Separate needs for the leisure-consumption choice

This paper explores the labour supply and consumer demand equations derived from a utility function created by adding two S-shaped utilities. An S-shaped cardinal utility for a commodity represents the individual’s experience of fulfilment of a need – deprivation (increasing marginal utility (MU)), subsistence (a point of inflection), sufficiency (diminishing MU), and either satiation at finite consumption with the possibility of surfeit, or satiation at infinite consumption. The utilities of commodities fulfilling the same need are weakly separable (multiplicative) and those of two commodities fulfilling different needs are strongly separable (additive). Functional forms are derived from a utility function created by adding two normal distribution functions with satiation at infinity, the parameters of which have meaningful psychological interpretations. The indifference map, demand and Engels curve diagrams are explored. The main outcomes: • Concave- (dysfunctional poverty) and convex-to-the-origin indifference curves are separated by a straight-line indifference curve, (an absolute poverty line). • Budget movements on the indifference curve map reveal: corner solutions and disequilibrium associated with dysfunctional poverty; optimisation occurs elsewhere, even with deprivation in one or other need. • The derived functional forms are functions of only the real wage rate and endowments of unearned consumption. • The derived functional form diagrams display: involuntary unemployment, disjointed curves, sticky wages and prices, wage- and price-elasticity associated with deprivation in a need, inferior normal and inferior-Giffen responses, and envelope curves. • The slope of the straight-line indifference curve, (defined by the relative-intensities-of-need), and its intercept on the endowment axis, play significant and dramatic roles in both Engels diagrams.