The Ubiquitous Giffen

This paper shows that a demand equation derived by adding two bounded leaning-S-shaped utilities includes the inferior-Giffen response. A leaning-S-shaped, bounded cardinal utility, (0 u 1), for a single commodity is identified as a representation of 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 separability rule states that utilities of commodities fulfilling the same need are weakly separable (multiplicative) and those of commodities fulfilling two 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. Concave- and convex-to-the-origin indifference curves, (the former defining ‘dysfunctional poverty’, leading to disequilibrium in the derived functional forms), are separated by a straight-line indifference curve with slope defined by the relative-intensities-of-need. Convex-to-the-origin indifference curves enable optimisation even for deprivation in one need. The boundaries between superior and inferior responses, and between inferior normal and inferior Giffen, are reflected in envelope curves in the derived functional form diagrams. The inferior-Giffen experience occurs when an individual responds to a price increase for an abundant, cheaper good by consuming more of it, enabled by relinquishing some consumption of a more expensive commodity fulfilling a different need, of which s/he is already extremely deprived.