EJBO Electronic Journal of Business Ethics and Organization Studies Vol. 9, No. 2 The utility function and the emotional well-being function By: Jose Rigoberto Parada Daza Introduction influenced the development of economic [email protected] thought. The essence of the present-day Just as the utility function forms the utility function grew out of the concept Abstract basis of economic and finance theory, of “useful”, initially a purely ethical aspect. Behind the utility function, which is explicit normative definitions and as- However, it would be an oversimplifica- sumptions form the basis of the utility tion to consider the utilitarianism of D. the basis for economic and finance function. The XVIII Century Utilitar- Hume (1711-1776), J. Bentham (1748- theory, is a philosophical and ethical ian School was the primary philosophi- 1832), and J. Stuart Mill (1806-1873) to approach based essentially on the cal backdrop for the utility function’s de- be the utility function’s only theoretical Utilitarian and Hedonistic schools. velopment. The Utilitarian School itself bases. Utility theory is also conceptu- Once qualitative, the utility func- was the product of schools of thought of ally based on the Hedonism of Socrates, tion’s approach shifted to a quan- many previous centuries. However, the Plato, and Aristotle; in fact, the true ori- normative nature of the utility function gin of the present-day utility function lies titative one based on the work of sometimes leads to a highly simplified within these schools. the mathematician, D. Bernoulli. This analysis of individual economic behavior, As a philosophical and ethical school, quantitative approach is norma- whereas other aspects, such as the cardi- Utilitarianism’s ultimate objective is to tive and based on a maximizing nal human virtues, including theological maximize the positive effects associated agent. In this paper, the “emotional virtues, are omitted. with pleasure and to minimize pain. well-being” function is developed This paper presents the emotional Pleasure is associated with happiness well-being function in an attempt to ex- and pain, or the absence of pleasure, with which mixes the ethics of a rational plain outlying cases within the economy’s unhappiness. In this sense, the primarily economic individual with those of normative context. Rather than invalidat- individual concept of “useful” can be tak- a more complete individual who is ing the classical utility function theory, en to a social level, so that “useful” is that simultaneously conditioned by eco- the emotional well-being function shows which provides the most happiness to the nomic, instinctive, social, religious, its predecessor to be an interpretation of greatest number of individuals. Utilitar- ethical, and esthetic values. This new a borderline mathematical solution. The ian thought, then, attempts to combine emotional well-being function attempts the pleasure and pain of different alter- utility function of emotional well-be- to incorporate aspects of human virtues, natives; in the course of its development, ing is shown to remain within the the bases of ethics as behavioral sciences, it even proposed calculations for pleasure envelope function of the Bernoulli- into the analysis and to explain why indi- and pain. type utility function. vidual decisions are not based exclusively Hedonism also had a strong influ- on the rational economic standard, also ence on the analytical construction of the known as the maximizer. present-day utility function. Hedonism, The paper is developed in two parts. according to Epicurus, seeks the ethical Keywords The first part focuses on the underlying objective of maximum pleasure, which is Utilitarianism, utility function, ra- philosophical aspects of the utility func- understood as that which is good but not tion, its conceptualization, and some of extreme. Schumpeter (pg. 103 op. cit) tionality, well-being, ethics, emo- its paradoxes. The second part is an anal- referred to this scheme as a mechanistic tional well-being ysis of the emotional well-being function, philosophy of the universe, noting that including its mathematical interpreta- the approach’s social attitude is hedonism tion, its interpretation of behavior, ideas or very sublimated egocentric eudaemon- of risk, and a conclusion. ism; Schumpeter considered J. Bentham to be a follower of the hedonistic line. Hedonism, its later schools, and Utilitar- I. Utility function and ianism, then, conform the philosophical utilitarianism basis of the present-day utility function. It is important to remember that various 1.1. Underlying philosophical aspects of the other philosophical and ethical schools of utility function thought have visions differing from those The utility function which is used in of utilitarianism. finance theory is the result of an analyti- Shifting from a qualitative concept of cal, reflexive process stemming from an- utility to a quantitative one allowed the cient philosophical bases. Schumpeter formalization of the present-day util- (1954), in his classic work on economic ity function and the later deduction of thought, made a refined analysis of how marginal utility. Between 1730 and 1731, utilitarianism, as a philosophical school, Bernoulli wrote the article where he pre- 22 http://ejbo.jyu.fi/ EJBO Electronic Journal of Business Ethics and Organization Studies Vol. 9, No. 2 sented his utilitarianism hypothesis. This contribution broad- ened the once-individual nature of utility to include a social wealth versus utility phenomenon is, therefore, central to level in which the degree of total satisfaction is determined to these definitions. Hence, the primarily mathematical con- be the sum of individual satisfactions, making way for the fol- ceptualization of the utility function. lowing expression: So, let u (w) = utility function dependent on the level of wealth w. The utility function and an individual’s economic prob- lem can be reduced to: U(w) = max E (e(w)), with E(U/w) = Σ(p(w))w; where x = individual income; k = different individual x proportionality factors; and a and b = satisfaction limits. The above formula is the hypothesis of the expected Bernoulli’s base was: dy = k(dx/x), where y = the “satisfac- utility of an individual’s “rational behavior” when expe- tion” provided by income x, thereby giving rise to the first riencing uncertainty. An individual having wealth w, the mathematical formulation of the utility function. In 1776, formula shows, can expect to maximize his or her utility Quesnay developed the approach’s economic conception. or satisfaction level at some point in the future; this can Thus, this formerly qualitative concept became the quan- have a probability of p(w). The question at hand is which titative economic formulation of the utility function. This distribution of wealth w will result in maximum utility. allowed the development of autonomous thought on the This utility function is, by definition, nondecreasing and utility function, which, in its modern development, has bounded. According to Laffont (1995, pg. 8), two vital in- grown into the ARA, RRA, and CRRA based on the work terpretations of the function should be highlighted: of Pratt-Arrow; Copeland and Weston (1992, pg. 85). a) First, it is necessary to accept that this definition is a The normative principle of utilitarianism, and conse- working hypothesis and, therefore, requires the deduction of quently, of the utility function, is maximum happiness. Ac- empirically verifiable implications. If these implications cannot cording to Schumpeter (op. cit. pg. 172), utilitarianism is be rejected on the basis of empirical work, then the conclusion a philosophy for real life, being both a normative system reached is that people do act as if to maximize the expected util- (with a strongly marked legal bias) and a social system. It ity. Laffont’s observation, based on philosopher Carl Popper’s is, then, a set of principles to be investigated, a working hy- method, is essential to the understanding and acceptance of the pothesis. For Schumpeter, however, utilitarian hypotheses utility theory, and are completely lacking in value when it comes to matters of b) Second, the normative interpretation, u(w), consists of historical interpretation or the driving forces of econom- demonstrating that rational agents “must maximize” their ex- ic history. He sees such hypotheses as being too weak to pected utility. explain the aspects that escape economic behavior. In the Rationality, therefore, is defined as the consistency of choos- field of economic theory, he adds, utilitarian hypotheses ing among lotteries characterized by several axioms. are useless, but not harmful. Both maximization and normativeness are essential aspects The philosophical aspects of utilitarianism are also, by for understanding the implications of the development of the extension, those of the utility function. Moreover, they are concept of a rational human under these assumptions. Any indi- fundamental to the understanding of what is behind quad- vidual behaving in accordance with these two aspects is rational. ratic or logarithmic utility functions; these kinds of utility A maximizer always prioritizes maximizing economic behavior functions are normally used, since they implicitly embody (a related concept, optimizer, will be elaborated in the second the utilitarian approach. Although the utilitarian approach part of this paper). Carroll (1998, pg. 14) develops the idea of is fundamental for understanding an investor’s analysis of maximizing economic behavior