Adam Smith, William Jevons, and the Tragedy of the Commons

Adam Smith, William Jevons, and the Tragedy of the Commons

Posted by Ed Leaver 26 July 2012

When confronted with economic policy, many people invoke Adam Smith’s ”Invisible Hand” and rest themselves assured all will be well if but they look after their own profit. Life is not so simple, and neither is classical economics. We explore some popular misconceptions in this central essay we expect to frequently revise and revisit.

At the end of the final review session at close of an attentively-attended two-semester introduction to Classical Economics, the instructor duly admonished:

”Congratulations on a year of productive study. In this brief time I hope we have whet your awareness of some of the subtleties of the field. It’s been a fine start, but only that. I’d leave you one sobering statistic: you have now completed more formal economics training than 95% of all people who have ever served in the United States Congress.”

Well... it is not for nothing they call it the ”dismal science”. Adam Smith is credited with its founding with his publication of The Wealth of Nations in 1776.

1 The Invisible Hand

”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. Nor is it always the worse for the society that it was no part of it. By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it. I have never known much good done by those who affected to trade for the public good.” 1

Adam Smith (1723 - 1790) was a philosopher and widely popular Professor of Moral Philosophy, Glasgow, for whom honesty and ethical behavior constituted the highest of virtues. He was also a Scot living at times of less than equitable economic relations with England. After attending Glasgow from age 14, Smith attended Balliol College as Snell Exhibitioner, at the time of the ’45 Rebellion. He apparently agreed with little at Oxford save its library, and returned to Glasgow in 1746. 2 In a thoughtful essay, Helen Joyce writes

”Smith... made it clear in his writings that quite considerable structure was required in society before the invisible hand mechanism could work efficiently. For example, property rights must be strong, and there must be widespread adherence to moral norms, such as prohibitions against theft and misrepresentation...”

Thus Smith recognized from the outset the necessity of ”good faith and fair dealing”, which are at the foundation of modern contract law, and enforced through our court systems as part of the aforementioned ”considerable structure” required to encourage ”widespread adherence to moral norms.” He was cynical of private communication among common-market industrialists, believing such invariably lead to ”a conspiracy against the public or some contrivance to raise prices.”

This is significant to Joyce’s discussion of the classic Prisoner’s Dilemma paradox, which illustrates several sub-optimal economic solutions (increased total prison time) that result from stifling the free-flow of ideas (communication) between the ”prisoners” by the ”police”. Note that TPD paradox is uniformly stated such that the prisoners’ alleged ”crime” is never identified. Joyce frames it thusly:

The ”Prisoner’s Dilemma”... describes two people in a simple situation, acting in an informed manner, both attempting to maximise their wellbeing, and yet making choices that lead to an unnecessarily poor outcome for both.

(The) two people, who are suspected of being accomplices in a crime, are held prisoner in separate, non-communicating cells. The police visit each prisoner, and tell both that if neither confesses, each will be sentenced to two years in jail. However, if exactly one prisoner confesses, implicating each other, the one who confesses will get off scot-free as a reward, and the other, who didn’t confess, will receive a punitive sentence of five years. If each confesses and implicates the other, both will be sentenced to three years.

Emphasis added, though Joyce’s phrasing can only be deliberate. The ”prisoners” are ”informed” only in the manner and to the extent their captors wish them to be. The result of this police-state censorship is the service of five or six total years of non-productive prison time, as opposed to the (allegedly) optimal four.


And within the ”optimal” lies the significance of Adam Smith’s Invisible Hand. Joyce discusses ”invisible hand” in the context of Game Theory, ”invisible” meaning while economic information is free to flow throughout the society, the individual actors need have no direct communication among themselves, other than through the prices of just those goods and services they each require to conduct their individual business. The result is extraordinary: by acting locally solely on the limited information needed to conduct his or her own business, and in the interest of maximizing just their own individual profit, the individual businesspeople as a group thereby also act such as to - in some sense - maximize the total wealth of the entire economy.

At the risk of vast over-simplification, one may temporarily suspend belief and consider the Invisible Hand as a communication field (or potential force) that allows the global allocation of goods and services to be viewed as a problem in (mis)applied Multivariate Optimization Theory, wherein the ”cost function” to be minimized is the net amount of human suffering, fraud, and waste or, in the alternate, the merit function to be maximized is the total yearly amount of goods and services produced, the gross annual production.

The two are equivalent only to the somewhat problematic extent human suffering can be quantified by poverty or low production, one obvious problem being one can have pockets of abject poverty within an otherwise affluent society. Left to itself, the Invisible Hand makes no such distinction, even if the poverty-stricken extract a long-term penalty left unaccounted in the annual report.

I like to think of multi-variate penalty function minimization as a generalization of the two-dimensional physical problem of finding the lowest energy state of a ball free to roll in a system of hills, hillocks, kettles, sinks, and valleys. In this physical analogy the ”potential” is the gravitational potential, and the driving force of the minimization is its gradient. Here the gravitational field has a uniform gradient over the dimensions of the problem. Everyone in the system of hills and valleys agrees which way is up, and it is the same everywhere.

This physical analogy is instructive precisely because one can readily visualize the problem the ball may face if it starts on the inward slope of an isolated kettle whose bottom unfortunately resides at some elevation higher than that of the nearby river. Free to roll, the ball will find its local energy minimum at the bottom of the kettle, where it shall forever remain — unless it receives a kick from an outside force energetic enough to send it over the kettle’s rim to where it may follow the river to a true global minimum.

It is thus with the Invisible Hand. Local distortions in its direction result in market distortions that may reflect a sub-optimal solution to the economic merit problem. Subject to certain constraints, the Invisible Hand drives an optimal local solution, and therein lies the great power of a free-market economy. And its weakness: the Invisible Hand has no kick: left to itself the Invisible Hand will guide an economy to a locally optimal state, which is not necessarily global. And the market has no foresight: while with our God’s Eye View we may identify the hills and valleys and high ridges and low passes in our 2D physical model, no such vision is afforded the actual market. No actor can foresee the future, and if one should guess at a more profitable course ”beyond yonder hill”, he may avail himself to such only at the expense of the capital needed for him to climb the pass. And pay the price should the path prove too high for the available investment, too long for the patience of the investors, or just plain false. 3

As analogies go, our physical geography model is not one to stretch. Smith introduced the Invisible Hand as a general principle of economic philosophy. Its supposed communications ”field” is much more complex than the simple gravity of our physical model. The Invisible Hand’s economic communication need only act locally between just those actors in a particular economic segment for its effect (beneficent or otherwise) to propagate throughout the society as a whole as the segments overlap. It is not uniform, and its speed of propagation varies. Quantifying such effects is the realm of game theory, and is no simple matter. Noted economist Paul Samuelson concluded ”Smith was unable to prove the essence of his invisible-hand doctrine. Indeed, until the 1940s no one knew how to prove, or even to state properly, the kernel of truth in this proposition about perfectly competitive market.” 4

Back in our analogy, the bouncing ball of the economy is not a perfect sphere, either. More like an irregular rolling stone that gathers and sheds moss as it wobbles and threads its way through a vast multi-dimensional cost function landscape that is itself hardly static, but shifts beneath the actors’ feet even as the game is played. Yesterday’s smooth path to a global minimum is tomorrow cut off, leaving the stoned, moss and all, stuck in a but locally minimum rut with seemingly no obvious path of escape.

If any of the actors even recognize that’s where they are. No God’s Eye View of this landscape!

Yet our mortal view as a mathematical optimization problem is nonetheless very powerful, and is central to a great deal of economic modeling. It allows us to readily identify a model’s inputs and outputs, and compare them with the supposed Real World. It also allows us to (not always readily) identify both internal and external assumptions and constraints (and lack thereof), and examine their counterparts in external society. Phrasing economic optimization as a linear (or non-linear) programming problem immediately invites the Hoary Programmers Maxim: ”Garbage in, Garbage out.” And invites one to identify the garbage.

As solution to an optimization problem, left to its own the free-market tends toward the particularly unconstrained variety. As anyone with experience with such can attest, the optimal unconstrained solution it will tend to will most certainly not be one that is desired. In particular, over time it will tend toward monopolies and oligopolies, which in seeking to maximize their own profits will raise prices – and net economic cost – above the optimum reached by a many small-actor society. Garbage. You want to maintain competition? Put in constraints on size and behavior. For technical reasons you want a particular monopoly? Regulate it. You want to prevent child-labor exploitation? Constrain it. Restrain industry and municipalities from dumping their effluent in local waterways? Enforce a Clean Water Act. Promote workplace safety? Healthcare? Retirement security? Well, some of these may be competitive factors in an employer seeking employees, or they might not, and they might vary with time and the extent of (perhaps international) competition. Regulation. Constraints. Yes, too much regulation can lead to market inefficiency. Absolutely. So can lack of regulation. What is certain is that when any one particular actor runs up against an imposed regulation he will feel it as a constraint upon his path to better (or any) profit. And he will be right. But each such complaint must be examined with perspective. 5

Here is a (very) preliminary list of Assumptions and Constraints:

  1. Free exchange of information and no private economic communication. Whatever economic information any two actors or subgroup of actors discuss among themselves must be made available to all. This constraint goes beyond our proscription against insider trading. The most open and communicative societies tend to have the best short-and-medium term economic success.
  2. Ingrained commitment to Good Faith and Fair Dealing. An efficient market is predicated upon honesty and trust. Agreements among actors should be in writing so the agreement may be quantified and preserved, differences fairly adjudicated, and terms formally enforced. Recognize the human condition.
  3. Relatively large number of individually small actors.
  4. Time averaged prices of raw materials and resources are the same function of demand over the lifetime of the model. There may of course be variations in the costs of individual suppliers, and fluctuations in time, for example due to fluctuations in weather.

There are undoubtedly others. The point is the Invisible Hand drives an optimal solution to the economics problem only within the bounds of certain assumptions and constraints. Of our list, the first two are codified in our laws and moral sense. 6

In nearly all modern markets in developed countries the third is a myth to be recognized and dealt with.

Contrary to popular expectation the last also does not hold, as the lifetimes of the models in which it does may be comparatively short relative to our own. Consequences may be severe, as discussed in the following sections on Jevons’ Paradox 2 and Tragedy of the Commons 3.

(The following is but a brief outline, a temporary placeholder.)

2 The long-term: Jevons’ Paradox

Long considered the first word in economic theroy, Wealth of Nations was hardly the last. William Stanley Jevons is credited with the concept of economic Marginal Thinking, thereby introducing the field to Isaac Newton, in his monumental The Theory of Political Economy (1871). In so doing Jevons placed classical economics on the sound mathematical footing required by modern economic modeling and optimization theory. Yet even without this masterpiece, Jevons had established himself as the pre-eminent economist of the nineteenth century with his earlier ”The Coal Question” (1865) 7 in which Jevons introduced what has become known as Jevons’ Paradox, ”the proposition that technological progress that increases the efficiency with which a resource is used tends to increase (rather than decrease) the rate of consumption of that resource.” Worse, should that resource be finite – Jevons was considering coal production in the island nation of Britain – the net economic benefit over the total lifetime of resource extraction would be less than had the extraction been less efficient and prices high.

This as consequence to what is today known as the ”Law of Diminishing Marginal Utility”: 8

Although the economic benefit gained by an individual consumer of a resource may increase with increased consumption of that resource, his marginal gain per unit consumed decreases with increased consumption.

Jevons also showed such loss of net societal economic benefit might be reduced and perhaps eliminated by maintaining an ”artificially” higher price (e.g. via judicious application of taxes) throughout the production lifetime of resource extraction. 9

A simple numeric example is described in Energy efficiency flawed due to rebound effects. (Needs further discussion)

In Petroleum Demand in Developing Countries, Robert Rapier has given a topical example of the Law of Decreasing Marginal Utility: the quadrupling of oil prices this past decade, while diminishing demand in Europe and North America, has had no such effect upon the rest of the world. Overall petroleum consumption continues its steady rise:

”A question I frequently encounter is, ”How high could gasoline prices ultimately rise in the U.S.?” Because the oil markets are global, the answer to that question is, ”It depends on how much value people in developing countries place on increasing their oil consumption to two or three barrels of oil per year.” Or, an alternative way to think about it is, ”If you were only allocated 3 barrels of oil per person per year, how much would you be willing to pay for those barrels?” The 20th barrel the average person in the U.S. consumes each year might allow us to drive that 12,000th mile. But the first barrel that someone in a developing country consumes might allow them to drive that very first mile and have heat in their home for the first time. They will be willing to pay a lot more for those initial barrels than we are for our excess barrels, and this explains why their consumption has increased even as oil prices have risen.

”And if future oil prices are dictated by how much developing countries are willing to pay for their second or third barrel of oil per capita, this number may ultimately be much higher than 100 dollars per barrel. This is a major reason that I dont ever foresee a sustained return to cheap oil. There are many who have placed most of the blame for increased oil prices on speculation, but the thirst for oil in developing nations means that there are fundamental issues of supply and demand at work as well.”

Of course, that forseen ”thirst for oil in developing nations” is what fueled the speculation in the first place. Didn’t take a weatherman. In the late nineteenth century Britain’s coal production declined as Jevons predicted, and Europe subsequently fought two horrible global wars. To the extent (citations needed) these conflicts were fought over access to coal’s fortuitously discovered replacement (petroleum), one might find sympathy for modern Europe’s penchant for exacting a modicum of government revenue from ”artificially” high gasoline and petrol taxes.

Or for why Rhodes Scholar Bill Clinton may have proposed a national BTU tax.

3 The long-term: Tragedy of the Commons

”The tragedy of the commons is a dilemma arising from the situation in which multiple individuals, acting independently and rationally consulting their own self-interest, will ultimately deplete a shared limited resource, even when it is clear that it is not in anyone’s long-term interest for this to happen. This dilemma was described in an influential article titled ”The Tragedy of the Commons”, written by ecologist Garrett Hardin and first published in the journal Science in 1968.”10

”Central to Hardin’s article is an example (first sketched in an 1833 pamphlet by William Forster Lloyd) involving medieval land tenure in Europe, of herders sharing a common parcel of land, on which they are each entitled to let their cows graze. In Hardin’s example, it is in each herder’s interest to put the next (and succeeding) cows he acquires onto the land, even if the quality of the common is damaged for all as a result, through overgrazing. The herder receives all of the benefits from an additional cow, while the damage to the common is shared by the entire group. If all herders make this individually rational economic decision, the common will be depleted or even destroyed, to the detriment of all.” 11

Tragedy of the Commons has long been recognized as central to many issues of public policy. Some of the areas in which it arises are grazing rights and fishing permits, public-lands timber allocation, and pollutant cap-and-trade such as successfully applied to the North-East American acid rain problem in the 1980’s. It similarly applies to the problems of Anthropogenic Global Warming and Greenhouse Gas, the subject of a future article. But as Hardin poignantly posits:

”The population problem has no technical solution; it requires a fundamental extension in morality.”

... and we have come full circle. Adam Smith again.

1Smith was prescient, his last sentence foreseeing the career of another great moralist, John David Rockefeller, over a century later.

2”(T)he traditions of the Chair of Moral Philosophy, as known to Adam Smith, required a certain amount of economics. A dozen years earlier he had himself been a student when Francis Hutcheson was professor. So far as we can judge from Hutcheson’s System of Moral Philosophy... Hutcheson lectured first on Ethics, next upon what may very well be called Natural Jurisprudence, and thirdly upon Civil Polity. Through the two latter parts a considerable amount of economics is scattered.” (From Editor’s Introduction to Wealth of Nations fifth edition, I.59)

3Hence the need for collective funding of research, and a large part of development. Examples are the nuclear power industry and everything reliant upon the Internet, neither of which would have happened without early - some would say questionable - government gambles on R&D.

4Samuelson, P. A./Nordhaus, William D., 1989, Economics, 13th edition, N.Y. et al.: McGraw-Hill, p. 825. (John von Neumann and Oscar Morgenstern published Theory of Games and Economic Behavior in 1944. The first edition of Samuelson’s own book appeared in 1948.)

5Smith himself admonishes that the interest of manufacturers and merchants ” any particular branch of trade or manufactures, is always in some respects different from, and even opposite to, that of the public... The proposal of any new law or regulation of commerce which comes from this order, ought always to be listened to with great precaution, and ought never be adopted till after having been long and carefully examined, not only with the most scrupulous, but with the most suspicious attention.” Gopnik, Adam. ”Market Man”. The New Yorker (18 October 2010): 82. Retrieved 27 April 2011.

6”What distinguishes Man from the Higher Animals is his Moral Sense: his knowledge of Good and Evil, Right from Wrong. And knowing Wrong, to go out and do it.” -Mark Twain

7Originally published as ”The Coal Question: an Inquiry Concerning the Progress of the Nation, and the Probable Exhaustion of our Coal-mines.”, available from Google Books.

8See e.g. Paul A. Samuelson and William D. Nordhaus Economics, McGraw-Hill 1948, 1951, 1955, 1958, 1961, 1964, 1967, 1970, 1973, 1976, 1980, 1985, 1989, 1992, 1995, 1998, 2001, 2005, Eighteenth Edition, pp 96-98, 109-11

9Its a relative term. One might wonder if consumers a century hence might not look back in amazement that we would today so profligately consume limited resources at prices we know to be ”artificially” low.

10Garret Hardin, Science 13 December 1968: Vol. 162 no. 3859 pp. 1243-1248 DOI: 10.1126/science.162.3859.1243

11From Wikipedia’s entry Tragedy of the Commons.