Engel curves and systems of demand functions

The functional forms of the Engel curves implied by several popular complete systems of demand functions are discussed. Among the systems are those generated by generalized quadratic indirect utility (the translog system, the generalized Leontief system, etc.), the linear and quadratic expenditure systems, and Deaton and Muellbauer's PIGL and AIDS. A new system, which can produce the Engel curves of all these systems as special cases, is suggested. The different Engel curves are tested against data from a Norwegian survey of consumer expenditure. This is done both in a complete system of Engel curves for eight commodities and commodity by commodity.