The concept of separate needs in cardinal utility theory: the leisure-consumption choice

Two propositions are required to introduce separate needs into utility theory. Firstly, the shape of the utility function must represent the different stages of fulfilment of a need as experienced by a consumer: deprivation, subsistence, sufficiency, satiation, surfeit. The second proposes weak separability for the utilities of commodities fulfilling the same need, and strong separability for different needs. A utility function, formed from the addition of two leaning-S-shaped, bounded cardinal utilities with satiation at infinity, is used to create an indifference curve map. Functional forms for the leisure-consumption choice are derived and their diagrams drawn – labour supply, consumption demand and their Engels curves. The main outcomes are: * Concave- and convex-to-the-origin indifference curves, (the former defining ‘dysfunctional poverty), are separated by a straight-line indifference curve, BA, (the slope of which is defined by relative-intensities-of-need), identifiable as an absolute poverty line. It leads to disequilibrium in the derived functional forms. * Each commodity responds as superior, inferior and even Giffen, in different areas of the convex-to-the-origin indifference curves. Their boundaries are reflected in envelope curves in the derived functional form diagrams. * An individual’s labour supply responses vary markedly according to three levels of unearned consumption/income, representing dysfunctional poverty (involuntary unemployment), functional poverty (working, but deprived of either leisure or consumption) and sufficiency. * The reservation wage is a U-shaped function of endowments of unearned consumption. The functional form’s parameters have meaningful psychological interpretations. The concept of separate needs in utility offers a new dimension in labour supply theory.