An Inverse Demand System for U.S. Composite Foods: A Comment

In a recent article in this Journal, Huang summarized the theoretical basis of inverse demand systems and estimated a set of price flexibilities for U.S. aggregate food groups. Following Anderson, attention focused on the theoretical constraints on compensated and uncompensated flexibilities. These constraints are analogous to the familiar "general restrictions" of standard demand theory-homogeneity, Cournot aggregation, Engel aggregation, and Slutsky relations. However, Huang neglected to record another aspect of the dual nature of inverse and quantity-dependent demand systems, the property, demonstrated by a number of authors including Anderson and Houck, that the matrix of price elasticities can be derived by inverting the matrix of flexibilities. This duality is important to note because it provides a link between inverse and "direct" demand systems and so allows all the elasticities and flexibilities to be computed, given the values of budget shares, once either set of parameter values has been estimated. Moreover, the derivation of elasticities provides an additional check on whether estimates obtained from an inverse de-