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

Miller, Anne (2024): The concept of separate needs in cardinal utility theory: the leisure-consumption choice.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: leaning-S-shaped utility, additive utilities, absolute poverty line, disequilibrium, Giffen good, envelope curve, involuntary unemployment, functional poverty, reservation wage
• Subjects: D - Microeconomics > D1 - Household Behavior and Family Economics > D11 - Consumer Economics: Theory; J - Labor and Demographic Economics > J2 - Demand and Supply of Labor > J22 - Time Allocation and Labor Supply

References

Blundell, R. “Consumer Behaviour: Theory and Empirical Evidence – A survey”, Economic Journal, 98, (March 1988): 16-65.

Davies, John E. “Giffen Goods, the Survival Imperative, and the Irish Potato Culture.” Journal of Political Economy, 102(3), (June 1994): 547-65.

Dougan, W.R. “Giffen Goods and the Law of Demand.” Journal of Political Economy, 90(4), (August 1982): 809-15.

Hagenaars, Aldi J.M. The Perception of Poverty. Amsterdam: North Holland, 1986.

Hirschleifer, Jack Price Theory and Applications. New Jersey: Prentice-Hall, 1976.

Johnson, Norman L. and Kotz, Samuel Continuous univariate distributions -1. Boston: Houghton Mifflin (Wiley), 1970.

Keynes, John Maynard. The General Theory of Employment, Interest, and Money. London: Macmillan, 1936.

Kohli, Ulrich “Inverse Demand and Anti-Giffen Goods.” European Economic Review, 27(3) (April 1985): 397-404.

Maslow, Abraham H. “A Theory of Human Motivation.” Psychological Review, 50 (1943), 370-396.

Miller, A.G. “A Needs-Based Demand Theory.” In Proceedings of the thirteenth colloquium of the International Association for Research in Economic Psychology, Volume II, edited by P. Vanden Abeele. Leuven: IAREP, Autumn 1988.

Miller, Anne “The Concept of Separate Needs in Cardinal Utility Theory: a functional form for added leaning-S-shaped utilities.” (MPRA, 121455, unpublished), 2024.

Mustonen, Seppo, SURVO: An Integrated Environment for Statistical Computing and Related Areas, Helsinki: Survo Systems Ltd, 1992.

Sen, Amartya “Capability and Well-Being.” In The Quality of Life. Nussbaum M. and Sen A. Oxford: Clarendon Press, 1991.

Silberberg, Eugene, and Walker, Donald A. “A Modern Analysis of Giffen’s Paradox.” International Economic Review 25 (October 1984): 687-94.

Stern, Nicholas, “On the specification of labour supply functions” in Unemployment, search and labour supply, edited by Blundell, Richard and Walker, Ian. Cambridge: Cambridge University Press, (1986): 143-189.

Van Herwaarden, Floor G., and Kapteyn, Arie “Empirical Comparison of the Shape of Welfare Functions.” European Economic Review, 15(3), (March 1981): 261-86.

Van Praag, B.M.S. Individual Welfare Functions and Consumer Behaviour. Amsterdam: North Holland, 1968.

Van Praag, B.M.S. and Kapteyn, A.J. “How sensible is the Leyden individual welfare function of income? A reply.” European Economic Review, 38(9), (December 1994): 1817-25.