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The Law of Association

Tags Free MarketsGlobal EconomyEntrepreneurshipHistory of the Austrian School of Economics

09/08/2010Abhinandan Mallick

During my recent return trip from India, I chanced upon a conversation with an interesting French lady at the airport. We exchanged some pleasantries about ourselves and our experiences. She had recently (and rather rigorously) been introduced to Buddhism, for which I found she had an admirable zest and appreciation.

When asked to explain my own passion, I of course began to extol — probably coming across as quite rhapsodic — the virtues and beauty I saw in this fascinating system known as the free-market economy and the incredible changes I saw it making in my country of birth, despite all the problems still remaining. Intrigued, she politely questioned me as to what would happen to the poor and the downtrodden in such a system, taken to its final conclusion, as I was suggesting. Wouldn't they be left in the dust?

Instead of answering, I decided to ask a simple question. Suppose two men are living on an island. One man is better at producing all kinds of goods and means of subsistence than the other. Would there be any reason or benefit for the better-endowed individual to trade and cooperate with the latter? My companion answered no. I smiled, proceeding to show her one of the most beautiful laws of the universe.

Let us begin by considering the case where two goods desired by both of the individuals on the island can be produced with the same input of labor hours by each. It is perhaps intuitive and "obvious" that if one of the men, Paul, gathers more berries, and the other, Peter, catches more fish, both would benefit from specialization, trade, and cooperation. It is also clear that total productivity must increase in such a case, because each focuses on producing the good he can produce more of.

This, however, does not yet highlight the most important factor in specialization: opportunity costs. For each man, the opportunity costs of producing each of the two goods can be expressed in terms of the amount of the other good that could have been produced in the same time. Other things being equal, both men will aim to reduce their opportunity costs.

Now, let us consider opportunity costs in a situation in which Paul produces both more berries and more fish than Peter. Here, we begin to see how productivity gains can be made by the two specializing, trading, and dividing their labor. Indeed, the lowering of opportunity costs also happens to determine specialization in the other case, where either had an "absolute advantage" in producing one of the two goods. The principle is thereby completely general in determining the advantages derived from trade.

We could represent the available production possibilities in terms of the amount of berries and fish that could be produced per hour of labor by Paul and by Peter. Suppose Paul can produce two berries per hour and three fish per hour, while Peter can produce twice as many berries and three times as many fish in the same time. The production possibilities are as follows.

Production possibilities




2 berries

4 berries


3 fish

9 fish

It is from here that information regarding both actors' alternative opportunity costs can be derived. For instance, producing two berries deprives Paul of three fish. Hence the opportunity cost in terms of fish per berry produced would be 3/2. We could therefore summarize the opportunity costs for both actors as follows.

Opportunity costs



To produce 1 berry

3/2 fish per berry

9/4 fish per berry

To produce 1 fish

2/3 berries per fish

4/9 berries per fish

Clearly the opportunity cost for Paul for producing a berry in terms of fish is less than that for Peter, and simultaneously determined by this is the fact that Peter suffers the lowest opportunity cost in terms of berries forsaken in the production of fish. We can see therefore that trade offers both actors the opportunity to lower their opportunity costs and make savings. It is better for both individuals to buy at rates lower than their opportunity costs, and to sell at rates exceeding them. If we define the price of berries in terms of fish as Pb, we can see that this "price" must lie somewhere between their respective opportunity costs.

(3/2) fish < Pb < (9/4) fish

As every sale of berries is a purchase of fish, and vice versa, we can determine the rate at which fish will be exchanged for berries, Pf, the price of fish, thus:

(4/9) berries < Pf < (2/3) berries

In fact, we can calculate the increased returns to production from this simple division of labor and compare it directly to the case where both producers only produced for themselves. Suppose both actors, unaware of each other's existence, divide 12 hours of their time evenly to produce fish and berries (6 hours for each). After 12 hours they would have produced the following amount of each.

Total produced









For every fish he produces, Paul forsakes 2/3 berries, and Peter only 4/9 berries. Likewise, Peter forsakes 9/4 fish for every berry, and Paul only 3/2. Now, if both become aware of each other's existence and opportunity costs, opportunities for mutual gain present themselves. Peter can "buy" berries at a price lower than his opportunity cost, while Paul can sell berries at a higher price in fish than his opportunity cost. The exact opposite is true if we state the sale and purchase in terms of fish.

Given the mutual gains they can make trading at a rate determined by the inequality of their respective opportunity costs, we may suppose that Peter agrees to buy 12 berries from Paul at a price of 2 fish each. He may then spend 3 fewer hours of his time having to produce berries to get the same amount, while producing 27 more fish. Paul can devote himself entirely to producing berries. The resulting distribution before trade is as follows.

Total produced before trade









Now, after 12 of Paul's berries have been exchanged for Peter's fish at a price of 2 fish each, we find the following to be true.

Total produced after trade









And, incredibly, the gains are bountiful for both men. We can even calculate the gains or savings made by each, in terms of fish or berries or labor hours saved. In terms of fish Paul gained 6, and Peter gained 3. Given that the substitution ratio from fish to berries for Paul is 2/3, while for Peter it is 4/9, they have saved 4 berries and 4/3 berries respectively. Given that Paul alone produces 3 fish every hour, he's saved 2 hours, while Peter has saved 20 minutes since he makes 9 every hour.

It is of course important to recognize that this does not present an alternative theory of value,[1] since the subjective valuations of both goods cause individual exchanges to deviate from the "prices" indicated above. Paul might actually desire a berry a lot more than Peter does. Value judgments and their effects on price formation must be considered separately.

What the law of association teaches, like the law of returns, is an analytic judgment, revealing how two producers, unevenly endowed in their productive capacities, due either to personal characteristics or their environment, can maximize their material returns.[2] The solution is exchange and cooperation, leading to the formation of the market and society.

In short, the law of association does not reveal why Paul exchanges the one berry he owns for some fish Peter owns. It explains, rather, why it would be in their long-term interest in the first place, when both are capable of producing both goods, to coordinate production on each other's behalf with the intention of trading and collaborating.

The Austrian School is not unique in promoting comparative advantage, but it is distinctive in recognizing its truly universal significance.[3] While Ricardo correctly formulated the law in solving a particular problem of international trade between two countries for whom products, but not capital and labor, were free to move across borders,[4] the universal nature and consequences of the law cannot be explained by treatments that relegate and isolate it to chapters and discussions concerning specific problems of international trade. Individuals, not countries, trade, exercising voluntary exchange as a fundamental manifestation of their property rights, which trade restrictions coercively violate.[5] This inhibits and interferes with individuals' attempts to advance each other's affairs in collaboration.

Furthermore, the law is categorical, and its empirical relevance apodictic when the necessary conditions underlying it have been established, in much the same way as the Pythagorean theorem and Euclidean geometry.[6] The shortest distance, or geodesic, between two points may be represented by a "straight line" in a flat space, while the same is not the case for a curved space.[7] In the same way, the law of association has no relevance in a world populated by actors whose productive capacities remain equal in every regard. Nor is it relevant in the other unlikely case of a world in which each actor is better or worse than all others in every regard by the same proportion.

Individuals begin to coordinate their production in order to trade for mutual profit, which means that they begin to value the goods they produce not for their use value but their exchange value.[8] It is not merely the case that participants gain what they subjectively desire more through exchange of differentially preferred property. Rather, as each individual begins to produce with the intention of trade, he expands not only his own individual material productivity and wealth but also the aggregate wealth of society. Production and distribution cannot be arbitrarily separated in this process.

As the division of labor expands, including ever-more individuals and producible goods, opportunities for profit and mutual gain through exchange multiply. A medium of exchange develops and facilitates this expansion of trade, engendering the institution of economic calculation. This allows participants to rationally evaluate the greater collection of resulting opportunities of trade. Indeed, there is no other way in which the law of association can be generalized.[9]

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With the incorporation of money, the expanding market and division of labor brought into existence as a consequence of man and nature's diversity and inequality further evolves. As knowledge and skills of particular professions are built, this inequality intensifies through specialization. The market, a term we use to describe the collective exchanges and production we take in order to advance our lives by advancing those of others, harmoniously directs this process. Through expanding productivity and wealth, this process spontaneously leads to the mechanization of production.[10] Entrepreneurs and specialists can utilize their knowledge to perceive and pursue the benefits resulting from expanding production in specific directions.[11]

Upon reflecting on the law of association and its implications, we begin to understand the futility and disastrous nature of interventionist policies that aim to restrict trade and redistribute and limit wealth. Such policy is driven by an ideology that posits that one man's gain comes only at another's expense.

Life is a zero-sum game, they say. There can hardly be a more tiresome or economically illiterate statement than this. Yet it must be recognized that for many, the validity of this assertion is largely unexceptionable, and most especially with regard to what is conceived of as the cruel, dog-eat-dog world of laissez-faire capitalism and the free market.

It is important to realize how such statements, which are essentially expressions of the perceived nature of causal relations, affect the formation of ideologies. After all, an ideology is not only composed of one's prescriptions for the resolution of social problems but also actively informed by one's beliefs about the causal factors determining social relations.[12]

Many people honestly believe that social classes are inevitably at odds with each other in such a way; hence they believe that the only way to advance the fare of the poor is to confiscate the assets of those who are the most productive and best enabled to expand society's production of wealth.

The law of association and the theorems regarding the division of labor radically challenge such conceptions. The rich businessmen and productive capitalists are precisely the ones with the greatest productive inequalities, and thereby the most contrasting opportunity costs in comparison to individuals who are presently less able to contribute to production. Yet this means they can offer them the most compensation in exchange for their services, out-competing more mediocre and substandard firms for whom the disparity in opportunity costs is not so wide.

By penalizing successful businessmen, interventionists invariably end up punishing precisely those who out-compete all others in providing the best deals for their customers, business partners, and laborers. The groups within the market between whom there are the greatest comparative disparities are not at odds as some simpletons imply; these groups are the ones who continually benefit each other the most through exchange and harmonious association.[13]

Even those who do not work in industries that are flourishing as a result of increasing productivity because of capital accumulation, specialized knowledge, and workforce skills are directly reaping the benefits of this increase in society's wealth. Their real income increases as the opportunity costs of their productive trading partners increase, explaining, for instance, why a barber in Chicago can earn more than one in Costa Rica.[14] Universally, capitalism, and the capital accumulation it allows for, is what raises the bargaining power of ordinary employees of all trades.

It is often said that opposites attract. We can certainly see this in many social and sexual interactions. The diversity and differences between us often intrigue us and characterize what we find compelling in our acquaintances. Even more so, our diversity socially unifies us and guides us in making exchanges, increasing our wealth and productivity through the market system. It is therefore truly odd that "diversity," a modern slogan of the Left, is what they fear and detest the most in the market. They wish to institute uniformity in its place, wiping out the specialization brought about by the division of labor.[15] Such a delusional goal, if actually achieved, would remove the very root of society and social cooperation.

I was once told a tale of a Native American man who, upon coming across Christianity, had a strange dream. He visited heaven and hell. Both places looked the same, populated by various people sitting at a table gloriously filled with the finest food and the greatest culinary delights beyond imagination. Yet in hell the people were starving, while in heaven they were eating and enjoying themselves to their hearts' content. In both rooms the cutlery was exceptionally long-handled. The difference was that in hell the people were struggling impossibly to feed themselves with such equipment, while in heaven they were gorging themselves by feeding each other.

No starker metaphor could describe the choice that humanity faces.[16] We may either incorporate ourselves into market civilization, the system by which we may serve ourselves as ends by serving other people as means, or return to the idyllic and isolated "noble" savagery that long characterized our human past.

May we choose wisely.


[1] Ludwig von Mises, Human Action, Scholar's Edition (Auburn, Ala.: Mises Institute, 2008), p. 161.

[2] Ibid., p. 161–162

[3] It is quite noteworthy, however, that Paul Samuelson was challenged by Stanislaw Ulam to name one law of the social sciences that was both true and nontrivial. After a number of years, Samuelson responded by citing the law of comparative advantage. Cf. P.A. Samuelson, "The Way of an Economist," in idem, ed., International Economic Relations: Proceedings of the Third Congress of the International Economic Association (London: Macmillan, 1969), pp. 1–11.

[4] It is worth noting in particular that factors of production serve analogously to skills in the case of individual trade, which conceivably we do not deem as having been "sucked" out of the less productive individual and given to the more productive one. For Ricardo's treatment, see especially D. Ricardo, On the Principles of Political Economy and Taxation, 3rd edition (Kitchener, Ontario: Batoche Books, 2001), pp. 90–91.

[5] Cf. M.F. Ayau, Not a Zero-Sum Game (Guatemala: Universidad Francisco Marroquin, 2007), pp. 23–26.

[6] For more on this point, cf. Mises, The Ultimate Foundation of Economic Science: An Essay on Method, ed. Bettina Bien Greaves (Indianapolis: Liberty Fund, 2006), pp. 9–12.

[7] Indeed, students of relativity know this as the reason light is bent in the vicinity of gravity, e.g., in a Schwarzschild metric.

[8] Murray N. Rothbard, Man, Economy, and State with Power and Market (The Scholar's Edition) (Auburn, Ala.: Mises Institute, 2004), pp. 88–90.

[9] This is because we have been able to compare the possible physical output in terms of two products, relative to changes in the application of a relatively scarce nonspecific factor of production (in our case, labor time), while the other specific factor (e.g., worker skills or capital) remains constant and uneven for both producers. See Mises, Human Action, pp. 161–162. Indeed, it is worth noting that simple representation of production possibilities among market participants in anything approaching a complex economy would require for tabulation not a two-by-two matrix like the one shown above, but a multiple-rank tensor of far greater degree. Even if established, this would not begin to solve the rational-allocation problem among the diverse means and ends and numerous stages of production, except in situations of very special circumstances. For more on this, see Mises, ibid., pp. 207–210.

[10] Ibid., pp. 163–164

[11] F.A. Hayek, Individualism and Economic Order (Chicago: University of Chicago Press, 1958), ch. 4.

[12] Ludwig von Mises, Human Action, pp. 178–184.

[13] Ayau, pp. 43–44.

[14] Ibid., p. 40.

[15] Rothbard, Egalitarianism as a Revolt Against Nature and Other Essays (Auburn, Ala.: Mises Institute, 2000), pp. 253–259.

[16] Indeed, given the analogy provided by the above example, it might be objected that greed was rather the manifest failure of those inhabiting hell. Yet what is greed? It is a value-judgement-laden term conventionally defined to describe an "excessive" desire to acquire material wealth. Though it may well be the case therefore that those in hell display a desire to acquire a greater quantity than those in heaven, this cannot be discerned from the information given in this case, and it is certainly not the characteristic distinguishing them in this example; since both groups are plainly motivated by their desire to acquire and consume the food. Rather, it is not greed, but shortsightedness to the benefits of trade and cooperation which dooms the inhabitants of hell.


Contact Abhinandan Mallick

Abhinandan Mallick is a market analyst at IHS Technology and a former summer fellow of the Mises Institute. He lives in the UK and holds masters degrees in theoretical physics and economics.