Individual Welfare Functions Research Articles

Empirical evidence on preference formation

To explain the empirical fact that different individuals have different individual welfare functions, a theory of preference formation has been developed by the first author. The theory essentially states that an individual's welfare function is identical to the distribution of consumption patterns the individual has observed over time. This includes both his own consumption and the consumption by others in his social reference group. The paper reviews the evidence collected with respect to directly measured individual welfare functions in Europe. Evidence obtained in related research by economists, psychologists, and sociologists is also discussed.

The estimation of welfare levels of a cardinal utility function

In order to measure an individual's welfare function of income, WFI [Van Praag (1968, 1971)], the individual is confronted with various welfare levels and asked to associate income levels with them. The welfare levels are given as verbal qualifications like ‘good’, ‘sufficient’, ‘bad’, etc. It is assumed that these verbal qualifications correspond to intervals of equal length of the range of the WFI. Here we want to test this assumption. A first principal component model is applied. The intervals of the range of the WFI associated with the verbal qualifications are estimated and a test of their equality is performed.

On measuring the cost of children

The primary objectives of this paper are to give a precise definition of the costs of a child and to compare various approaches in the literature to estimating these costs. Two alternative approaches are discussed at length. The first goes back to the work of Engel (1895) on household consumption patterns. The second is based on methods to directly estimate Individual Welfare Functions of Income (van Praag, 1968). Both approaches produce well-defined measures of levels of well-being. These measures are adopted to define the cost of a child. We will show that both approaches can be viewed as stemming from the same general methodological framework. A short discussion of methodologies that do not fit this framework is included. It is concluded that there exists in the literature no consensus on the exact value of the cost of a child. The estimates for a first child range from 0–42% of a household's yearly income. However, the century-long development of this topic in the economic literature has produced a precise definition of the cost of a child that—once adopted—will enable researchers to improve their estimates and narrow down this disappointingly wide range.

Interdependent welfare functions and optimal income distribution

The relationship between income distribution and social welfare is empirically analyzed, while explicitly allowing for the interdependence of individual welfare functions. The social welfare function is taken to be an additive function of individual welfare functions of income (WFIs). On the basis of Dutch data it is found that under certain conditions (such as absence of effects of income redistribution on productivity) an equal distribution of incomes is suboptimal. The interdependence of WFIs appears to have a pronounced effect on policy conclusions concerning the desirability of income redistribution vis-à-vis economic growth.

On "A Programming Model of Consumer Choice Among Multiattributed Brands"

Finding an overall ranking of a group of products from rankings over multiple salient attributes is a problem of considerable interest. Assume an individual is faced with ranking m products or choice items. Assume the individual has n attributes, which s/he is using to describe the products, and has, for each attribute, an ordinal preference function ranking the choice items over that attribute. In other words, s/he has n rankings, each corresponding to an attribute. The problem of overall ranking involves combining these n rankings in some rational manner to form an overall preference ranking. This problem is analogous to a multi-objective decision problem in which the attributes constitute the objectives and the choice items are the alternatives. The problem is also analogous to the selection of a social welfare function from individual welfare functions. In this case, the attributes would correspond to the individuals in the society, and the choice items would correspond to the various possible economic bundles. A considerable body of literature has been written on these problems (see Arrow 1951; Luce and Raiffa 1957). Of particular interest are some of the concepts concerning criteria for rationally combining the attribute rankings to form the overall ranking. The first concept of interest is Pareto optimality. Assume A and B are two choice items, and that B is ranked above A by every attribute. Pareto optimality requires that B be ranked above A in the overall ranking. The second concept is that of positive association between the individual orderings and the overall ordering. All else being equal, this requires that if Item A improves with respect to Item B on one attribute's ranking, then A's ranking with respect to B in the overall ranking will not decrease. In a sense, this requirement ensures that the overall ranking is determined by the individual rankings. The final concept of interest is indifference to irrevelant alternatives. Assume we have a set of choice items and a group of attribute preference orderings, and that this leads to an overall ranking in which A > B. Assume we add an additional choice item, and that the attribute rankings are only modified by the insertion of this new item at its appropriate place in the individual rankings. Then the criteria of indifference to irrelevant alternatives implies that A will still be higher than B in the new overall ranking.

A new approach to the construction of family equivalence scales

The question of the money compensation which should be given to families of different sizes in order that they enjoy equal welfare levels is considered. By comparison of individual welfare functions, estimated for 3,000 individuals in the Netherlands, family welfare equivalence scales are derived. The obtained equivalence scale depends on family size and the ages of the family members. There are considerable ‘economies of scale’. The method employed may be used to derive money compensations for other situational differences. Evidence was found that people adapt their needs to situational changes. That effect was quantitatively assessed. Results are obtained and compared for various social subgroups.

MEASURABILITY, COMPARABILITY AND SOCIAL WELFARE

If everyone were indifferent between more and less and between this and that, the problems of allocating scarce resources would be trivialized. The necessity of choice, whether social or individual, would seem absurd. However, people persist in preferring certain “states of the world” to others. As a society is made up of individuals, it seems reasonable that a society's preferences should be “made up” of the preferences of its members. Therefore, any social welfare function, W, should be a function of the individual welfare functions, wi. That is,

Individual welfare functions and social reference spaces

A model of interdependent welfare functions is developed. The relationship between the parameters of an individual's welfare function and the income distribution in his Social Reference Space is established. Results based on Dutch data are presented.

The dynamics of preference formation

Individual's preferences are explained on the basis of two types of influences, his own past consumption and the consumption of others which is directly observable by him. These effects are estimated using the “individual welfare function” approach of Van Praag, and a model of preferences formation.

The individual welfare function of income: A lognormal distribution function! A rejoinder

The individual welfare function of income: A lognormal distribution function! A rejoinder

The individual welfare function of income: A Lognormal distribution function?

The procedure used by Van Praag and Kapteyn to test the theory that the individual welfare function of income is a lognormal distribution function is critically evaluated. It is shown that random data give the same test results as the income levels actually collected from real consumers. Thus it is doubtful whether Van Praag and Kapteyn's results, even although they are based on data collected from as many as 12000 consumers, provide any support for the lognormal model. It is concluded that more powerful methods are required to test the lognormal model thoroughly.

Twelve thousand individual welfare functions: A comparison of six samples in Belgium and The Netherlands

The paper summarizes evidence with respect to the individual welfare function of income. Moreover a number of new empirical results is presented. Data are used from six surveys in Belgium and The Netherlands. The relationships considered appear to be stable across the different samples. The implications of the results for social policy are briefly discussed.

Evaluating public goods from individual welfare functions

This paper suggests a method for evaluating public goods based directly on individual welfare functions. A hypothetical project for reducing air pollution is used as an illustration. The paper describes a technique for estimating welfare functions: the approach is applied to a limited experimental sample. The individual marginal rates of substitution between air income are then added up in order to yield estimates of values associated with air quality variations by the group under consideration. Further it is illustrated that the utilization in the aggregation process of heights based on individual differences in marginal utility of income as computed from the welfare functions, can modify the measures of social profitability and yield evaluation more consistent with basis criteria of social welfare.

De verdeling van inkomen en macht

In this paper it is assumed that individual welfare depends on the individual's income and that social welfare functions are of the Harsanyi-type: a weighted average of individual welfare. Individual welfare functions are specified according to empirical findings by Kapteyn, Van Praag*. Assuming that the Dutch income distribution maximizes a social welfare function one can estimate the distribution of weights over the individuals. This is called the power distribution. Since each observer applies his own individual welfare function when estimating the individual welfare of his compatriots, the perceived power distribution varies with the observer.

Further evidence on the individual welfare function of income: An empirical investigatiion in The Netherlands

The theoretical foundation for this paper has been laid [3]. One of the theory there exposed, is that every individual can evaluate his welafre position with respect to his income level on a bounded scale. A description of this evaluation may be given by the individual welfare function of income. One of the outcomes of the theory is that under fairly general assumptions the individual welfare function will tend to a lognormal distribution function Λ(.; μ, σ). In this paper we estimated the welfare function of this income on the basis of a survey by the Consumer Union in The Netherlands. Besides yielding further evidence on the Belgian results, we handled a much finer social differentation; accordingly, we could measure the preference drift and the influence of the family size on individual welfare for much finer specified social subgroups. Finally, we compared our new results for the Dutch survey with the results of the Belgian survey on which we reported in this journal in 1971.

PARETO OPTIMALITY AND THE CHURCH AS AN ECONOMIC ENTERPRISE

SUMMARY In order to test the general applicability of Paretian welfare principles and to explain intermittent changes in Church regulations, this paper explores the economic implication of Roman Catholic moral philosophy. As a first step, Catholic (or Scholastic) ethical norms are incorporated into the familiar form of individual and social welfare functions. Because Church behavior ought to promote the welfare of the membership, these functions become, in turn, building blocks for a theory of hierarchical decisionmaking. The analysis establishes an analogy between the Church and an oligopolistic business firm and supports two principal conclusions. First, conditions for Pareto optimality which are consistent with Scholastic welfare criteria do not coincide with those of ordinary welfare economics. This is because individual preference (utility) functions often rank material over spiritual good, something which Scholastic functions may never do. Second, treated as objective functions, Scholastic welfare indices afford valuable insight into the doctrinal history of the Church: into the process governing secular changes in the Church's interpretation of the current moral implications of Natural Law.