Pareto’s Approach to Economic Welfare as ‘Economic Welfarism’

Pareto (1894) investigates the relationship between efficient production and utility maximisation. The Cours d'Economie Politique (Pareto 1896-7 [1971]), published a few years later, includes the proof of the main pro­positions presented in Pareto (1894), but, for our purposes here, the primary importance of the Cours is that it situated the issues of economic equilibrium and economic welfare within a broader context that reflects value propositions.

6.2.1 Policy Problem That Culminates in Analysis of Efficiency in Production

The theoretical exposition of the relationship between production, compe­tition and economic welfare presented in Pareto (1894) was written with a practical problem in mind. Specifically, Pareto wanted to develop a general analysis capable of challenging the following proposition, which he ap­peared to associate with the labour movement: consumers experience a gain when entrepreneurs adopt more labour-intensive methods of produc­tion because this increases the aggregate value of wages, which, in turn, fund expenditure on consumer goods. To test, and ultimately reject, this proposition, Pareto presented three basic problems for resolution, which, for convenience, are labelled in this paper as the problem of production and distribution, the problem of utility maximisation for society as a whole and the problem of utility maximisation without interpersonal comparisons.

Pareto (1894) was published in two distinct parts, with the problems of production and distribution and the utility maximisation considered in the first part of the paper without raising the issue of the interpersonal com­parison of utility implied by the analysis. It is only in the second part of the paper, drafted in response to concerns raised by Maffeo Pantaleoni and Enrico Barone, that Pareto extended his analysis to make it explicit that his solution to the problem of utility maximisation does not depend on an interpersonal comparison of utilities, which is, of course, a critical plank of ‘economic welfarism'.

The problem of production and distribution is formalised by intro­ducing variable coefficients of production within the Walrasian system of general equilibrium. Pareto succinctly presented that system as three sets of equations, which indicate that: (i) from the demand side, the prices for each good are given at the point where relative prices equal relative marginal utilities, provided the sum of the excess demands is zero; (ii) from the supply side, the prices for each good are given by the cost of production;^[39] and, to close the system, (iii) the total quantity of each productive service required to produce the total quantity of each consumer good demanded is available to entrepreneurs.

Given the above system, prices and quantities are influenced by the coefficients of production, which, in turn, are determined by the prevailing production technologies. More specifically, Pareto treats relative prices, the quantities that individuals demand and the total quantity of goods avail­able as functions of the coefficients of production. He then solves his production and distribution problem by finding the marginal conditions under which variable coefficients of production will minimise the unit costs of production for each good on the assumption that each entrepre­neur is a price taker.

In regard to the problem of utility maximisation, Pareto’s initial assess­ment (in part one of the paper) considered the net effect of utility gained from consumer good consumption ‘for society as a whole’ and the utility expended in production for ‘society as a whole’, with utility ‘reckoned’ in terms of the numeraire good A. The net impact on utility can, on that basis, be considered for a variation in the quantity of labour used in the produc­tion process (∂a_s), with the marginal condition for maximisation given by equation (1):

Where:

R_a, R_b are the aggregate quantities of the two goods a and b for society as a whole.

R_t, R_s are the aggregate quantities of productive services t (land) and s (labour) for society as a whole.

∂a_s an infinitesimal variation in the production coefficient for labour, i.e. variation in the quantity of labour used in the production of one unit of numeraire good a.²

p_b the price of economic good b, given by the ratio of the final degree of utility of good b to the final degree of utility of numeraire good a.

p_s the price of productive services s, given by the ratio of the final degree of utility of the services of labour to entrepreneurs (or the final degree of utility sacrificed by workers) to the final degree of utility of numeraire good a.

The quantity demanded for each factor of production alters following a variation in the production coefficient for labour. The change in the quantity of each factor of production is then multiplied by its price to estimate the change in the value of the factors of production in terms of the numeraire. The resulting equation reduces to equation (1) when it satisfies the conditions for unit cost minimisation, which reflects the production coefficients determined under free competition. From this result, Pareto presents the following ‘theorem’: ‘The fabrication coefficients determined by free competition have values identical with those obtained by determin­ing those coefficients subject to the condition that they produce the maximum utility with minimum sacrifice’ (Pareto 1894 [2008: 393]). The second part of the paper commences with Pareto noting that Pantaleoni and Barone had warned him that the first part of the paper was ‘too imperfect and incomplete’: ‘The observations of these distinguished gentle­men applied to those parts of the demonstration in which... it appeared that my approach ran counter to the principle that the different individual utilities are reckoned in different units and cannot therefore, at least without special precautions, be added’ (Pareto 1894 [2008: 395]).

Pantaleoni’s and Barone’s comments to Pareto are not extant, but it is certain they advised Pareto that equation (1) treats utility, which is not subject to interpersonal comparison, in terms of values based on the numeraire good, which are comparable across individuals. Pareto therefore added a second part to his paper to explicitly address the utility problem without interpersonal comparisons. He addressed this concern by defining all elements of production and utility with respect to each individual; and by identifying and isolating the objective and the subjective aspects of each individual’s change in utility as a result of a change in the method of

Variations in the labour production coefficient can be considered for any good, not just the numeraire good a.

producing. The term λ_i is specified as the quantitative change in individual i’s income expenditure, as valued in units of the numeraire, following a change in the production coefficients; and φ_ia is individual i’s final degree of utility^[40] of the numeraire (i.e. good A). Each individual’s variation in utility from a change in the production coefficients is, therefore, the product λ_iφ_iα. The first term, λ_i, is the objective and observable element of utility and the second term, φ_iα, is the subjective element of utility that is explicitly reckoned in different units by different individuals.

As the numeraire is an economic good, its final degree of utility is positive. Consequently, individuals with positive λs will have experienced a gain in utility following a change in production coefficients for labour (da_s);^[41] whereas individuals with negative λs will have experienced a loss in utility. In regard to the problem of utility maximisation, when every individual's λs is positive, each individual's utility is necessarily enhanced by a small positive change in the quantity of labour used to produce one unit of the numeraire good das.

At this point, Pareto needed a criterion that does not require interper­sonal comparisons of utility yet still accounted for the possibility of im­provements in welfare as productivity being concurrent with harm to some individuals. He settled on a compensation criterion, another of the key concepts of economic welfarism, under which a welfare gain is obtained when the numeraire value of the gain, to those with a positive λ, exceeds the numeraire value of the loss, to those with a negative λ. In that case, the change in production coefficients would create a positive economic ‘re­sidual' for society as a whole. With an appropriate distribution of that residual, it is, therefore, possible to realise the maximum of the utility of each individual in society up to the point where the sum of the positive and negative λs from any change in production coefficients is zero. At that point, utility is maximised for all individuals as further change will mean that someone is necessarily harmed because those who gain no longer have the capacity to pay full compensation to those who lose.

In regard to the problem of utility maximisation without interpersonal comparisons, Pareto contended that the maximisation of production of economic goods is, once again, matched with the maximisation of individ­ual’s welfare via the introduction of a compensation criterion. If an in­crease in the quantity of labour reduces the unit cost of production, an economic ‘residual’ measured in terms of the numeraire good will be produced that can be distributed among the community in a manner that increases the welfare of everyone.

6.2.2 Values When Economic Welfare Is a Production Problem

The most distinct consequence for economic welfarism, especially the aspect associated with the ‘new welfare economics’, derives from Pareto’s dichotomisation between the problem of producing goods that people value and the problem of distributing those goods among society. This led Pareto to posit that, if the goal of a socialist state was to maximise utility, it should differentiate between the roles of the ‘Minister of Production’, to establish the production coefficients that minimise unit cost and maximise the production of economic goods, and the ‘Minister of Justice’, to distrib­ute economic goods in the manner that obtains distributive justice. If, for example, the ‘Minister of Justice’ wishes to advantage a certain group of workers at the expense of others in society, it would be inefficient for the ‘Minister for Production’ to alter the production coefficients to achieve that goal. Rather, efficient redistribution would be achieved by the ‘Minister for Production’ adopting production coefficients that are identical to those adopted by entrepreneurs under free competition;^[42] and the ‘Minister for Justice’ then directly taking the product from individuals and transferring it to the favoured workers.

In other words, Pareto took his theorem, in conjunction with the compensation criterion to avoid interpersonal comparisons of utility, as the basis for achieving the desired redistribution at the minimum cost. But given the partial treatment of exchange in Pareto (1894), there was little prospect of him fully deriving the second law of welfare economics. Even though the general interdependence of Pareto’s own equations for produc­tion and distribution actually suggest that the same pattern prevails for demand and the associated equilibrium price system, Pareto’s verbal ac­count is predicated on an implied direction of causation that runs from the coefficients of production to quantities produced and exchanged as well as equilibrium prices. At that stage, then, Pareto appears to have conceived of an economic maximum as a point in commodity space irrespective of the distribution of goods between individual members of the society.^[43]

In terms of laying a foundation for economic welfarism, however, especially the part associated with new welfare economics, the most im­portant point is that Pareto (1894) provided the distinct assignment of roles between the ministers of production and justice. And he did so in a manner that contemplated the demarcation between the economic analysis of welfare and the value judgements later associated with Hicksian eco­nomic welfarism. In other words, the domain of ‘welfare economics’ concerns the efficiency of free competition in terms of welfare; and the mechanism by which ‘extra-economic redistribution’, as determined by the ‘Minister for Justice’, can be achieved in an efficient manner. The value

propositions in Pareto (1894) associated with the domain of welfare eco­nomics are:

(i) that an increase in an individual’s utility is good and the maximisa­tion of each individual’s utility is best;

(ii) to avoid interpersonal comparisons of utility, maximisation of each individual’s utility is determined via the compensation criterion; and

(iii) the individual’s property rights are preserved (such that exchange is either voluntary or, if involuntary, compensation is paid for that harm) unless extra-economic goals for redistribution are set by the Minister of Justice, in which case the task of welfare economics is to minimise the cost of such redistribution.

However, when setting the ‘extra-economic’ goals for redistribution, the role of the ‘Minister for Justice’ is formally unconstrained and may under­take interpersonal comparison of utility or use of any type of value prop­osition deemed fit.

The main additional contribution of the Cours was to set the analysis of Pareto (1894) in a much broader context. Pareto achieved that by replacing his Jevonian focus on utility by distinguishing between utility and (his neologism) ‘ophelimity’. Utility, in the Cours, involves judgement as to whether an action is useful, especially in the long term. More specifically, utility concerns ultimate ends, of which Pareto highlights two classes: ‘individual utility’, which relates to the abstract qualities of things likely to procure the physical, intellectual and moral development of an individual while assuring, and prolonging, his or her existence; and utility of the aggregate,⁷ which relates to the abstract qualities of things that can assure the reproduction of the aggregate (or of the species) and the reproduction of physical, intellectual and moral prosperity of the aggregate (Pareto 1896-7 [1971: 1085]). In contrast, ophelimity is simply concerned with the pleasant sensations derived from the satisfaction of desires or needs without regard to physical, intellectual or moral well-being or the legitimacy, or otherwise, of satisfying desires or needs (Pareto 1896-7 [1971: 1086]).

When Pareto (1894) is read in light of the scheme presented in the Cours, the word utility should be read as ‘ophelimity’ (and the phrase ‘final degree of utility’ would be read as ‘elementary ophelimity’). That is, his 1894 discussion of the ‘maximum of utility’ must be read as a reference to the

Utility of the aggregate may be so broadly defined to be concerned with the utility of the species.

‘maximum of ophelimity’; and the prohibition on interpersonal compari­sons of utility becomes a prohibition on interpersonal comparisons of ophelimity. The intuition behind this is clear: although Pareto regards welfare in its fullest sense as dealing with the physical, intellectual and moral development of an individual, as well as the physical, intellectual and moral prosperity of the community in aggregate, he recognised such issues cannot be treated without resort to value judgement of some kind involv­ing interpersonal comparisons of utility. So ophelimity is a concept created to facilitate the form of simplification that culminates in abstract model­ling. The method of concrete deduction is employed to consider homo oconomicus as a molecule that responds to the force of elementary ophe­limity and nothing else. On that basis, Pareto’s theorem of welfare eco­nomics and his tentative developments towards what is now known as the second law of welfare economics were ‘first approximations’ under which the ‘extremely varied and complex motivations of human action’ are replaced by a one-dimensional homo oconomicus, for whom interpersonal comparisons of ophelimity were simply not necessary.

But the context for a more comprehensive welfare analysis is evident from the Cours, which introduces different classes of utility so that branches of knowledge within the social sciences could be developed. In that regard, Pareto (1896-7 [1971: 129]) identifies three different types of utility: economic utility, which assures ‘material wellbeing’; moral utility, which furnishes more perfect morals; and religious utility, which provides more perfect religious beliefs. The problem that Pareto points to is that none of these categories, including economic utility, lend themselves well to scientific investigation, which typically breaks ideas and notions into smaller and less vague terms with an objective meaning that can be related to the observable world. While Pareto’s own theoretical analysis stopped at economic equilibrium and welfare based on ophelimity, he implied in the Cours (Pareto 1896-7 [1971: 129]) that it may be possible to undertake studies of moral ophelimity, dealing with the relationships between pleas­urable sensations and acts motivated by morals, and religious studies, dealing with the relationship between pleasurable sensation and acts mo­tivated by religious beliefs. Indeed, in the Manual of Political Economy, he even coined the phrases homo ethicus and homo religiosus (Pareto 1906 [1909; 2014: 9]) as possible subjects of moral and religious theories.

In Pareto’s subsequent economic works, the relationship between wel­fare analysis and value propositions outlined in Pareto (1894) was con­tinued. Indeed, in some respects, his position on the matter became more ardent and less compromising. Notably, notwithstanding the introduction

of his clear distinction between ophelimity and utility in the Cours, in the preface to the Manual of Political Economy Pareto chastised himself for letting his values intrude into science.

[T]hroughout the Cours, it can be seen that here and there the author regards peace and economic and political freedom as the best means of obtaining people's welfare. But he does not and cannot provide any scientific proof of that propos­ition, that is, a proof which is based solely on facts; hence that belief transcends, at least for the time being, objective reality, and seems to originate largely in senti­ment. Precisely for that reason, it should have been absolutely excluded from a work whose sole aim was to study the facts scientifically. (Pareto 1906 [2014: xiv])

But it should also be noted that the increased importance he assigns to the distinction between logical and non-logical actions in the Manual also provided the platform from which he subsequently ruled out any prospect of welfare economics, based on the economic ophelimity of homo ‘using ordinal indexes of preference only’. This is, of course correct, but it must be recognised that inclusion of the initial numeraire in equation (1) by Pareto (1894) predates his formalisation of equilibrium using a preference-based ordinal system (Pareto 1900); and his treatment of welfare maximum subsequent to that (Pareto 1902) still

reflected a formalism that referenced elementary ophelimity (marginal utility). In Pareto’s mind, establishing the existence of an identifiable link between the abstract (ophelimity or welfare) and the concrete (the numer­aire) was evidently far more important than the use of ordinal preferences in theory because that link gave mathematical formalism its concrete economic meaning. The other important aspect of the abstract-concrete linkage in welfare economics was that that linkage does not provide a way of sidestepping Pareto’s ‘no bridge’ rule. That is, an economist cannot indirectly compare the ophelimity or welfare of person A with person B by comparing their respective wealth or income in terms of the numeraire, because each individual still evaluates the elementary ophelimity of the numeraire in different units.

In summary then, beyond the implicit proposition that an increase in ophelimity is good and a reduction in ophelimity is bad, the development of Pareto’s welfare economics between 1894 and 1909 was fundamentally ‘ethically neutral’. That neutrality was attained by: differentiating the role of the Ministry of Production from that of the Ministry of Justice; recog­nising that there is ‘no bridge’ by which economists can make comparisons of ophelimity between individuals;^[46] subjecting welfare analytics to the Pareto test or the compensation criterion; and providing an ordinal link between the outcome of welfare analysis, as represented by ophelimity, and the economic meaning of that analysis, as represented by the numer­aire good.

6.3