the past using ag gregate data with explicit treatment of the problem of aggregation ac ross individuals. It includes extensions of the PIGLOG and PIGL class es that have similar properties to these classes, but allow for more general Engel curve shapes. This paper extends W. M. Gorman's study o f these forms primarily by characterizing systems of rank two. The ap plication of the characterized systems to problems of nesting, separa bility, flexibility, Engel curve analysis, estimation, and aggregatio n are briefly discussed. Copyright 1987 by The Econometric Society.
