The Concept of Separate needs in Cardinal Utility Theory: A Functional Form for Added Leaning-S-shaped Utlities

The introduction of the concept of separate needs into cardinal utility theory requires two propositions. The first specifies that the shape of a utility function for a commodity (good, service or event) fulfilling a need should reflect the experiences of an individual as the commodity fulfils that need: deprivation, subsistence, sufficiency, finite satiation with the possibility of a surfeit, or satiation at infinity, referred to as a ‘leaning-S-shaped’ utility. The second is a separability rule, specifying weak separability for choices within the same need, and strong (additive) separability for those between different needs. This paper creates a utility function for two goods fulfilling two different needs, from which the functional form for a demand equation is derived. The indifference curve map and demand and Engels curve diagrams are interpreted, and their outcomes inferred. The main outcomes are: - A straight-line indifference curve, BA, defined by relative-intensities-of-need, separates the concave- from the convex-to-the-origin indifference curves, and can be identified as an absolute poverty line. It leads to disequilibrium in the derived functional form diagrams. - Concave-to-the-origin indifference curves represent dysfunctional poverty. - The convex-to-the-origin indifference curves can be divided into four areas. Where the individual experiences a greater sufficiency in one need combined with a modest deprivation in another, s/he will respond to changes as an inferior, or even Giffen, good. Their boundaries are reflected in envelope curves in the derived functional form diagrams. - Three types of experience can be identified: dysfunctional poverty, functional poverty and sufficiency.