Thursday, March 5, 2015

Pareto on Pareto optimum

Kathleen Geier commented on my blog “What remains of Pareto?” that I failed to mention Pareto’s key contribution to economics, which is with us on an almost daily basis, namely the Pareto optimum. Kathleen is right. I just forgot to mention it because I focused on Pareto’s contributions to the measurement and theory of personal income distribution. But Pareto optimum is  indeed related to both.

There are two points, in my opinion, worth mentioning in this respect: Pareto’s insistence on heterogeneity of personal utilities which led him to the definition of the Pareto optimum, and the link between various measures of inequality and welfare.

As is well known, Pareto, and Corrado Gini after him, insisted on heterogeneity of individual utilities. To quote Gini from 1921, this was the approach of the Italian writers, as opposed to Dalton’s, and generally the approach followed by English writers. 

Here is Gini: “The methods of Italian writers…are not…comparable to his [Dalton’s] own, inasmuch as their purpose is to estimate, not the inequality of economic welfare, but the inequality of incomes and wealth, independently of all hypotheses as to the functional relations between these quantities and economic welfare or as to the additive character of the economic welfare of individuals.”

The view of the English school  was that either individual utilities can be (more or less) summed to get some “social” utility (this would be pure Bentham), or if they cannot be  summed, that there exists such a thing as a “social welfare function”, depicting welfare positions of different persons and then transforming them into an overall welfare index.

What is perhaps not well known is that while  Pareto decisively rejected this idea for economics, he accepted it for sociology and political science. Economists, according to Pareto, have to accept that utilities are heterogeneous, and if, in order to improve somebody’s utility we have to drive somebody else’s down,  economists as economists cannot advise such a move. This is because what we today call the Pareto optimum has been reached. Pareto called it optimum FOR a community.

But after that point, when the economist has quit, the realm of decision-making is left open to sociologists and political scientists (or more generally to the state) to decide whether it is worthwhile to sacrifice the utility of one person if utility of somebody else is to be increased. Trade-offs are acceptable: it is just that  economists cannot say anything about them. The decisions regarding the optimum utility OF a community belong to other social sciences.  (When we speak of  “OF a community", we treat community as if it were one person.)

It is interesting to note that Pareto explicitly contrasts a society that is equal and poor with a society that is unequal and rich. The choice between the two, assuming of course that the movement from the former to the latter is going to make at least one person worse off, is not an economic choice. It belongs to the politicians. For some reasons, it may be better for the welfare OF a community if it is poor and equal; say, it would fight better in a war and preserve itself as a society better. For other reasons, if may be better for a society if it is unequal and rich.

Pareto also takes into account social norms and laws. If we have a situation A (with given endowments) but such also that something has been stolen by a thief, putting him in jail leads to a situation  B where he is worse off while other “honest” people are (in principle) better off. But this is a decision for politicians to make, as they clearly believe that the gain to society from putting the thief in jail  is greater than the loss of thief’s utility. It is not a decision that an economist can make.

(On a personal note,  I remember many years ago when I read for the first  time about the Pareto optimum and welfare—it could have been in Samuelson’s “Economics”—that I noticed than no sooner had Samuelson (?) spoken of giving equal importance to utility of all individuals that an example where a law-breaker would  be put in jail would crop up--but now apparently we are ignoring the fact that thief’s utility was thereby reduced. Implicitly, I realized, personal utility of those who break the law  is taken as zero. But that means that  we have gone past the point of the Pareto optimum: we are indeed comparing individual  utilities even if we do not say so. Pareto, as the example above makes clear, was aware of the problem.)

The second point has to do with measurement. Since Sen showed in “On Economic inequality” that every inequality measure can be seen to imply an implicit welfare function (“the equivalence theorem”), there was a view that measurement of inequality is more than a simple registry of the phenomenon. It is not, the argument goes, like for example the measurement of temperature, which does reflect in any way our opinion as to desirability of cold or warm weather. Pareto and Gini (as quoted above) do not agree.  

Even when the “equivalence” of an inequality measure and a welfare function exists,  it would have meaning only if all individuals had this same welfare function. But we know that they do not. So the “equivalence theorem” is meaningless. Measurement of inequality is simply…measurement of inequality, like measurement of temperature, weight, height or whatever else without any welfare judgment contained in it.

Where does then Pareto’s insistence on heterogeneity of utility leave us? First,  to argue that in matters of social policy the role of economists is very limited, and second, to divorce the issues of inequality measurement from any welfare implications.  On the latter point, we know that the Gini index of 50 implies greater inequality than the Gini index of 40, but we cannot say either than it implies more or less “social welfare” (given an equal overall income), nor  whether society should reduce inequality or not.

The desirability of lower inequality ought to be demonstrated on other grounds, for example, that it is detrimental to growth, or to democracy, and the decisions about the optimal level of inequality have to be left to the politicians. In that process  economists participate as much as any other citizen does.

Note: the interpretation of Pareto here is based on “The mind and society”, vol. 4, §2111-41 (also known the “The general treatise on sociology”).

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