Some Engel Curves

Abstract

This paper was first published in 1981 in the Festschrift for Sir Richard Stone (Essays in the Theory and Measurement of Consumer Behaviour in Honour of Sir Richard Stone, ed. A. Deaton. Cambridge: Cambridge University Press). The question addressed is straightforward, and its consequences surprising: what restrictions, if any, are placed on the preferences of a rational individual whose Engel curves (curves showing the relationship between income level and spending on the consumption of some good, at a given price) are of the particular form examined in the paper.It turns out that it is as though there are only three commodities. It is as if the consumer purchases a quantity x with which he or she can produce intermediate goods a, b, and c from which actual utility is derived; the optimization problem simply ensures that each of the three intermediate goods is produced efficiently. One of Gorman's suggestions is to explain that this equation arises naturally in the context of an aggregation problem.