This paper is from an unpublished typescript prepared at the University of North Carolina in 1970. It is a thorough analysis of the distance function that Gorman first discovered in ’Consumer budgets and price indices’ (Ch. 5), where it was used to recover the form of the direct preferences from a dual representation. In this paper, it stands on its own and is shown to be the natural dual of the cost or expenditure function; natural in this context means that the distance function has the same properties in quantities as the cost function has in prices.
Keywords: cost functions, distance functions, expenditure functions, prices, quasi-separable preferences, separable preferences