Individueel en collectief nut : een overzicht van de ontwikkeling van het denken over welzijn, welvaart en nut, en een schets van een economische nutstheorie

This study contains a review of the development of thought on welfare, and an outline of an economic utility theory: a utility concept is described from an individual and a collective point of view and simple models are given to test this concept. The inquiry into the evolution of thought goes back to the time of the Enlightenment, to include the ideas of the Physiocrats, their central idea being 'le droit naturel' with respect to economic freedom. These Physiocrats are regarded as part of the Classical School, in the broad sense of the word. This school includes, besides the central figure Smith, his followers Ricardo and Say, and writers like Malthus and Stuart Mill, the authors Lauderdale and Bentham. In this Classical School the formation of 'richesse' or 'wealth' was examined. It was considered as an expression of the productive efforts of the community. In the Classical Thought, production is realised in a liberal order, whereby Lauderdale paid attention to the consumption aspect of economic freedom. Moreover this author, like the Utilitarians Bentham and Mill, placed the formation of wealth in the striving for general welfare, with an economic as well as a non-economic content.

Although the Classics saw that a positive valuation of produce by the consumer is necessary if the goods are to have value, they thought that the value was determined by the production costs. The members of the Marginal Utility School - whose foundations were laid by Jevons, Menger and Walras - thought that the subjective valuation of a good, and particularly the estimation of its last unit consumed, determines the value, while the scarcity of the good is therefore a condition. Just as in the Classical theory, the liberal order was thought to be a 'trait d'union' between individual and collective economic welfare. If one increases it implies that the other also increases.

At the turn of the century, the Neo-classical authors Marshall and Pareto integrated the theories of the Classical and the Marginal Utility Schools. The writers identified value with market price, which they considered was determined by both demand and supply. In Marshall the relation between individual and collective welfare is defined by the liberal economic order. This is also so in Pareto, but this economist formulated the relation somewhat more subtly. Pareto only talks of an increase in collective economic welfare, if the economic welfare of at least one member of the society increases and the welfare of no one decreases.

An outstanding, more recent Neo-classical writer is Hicks, who replaced in the economic theory the concept of marginal utility, measurable with an interval scale, by an ordinal utility concept. His idea 'marginal rate of substitution' is related to the indifference function of Edgeworth, which was also an important function in the theory of Pareto. Another outstanding author is Samuelson, who substituted his 'revealed preference' idea for the traditional utility function and the indifference function, which is derived from it. The relation between individual and collective economic welfare is built by this economist on the theory of the New welfare economist Bergson. In Bergson and Samuelson the collective welfare is an increasing function of the welfare of any of the members of a society. In this theory the individual welfare changes of the members are weighed against one another.

By describing a topical utility theory, 1 attempted to synthesize the ideas of leading authors. The basis of the given analytical utility concept is formed by the individual general welfare function. From these variables that determine the existence level of the individual, the non-economic variables are transformed into parameters, according to Graaff. This function can be written as follows:
W e = W e (x 1 , . . . x k , x k+1 , . . . x 1 , x 1+1 , . . . x m ) (S.1)
in which:
x 1 , . . . x k : quantities of private consumption goods X 1 , . . . X k
x k+1 , . . . x 1 :quantities of collective goods X k+1 , . . . X 1
x 1+1 , . . . x m :values of the environmental factors X 1+1 , . . . X m

Collective goods are expressions of public expenditure in different directions. Environmental factors are quantitive characteristics of the environment. Physical external effects of production and consumption change the values of these environmental factors. Psychological external effects of the consumption are included by the idea of the Homo exemplaris, an imaginary man on whom the individual consumer models himself. The individual economic behaviour is related to the intensity of this ideal figure.

The individual utility function is formed by parameters which give an indication of the welfare determining variables which can not be influenced by the individual. The variables x 1 , . . . x k in Eqn (S.1) are the existence level determining variables in the most complete individual utility function.

The collective part of the given utility concept is based on the collective utility function of the Bergson-Samuelson type:
U c = U c (W 1 , W 2, . . . W p ) (S.2)

The function refers to a society with p members. Substitution of (S. 1) in (S.2) gives:
U c = U c (x 1 , . . . x k , x k+1 , . . . x 1 , x 1+1 , . . . x m , α) (S.3a)

In this equation the variable a shows the degree of income inequality. One can only talk of an autonomous influence of the income distribution on the collective welfare, if this function satisfies the condition:
δUc /δx 1. δ x 1 /δα+ δUc /δx 2. δ x 2 /δα+ . . . δUc /δx n. δ x n /δα= 0 (S.3.b)

In pure or positive economics both the individual and the collective utility functions are empirical functions. In the empirical collective utility concept, the government behaviour is endogenous. However ethical functions have meaning in an applied economic context: individual utility functions in home economics and product development and collective functions in welfare economics considered as an applied science.

Finally some conclusions are mentioned which are indicated by the given utility optimalization models. Thus Gossen's theorem of equalization of marginal utilities is applied on collective goods. If there are 1-k collective goods (X j ), to be measured. in relation to public expenditures (x j ), so that j = k+l, . . . 1, and the p members of the society are charged for amounts t i , i = 1,2.... p, then:
δUc /δx j = - δUc /δt i = χ (S.4)

The Lagrange multiplier χin this formula reflects the collective marginal utility of money spent on collective goods, while -χcan be seen as the collective marginal disutility of taxed money. Since there is place left for negative values of t i transfer payments can be included in this trend of thought.

In another model an individual utility optimum is determined in such a way that one of the consumption goods is included in the utility function as a collection of properties of that good. This economic product analysis is based on the assumption that the consumer is free to choose from an unlimited number of differentiated designs of the good, while the price of the good is a continuous function of quantitative expressions of the properties of the good. If the good has a number of a properties, the 'price function' takes the form:
p = p (x 1 , x 2 , . . . x a ) (S.5)

At the optimum:
ur /u s = pr /p s (r = 1, 2, . . . a) (s = 2, 3, . . . k) (S.6)

In the last formula the left term gives the rate of marginal utilities, or the marginal rate of substitution of a property ( Xr ) of a good X 1 for another good (X s ). The numerator of the right term is the partial derivative of the price function (S. 5) for the variable pxr . This variable represents the quantity of property Xr . The denominator expresses the price of good X s . Further the Equation of Slutsky, with a certain restriction, holds in a model with properties as utility determining factors as well.

Likewise the price can be included in the individual welfare function as a property of the good. With a graph of a three-dimensional individual welfare space, we can show how, with a 'status good', demand can increase as a consequence of a rise in price.

On the basis of a collective utility maximalization model, some characteristics are described of a 'positive' income distribution optimum. This optimum is connected to the concept of the empirical collective utility function. On the basis of another collective model a hypothetical environmental optimum is formulated. For this optimum two variants are given: at one optimum the government activity is confined to environmental legislation and at the other the government takes measures for the preservation and improvement of the environment.