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The idea of the invisible hand could be expressed as: in a competitive market, agents acting selfishly in their own self interests will make choices that benefit others. There are innumerable popular articles that will describe why this is so but I am trying to find more academic literature, i.e. in peer reviewed journals that demonstrate this idea more rigorously, perhaps in the context of some simplified model economy and an agent's choice between multiple possible actions. I am not sure where to look and am concerned that "invisible hand" might not even be the correct key phrase to search - maybe such papers may express their results in terms of Pareto efficiency or some other language.

So my question is in several parts: Do such papers exist? And if so, would they express their results using the phrase "invisible hand", and if not, what other expression would they use.

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    $\begingroup$ Can you please back up your claim that "The idea of the invisible hand could be expressed as: in a competitive market, agents acting selfishly will make choices that benefit others.", because this is not at all how I would put it. $\endgroup$
    – Giskard
    Oct 31, 2021 at 11:12
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    $\begingroup$ Also, have you heard of the first welfare theorem? Would the paper stating that answer your question? If not, can you please elaborate on what you have in mind? $\endgroup$
    – Giskard
    Oct 31, 2021 at 11:12
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    $\begingroup$ @Giskard: I did not know about that theorem - I'm looking into it now. $\endgroup$
    – Mick
    Oct 31, 2021 at 12:44
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    $\begingroup$ My problem is not with this exact phrasing of self-interest (: The invisible hand guides the market to equilibrium, it "sets the prices". And then, there are all these consequences of the market being in a state of equilibrium, but that is not because the invisible hand is kind or anything. $\endgroup$
    – Giskard
    Oct 31, 2021 at 13:00
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    $\begingroup$ No, I am saying that your description of the invisible hand concept is essentially the first welfare theorem. The invisible hand is quite nebulous, but I have always interpreted that it is more about the market reaching an equilibrium just by functioning, i.e. there is no need for a central planner. The invisible hand (IMO) is not about the exact properties of said equilibrium, though clearly one only participates in a market if it is in one's interest. $\endgroup$
    – Giskard
    Oct 31, 2021 at 14:52

2 Answers 2

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tl;dr

Your description of an invisible hand is a straw man, and academic literature typically avoids straw man ideas.

When it comes to proper non-strawman version of the invisible hand argument there are several interpretations of the invisible hand in the literature as describing:

  1. First Fundamental Theorem of Welfare Economics. For derivation and description of the Arrow (1951) and Debreu (1951)
  2. Spontaneous beneficial order that is a result of unintended individual action - this is covered by cornucopia of various models that have this property. Even Ricardian model of trade would technically apply.
  3. There could be other interpretations such as just making relatively vague argument that the economic growth raises income of the poor/economics is generally not zero-sum game.

Full Answer

Correction of misconceptions in the question:

Let me start by correcting some misconceptions

The idea of the invisible hand could be expressed as: in a competitive market, agents acting selfishly will make choices that benefit others.

That is not an expression of invisible hand idea it is a straw man of invisible hand. Academic literature, at least the high quality portion of it, does not examine straw mans of ideas (e.g. you would not expect serious climate paper to address straw mans like "if there is a climate change how is it possible there is a snow in a winter?").

First, Adam Smith used the metaphor invisible hand very sparingly, only 3 times in the whole corpus of his writing and only once in Wealth of Nation (WoN), which is the most relevant, where he states that:

But the annual revenue of every society is always precisely equal to the exchangeable value of the whole annual produce of its industry, or rather is precisely the same thing with that exchangeable value. As every individual, therefore, endeavours as much as he can, both to employ his capital in the support of domestic industry, and so to direct that industry that its produce maybe of the greatest value; every individual necessarily labours to render the annual revenue of the society as great as he can. He generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain; and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention.

Adam Smith never mentions selfishness here (nor self-interest), but person's own gain, i.e. in modern lingo that person is trying to maximize their own utility. What everyone's greatest gain is depends on their preferences and pursuing charitable activity fully qualifies.

Adam Smith does say also say in other passages of WoN that purely selfish activity can increase public welfare, but in those passages he does it to emphasize that that his claim does hold even if people would be selfish. No fair interpretation of Smith would say that he stated that it is selfish action in particular, that is required here. Rather any pursuit of one's self-interest (greatest value judged by one's own preferences) would qualify whether it is one that is selfish or not.

Second, Adam Smith never referred to competitive markets (the notion of perfect competition did not even existed at the time of Smith's writing). Adam Smith referred to free market, which is not the same as competitive market. Perfect competition was first developed by Cournot in 1838.

Third Adam Smith does not make claim that this necessarily increases welfare of others (there are other passages where he says it often does). In fact, Smith clearly states that because:

annual revenue of every society is always precisely equal to the exchangeable value of the whole annual produce of its industry ... As every individual, therefore, endeavours as much as he can, both to employ his capital in the support of domestic industry, and so to direct that industry that its produce maybe of the greatest value; every individual necessarily labours to render the annual revenue of the society as great as he can

In essence, Smith simply states here that the welfare/revenue of society is sum of individual welfare/revenue, that is $W = \sum_i w_i$, and thus if you maximize your own welfare you will contribute to the maximization of public welfare as well. But there is no requirement for your welfare improvements to also help others (although it could). For example, if one person gains but no-one else looses anything that counts as well as situations where one person gains, but other gain as a result as well.

Research Relating to Invisible Hand

The style of 18$^{\text{th}}$ century academic writing was less precise than we use at the present, and Adam Smith used the phrase "invisible hand" only 2 times in all of his published works, and 3 times if we count all of his unpublished works (Blaug 2008). Hence, there is a bit of ambiguity in the meaning of the term, but we can certainly exclude straw man interpretations such as made in the question.

Next the following few interpretations are the ones that are most widely accepted are:

  1. Adam Smith was implicitly describing the first fundamental welfare theorem. This is the claim made by Arrow and Hahn (1971) and MasColell et al. (1995) Microeconomic Theory (pp. 308, 327, 524, 545, 549).

You can see the original work on first fundamental theorems of welfare economics in Arrow (1951) and Debreu (1951).

The above interpretation is popular but a criticism of this interpretation is that it seems to read too much into Smith's work. First fundamental theorem of welfare economics requires perfect markets, no externalities and other assumptions that Smith was never explicitly discussing (see Berg 2008). Thus some economic historians would rather say that Smith was not describing fundamental welfare theorem.

  1. According to Vaughn (1987) and Hayek (1973), Adam Smith was describing a

the principle by which a beneficent social order emerged as the unintended consequence of individual human action

This principle is much more wider that the one suggested in 1, and it is difficult to just recommend single paper. Technically the interpretation of first welfare theorem is an example, of beneficial social order emergence, so the same models can be used. The difference between this and the first interpretation is that this second one allows for much wider set of models and conditions than those of the first theorem of welfare economics. For example, classical Ricardian model of trade can be considered model of beneficial spontaneous order emerges as unintended consequence of individual action.

  1. There could also be some other less popular interpretations. The statement could interpreted much more narrowly just as Smith stating that increases in economic output generally increase incomes of the poor as well (Blaug 2008). There are growth models in growth literature that (depending on their parameters) show this. You can see overview of various growth models in Introduction to modern economic growth by Acemoglu.
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    $\begingroup$ I am really not sure what you mean by "straw man" in "Your description of an invisible hand is a straw man, and academic literature typically avoids straw man ideas." I am familiar with the term straw man argument, but I don't think this fits the bill. $\endgroup$
    – Giskard
    Oct 31, 2021 at 15:20
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    $\begingroup$ Yeah, I don't think that is what straw man argument is. It is more like "bad faith argument"/not a point someone supporting something would actually make. $\endgroup$
    – Giskard
    Oct 31, 2021 at 15:24
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    $\begingroup$ @Giskard my understanding and reading of Smith is following: 1. Selfishness = Narrow self interest. 2. Self interest = following ones interests - smith actually almost never uses word self interest only once referring to the interest to Roman church. Typically people translate following ones interest etc as self-interest in modern translation but then self-interest does not mean selfishness.3. Smith uses word gain in a bit vague way that is probably most closely related to notion of utility $\endgroup$
    – 1muflon1
    Oct 31, 2021 at 15:34
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    $\begingroup$ I gave you my critique, but it is your answer, you do not have to change it if you don't want to. I feel that these more combative parts shift focus away from the other - IMO better - part of the answer. $\endgroup$
    – Giskard
    Oct 31, 2021 at 15:40
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    $\begingroup$ @Mick I respectfully disagree, just because there is more than 1 possible interpretation that does not mean that we can’t exclude some that we know for a fact that they don’t apply, your original statement was in my opinion straw man because it’s genuinely a bad version of smith’s argument. Also to be clear I do not assume bad intent on your part, I assume you probably read it in some blog post from someone because this is actually a common straw man version of Smith’s argument floating around internet $\endgroup$
    – 1muflon1
    Oct 31, 2021 at 18:13
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Invisible Hand is a metaphor wherein Adam Smith assumes that God causes human beings to benefit others when acting in their own self-interest. So it is the invisible hand of the designer or creator that brings about the beneficial outcomes. (This is my effort paraphrase Evensky page 200).

See Evensky, J., Retrospectives: Ethics and the Invisible Hand, Journal of Economic Perspectives—Volume 7, Number 2—Spring 1993—Pages 197–205:

https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.7.2.197

ABSTRACT

As modern economists, we use Adam Smith's "invisible hand" metaphor confident that we all know what it means in our discourse: it reflects our admiration for the elegant and smooth functioning of the market system as a coordinator of autonomous individual choices in an interdependent world. But in Adam Smith's moral philosophy, the invisible hand has a much broader responsibility: if individuals are to enjoy the fruits of a classical liberal society, the invisible hand must not only coordinate individuals' choices, it must shape the individuals into constructive social beings—ethical beings. Revisiting Smith's metaphor provides a valuable lesson: the foundation of success in creating a constructive classical liberal society lies in individuals' adherence to a common social ethics.

Evensky page 200:

Smith's "invisible hand" metaphor reflects his view that he is representing the invisible connecting principles of the "immense machine of the universe" (Smith, 1976b, p. 236) that are the handiwork of the Deity. To fully appreciate the impact of this perspective on Smith's moral philosophy, however, one must bear in mind that Smith (1976b, p. 166) saw the Deity as not only handy, but also benevolent.

"The happiness of mankind, as well as of all other rational creatures, seems to have been the original purpose intended by the Author of nature, when he brought them into existence. No other end seems worthy of that supreme wisdom and divine benignity which we necessarily ascribe to him . . ."

Stiglitz, Joseph E., THE INVISIBLE HAND AND MODERN WELFARE ECONOMICS, NBER Working Paper No. 3641. This reference is available online via SSRN and NBER. It discusses the limits on the concept of the Invisible Hand in the context of theorems of modern welfare economics.

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=227430

ABSTRACT

This paper reviews and puts into perspective recent work reassessing the first and second Fundamental Theorems of Welfare Economics. It assesses the implications of the Greenwald-Stiglitz theorem establishing the (constrained) Pareto inefficiency of market economies with imperfect information and incomplete markets as well as recent work on endogenous technological change. The information theoretic limitations to the Second Fundamental Theorem are also discussed, including the inability to separate out issues of equity and efficiency. The final sections of the paper consider the consequences of these problems for economic organization, economic policy, and the role of ideology in the belief in the Invisible Hand.

The Wikipedia article on Carlo M. Cipolla contains the following image:

https://en.wikipedia.org/wiki/Carlo_M._Cipolla

enter image description here

Pareto requires that no one is worse off (incurs loss) when the self or others become better off (benefit). So Pareto efficiency requires not only acting in the self-interest but the anticipation that self and/or others will be better off and no one will be worse off. A rational bandit might gain more than the loss to a victim but that would not be Pareto efficient because the victim is worse off to make the bandit better off.

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    $\begingroup$ -1 you are grossly misciting Evensky. As Evensky clearly sates Smith like Newton believed in a watchmaker idea of god (i.e. god as a designer). Following the idea god is some sort of watchmaker that sets a system in a certain way, not that god is some active entity. 2. As Evensky explains, Smith did not even considered this outcome inevitable, but most natural outcome and believed the nature is designed in this way by creator. So Smith did not assumed that god just magically turns individual action into collective benefit when acting in self interest, but that nature is designed that way $\endgroup$
    – 1muflon1
    Oct 31, 2021 at 16:27
  • $\begingroup$ I quote the Evensky ABSTRACT verbatim. Evensky explains that Smith had two views which changed over time. First view is that the invisible hand guides each agent to produce benefits to others via the pursuit of self-interest. This invisible source of beneficial "force" or "tendency" or "virtue" or whatever does not have to be attributed to God but Newton and Smith recognize the Diety as the ultimate source of cause. Second view is that moral and ethical virtue must exist among the agents for self-interest to provide benefit to others. This virtue may not be innate to human beings. $\endgroup$ Oct 31, 2021 at 16:49
  • $\begingroup$ I am not referring to your quote of abstract but first paragraph. If that paragraph is not based on Eversky then please provide citation to that information. Because your first paragraph is literally contradicted by the paper quoted below it $\endgroup$
    – 1muflon1
    Oct 31, 2021 at 16:52

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