by Pierre Lemieux

Individuals are different and assuming the contrary assumes away most of the social phenomena we are trying to understand.


There is a good chance that my economist readers will recognize the unicorn. My non-economist readers may have met the animal in disguise. The unicorn is called “social indifference curves” or alternatively “community indifference curves.”

Start with ordinary indifference curves, a device used in (neoclassical) economics to (conceptually) depict an individual’s preferences. This is not a unicorn, but a very useful device permitting the formalized treatment of subjective preferences. An ordinary indifference curve shows all the baskets of goods the consumption of which brings that individual the same utility (“utility” meaning roughly satisfaction). For example, you may be equally happy with either of two bundles: two TV flat screens and one turkey; or one flat screen and two turkeys. More flat screens or more turkeys will get you on a higher indifference curve. For more explanations, the lay reader may want to read David Friedman’s Hidden Order: The Economics of Everyday Life (page 28 and ff).

Now, jump to social indifference curves, conceived as the indifference curves of a society. One social indifference curve is supposed to indicate the combinations of goods and services that give society the same social utility. For example, the consumption of 40 million flat screens and 240 million turkeys may give the same utility as 30 million flat screens and 400 million turkeys. If a society’s social individual curves are known, one can determine which combination of flat screens and turkeys (or, in general, all goods and services) would place society on its highest indifference curve, thus maximizing collective utility.

Trade economists sometimes are especially prone to using social indifference curves in order to conceptualize how many goods an economy should import and export with a view to maximizing utility. Jagdish Bhagwati, a leading trade theorist and market-friendly economist, uses them. So does Paul Krugman in his famed international trade textbook (coauthored by Maurice Obstfeld and Mark J. Melitz), adding in a footnote that the existence of social indifference curves can be assumed if “all individuals have the same tastes” or if “the government redistributes income so as to maximize its view of overall social welfare.” These strange qualifications look unicorn-esque.

Indeed, we have met the unicorn: social indifference curves. Except if unicornesque assumptions are made, social indifference curves do not exist. This was formally demonstrated by Nobel prizewinning economist Paul Samuelson six decades ago in a famous article of the Quarterly Journal of Economics, titled “Social Indifference Curves.” My non-economist reader may want to skip the following (longish) paragraph and jump to the even more impressionistic one that follows.

Samuelson showed that any two points on an assumed social indifference curve can only be indifferent to “society” if they are accompanied by an unchanged distribution of the goods (that is, of real income) among all individuals. This is because social utility must partly depend on who gets what. Samuelson then showed that two conditions are necessary for this constant social utility to be realized along a given social indifference curve. Either all individuals have the same preferences (which must also be “homothetic”) so that, in fact, any individual is perfectly representative of the collective, and any individual’s own indifference curves can be used for the whole of society. Or else, the government must continually operate lump-sum redistributions of income to insure the maximization of social welfare (The redistribution must be through lump-sum transfers to guarantee that it does not reduces individual incentives to produce.)

In other words, a set of social indifference curves describing a society’s preferences and utility only exists (is only defined) if one or two assumptions are made (as Krugman et al. reported). Either all individuals have the same preferences, or the government can continuously and costlessly redistribute income so as to maximize what it considers social welfare.

As any amateur unicorn hunter will have noticed, neither assumption corresponds to anything recognizable in reality. Individuals are different and assuming the contrary assumes away most of the social phenomena we are trying to understand. And even if we accept (at a moral level) that government implement what it considers maximum social welfare (obeying which special interests?), government redistribution cannot be continuous and costless; government is not God. Hence, social indifference curves do not exist.

The idea of social indifference curves – that is, of society’s preferences – has translated into, or perhaps more exactly has confirmed, non-scientific intuitions represented in statements like “society wants [this or that],” “we as a society want,” or this is “good for the country” or “bad for the country.” Many people think that such statements are meaningful and (potentially) scientific. Since Samuelson, economists know, or should know, how they rest on unicornesque assumptions.

So why do some economists continue to use social indifference curves – even if with abstruse qualifications?

One reason may be that economists carelessly draw social indifference curves on the blackboard, the whiteboard, or in their PowerPoint slides because they are simply unaware of Samuelson’s demonstration. It is difficult to miss Samuelson in the history of 20th-century economics, but the discipline has become so extensive and thus so specialized that one is bound to miss something. I would argue, though, that missing a unicorn as big as a social indifference curve is not easy to justify (and will hopefully be eliminated by this blog post of mine!).

Another reason why some economists continue drawing social indifference curves may be that they are a “useful heuristic,” as a leading economist told me. To understand the (physical or social) world, we need models, which are simplified representations of the world. Models necessarily rely on unrealistic assumptions. Yet, it would seem that the assumptions must be not too unicornesque. Imagining society like a big individual is unicornesque. Samuelson complained against “Santa Claus economics.” Some assumptions and models are useful for understanding, others are not. Good theorizing requires distinguishing between the two sorts. These methodological issues are complex.

Yet, proceeding from the assumptions underlying the existence of social indifference curve and deriving policy prescriptions on that basis looks similar to the following line of argument. Let’s assume that unicorns exist. Now, let’s theorize about the proper methods for hunting them. Don’t tell me that they don’t exit, for that’s what we have assumed.

Still another reason why economists choose certain assumptions – the ones justifying social indifference curves are one example – instead of others may be that the chosen assumptions support the analyst’s values, that is, his preferences for certain states of the world. The necessity of separating facts and values, positive and normative statements, is a well-known problem in the social sciences. The biologist (think of eugenicists) is more tempted than the physicist to let his values influence the choice of his assumptions and models; and the economist is more tempted than the biologist – not to mention other even softer social disciplines. The existence of social indifference curves would provide an easy justification for “society” to override individual choices.

In a 2014 article published in the European Journal of the History of Economic Thought, “The Individual and the Market: Paul Samuelson on (Homothetic) Santa Claus Economics,” D. Wade Hands (University of Puget Sound) suggests that, on the contrary, Samuelson may have thought that denying the existence of social indifference curves supported his progressive values, because their existence could lend a hand to the theory that the market reaches the optimal outcome desired by “society.” There is actually some indication of that in Samuelson’s famous article.

But the proof that social indifference curves do not exist (except under unimaginable conditions), it seems to me, is damaging to collectivism, not to individualism.