## Monday, June 10, 2024

### A Robinson Crusoe Story

1.0 Introduction

Here is a simple parable. Consider an island with a particularly simple society with two people, Robinson and Friday. Robinson and Friday live on one good, call it corn. At the start of our story, Robinson and Friday have just finished a feast. Both Robinson and Friday have each eaten food baked out of 50 bushels of corn. Also, Robinson has 50 bushels corn remaining. Friday, perhaps because he's newly arrived, has none.

2.0 The Initial Deal

Both Robinson and Friday can see that they must continue to eat in the future. They understand that their continual survival could be achieved by planting the remaining corn, saving 50 bushels corn in next year's harvest, and living off of the remainder. (In this story, Robinson and Friday are each able to go a year between meals.)

So Friday says to Robinson, "Why don't you share your seed corn with me. We'll each plant 25 bushels, and tend it half our time throughout the year. If your island is like my tribe's, that will allow us to harvest three bushels of corn for every bushel we plant. So at the end of the year, each of us will have 75 bushels. We can each eat 50 bushels and use the remaining 25 bushels for seed in the next year."

Robinson says, "Why should I give you anything? I happen to believe in property rights."

Friday says, "You don't want to see me starve, do you? What do you propose I do?"

Robinson says, "I'll tell you what. Why don't we come to the following voluntary agreement. You take the 50 bushels of corn, plant it, and tend it throughout the year. After harvesting, I'll take the 150 bushels we'll get and pay you 50 bushels for your helpful work."

Friday says, "Why should I agree to that? I do all the work, and you loaf around all year in a tropical paradise."

Robinson says, "Well, it's my seed corn."

Friday says, "Oh, all right. It's a deal."

3.0 The Story Continues

At the end of the year, Friday consumes his wages of 50 bushels. Robinson consumes his profits of 50 bushels. They are in the same situation as they were originally. They strike the same deal again and continue year after year.

It seems Robinson has brought the captain's library off the shipwreck with him. One day Friday happens to notice this library. He says to Robinson, "What are all these books?"

Robinson says, "I don't know. Being a practical person of the middle order of society, I never bothered to read them."

Friday says, "Well, can I have that big tome by that fellow Marx."

Robinson says, "Unlike the corn, it's of no use to me. You can have it."

Friday takes away the book and tries to read Marx. He finds it quite head-scratching in places, particularly the Hegel. That part seems so deep as to be incomprehensible. But he does get some glimmers from it.

5.0 A Debate

One day at the end of three years of work, Friday confronts Robinson and tells him, "You're exploiting me. I only get a third of the produce. This year I should get 26/27th of it. And if we continue on in this way, I should get all of it eventually."

Robinson can't make anything out of this. He says, "But I provide the seed corn. Labor and seed corn are measured in different units. How can you make a fair claim on any portion of the output but what we have agreed to?"

Friday says, "It will take me a little while to explain." Robinson says, "Unless some pirates show up, we have time. Go on."

Friday says, "Each year we harvest 150 bushels corn using 1 year of labor and 50 bushels seed. We can see that any proportion of the harvest was due to the corresponding proportions of the labor and the seed corn. Here's some examples." And Friday draws the following table in the sand:

 Proportion Seed Corn Labor Harvest 1 50 Bushels 1 Year 150 bushels 2/3 33 1/3 Bushels 2/3 Year 100 bushels 1/3 16 2/3 Bushels 1/3 Year 50 bushels 2/9 11 1/9 Bushels 2/9 Year 33 1/3 bushels 1/9 5 5/9 Bushels 1/9 Year 16 2/3 bushels

Robinson says, "That seems fairly obvious. I don't see where you are going with this." Friday says, "We can use these numbers to break down my work in each year to produce the output in the following years:"

 Year Work TorwardYear 3 Harvest Work TorwardYear 2 Harvest Work TorwardYear 1 Harvest 1 5 5/9 Bushels seed& 1/9 year's laborproduce16 2/3 Bushels 11 1/9 Bushels seed& 2/9 year's laborproduce33 1/3 Bushels 33 1/3 Bushels seed& 2/3 year's laborproduce100 Bushels 2 16 2/3 Bushels seed& 1/3 year's laborproduce50 Bushels 33 1/3 Bushels seed& 2/3 year's laborproduce100 Bushels 3 50 Bushels seed& 1 year's laborproduce150 Bushels

Robinson says, "I guess that's fairly clever. If I add horizontally, I see that you have allocated each year's seed, labor, and output to your columns. That's good. But if I add the first column vertically, all I see is that our 150 bushels corn is the result of 1 4/9 year's of your work and 5 5/9 bushels of my initial seed corn. What's your point?"

Friday says, "Wasn't that seed corn the result of your work before I showed up?"

Robinson says, "Well, yes. I worked hard for it. And I was even generous enough to feed you at first."

Friday says, "That may be. But can't we say that the 150 bushels we have now embodies the sum of 1 + 1/3 + 1/9 + 1/27 and so on year's labor? And therefore that, the total labor embodied in this third year's harvest is 3/2 year's of effort?"

"I don't know."

"It's just arithmetic. My contribution to this year's harvest, as you saw, is 1 4/9 years of work. The 5 5/9 bushels you originally contributed represents the remaining 1/18 years needed to produce the harvest. Since [ 1 4/9 ]/[ 1/18 ] is 26, I should get 26 bushels for every one of yours in the harvest."

Robinson says, "Um..."

"In other words, I, Friday, should get 26/27ths of this year's produce as I said originally."

"Furthermore," Friday continues, "as long as we continue to follow your deal, your fair share should become smaller and smaller. In the limit, all of the annual harvest has been produced by me alone if you don't help out at all."

6.0 The Upshot

Robinson says, "Aren't you denying my capital is productive?"

Friday says, "We certainly need the seed corn. But how is your ownership of it productive?"

"Sure it is. You need me to make the decisions what to do with it."

"Maybe so. My labor's the horse, and your capital is the lash."

This comment seems subversive to Robinson, and he gets angry. "Look, your argument only works because of the simplicity of our island. Excess profits and losses indicate where investment can be directed most advantageously."

Friday says, "You are only arguing that the rate of profit be calculated, not that profits be paid out. That indicator is only one among several. We could have any of many different incentive schemes."

Frustrated, Robinson says, "A deal's a deal. Whatever comes out of our market transactions, that's what's fair. I refuse to do arithmetic, so I can continue to talk nonsense."

This blockheadedness on Robinson's part so angers Friday that he stages a revolution and kills Robinson. The island lives on in communism from that day forward.

7.0 Some Notes

This story is un-Marxist. According to Marx, capitalism did not arise through people rationally constructing capitalist institutions, property rights, markets, etc. Nor will it fall by convincing people of its unjustness by rational argument. Rather historical materialism describes beliefs as reflecting changes in productive forces as part of an historical process. My story is much too idealist for Marx. Also, my story does not contain money, and money is central to Marx's account of value.

The story can be made more realistic. We can add many workers and capitalists, and assume perfect competition. We can also assume continuously differentable production functions. For example, this parable is consistent with the Cobb-Douglas production function:

Q(L, X ) = 3 (50)1/3 L1/3 X(2/3)

where Q is the corn harvested at the end of the year, L is the number of person-years of labor during the year, and X is the bushels of seed corn. Whatever wage comes out of the market will be equal to the value of the marginal product of labor. These assumptions and this equality of the wage and the value of the marginal product of labor are compatible with some such calculations as in the story. Unless the workers eventually get the entire product, they are exploited, as above.

While my parable is non-Marxist, the arithmetic for the concept of exploitation used in it is based on my understanding of some aspects of Marx's theory.

"...we must understand the importance which Marx attached to his distinction between 'labour' and 'labour-power': an importance essential for the context of exploitation as a key to understanding the bourgeois (or capitalist) mode of production. The role of the labour theory of value in relation to the theory of surplus value is frequently misunderstood. Often this is interpreted as embodying a Lockean 'natural right' principle, to the effect that the product of a man's labour belongs 'of right' to the labourer; whence it is held that the appropriation of part of this product by the capitalist is 'unnatural' and unethical. Hence exploitation is interpreted as a quasi-legal or ethical concept rather than a realistic economic description. If what we have said about labour and the labour process has been appreciated, it should be clear that this is an incorrect interpretation. What could be said, of course, is that the notion of labour as productive activity implicitly afforded the definition of exploitation as an appropriation of the fruits of activity by others - appropriation of those fruits by those who provided no productive activity of their own. But far from being an arbitrary or unusual definition of 'productive' and 'unproductive', this would surely meet with general aggreement as normal usage of these words. The problem for Marx was not to prove the existence of surplus value and exploitation by means of a theory of value: it was, indeed, to reconcile the existence of surplus value with the reign of market competition and of exchange of value equivalents. As he himself expressed it: 'To explain the general nature of profits, you must start from the theorem that, on an average, commodities are sold at their real values, and that profits are derived from selling them at their values ... If you cannot explain profit upon this supposition, you cannot explain it at all.'

The point of this can the better be appreciated if it is remembered that the school of writers to whom the name of the Ricardian Socialists has been given (such as Thomas Hodgskin, William Thompson and John Bray), who can be said to have held a 'primitive' theory of exploitation, explained profit on capital as the product of the superior bargaining power, lack of competition and 'unequal exchanges between Capital and Labour' (this bearing analogy with Duhring's 'force theory' which was castigated by Engels). This was the kind of explanation that Marx was avoiding rather than seeking. It did not make exploitation consistent with the law of value and with market competition, but explained it by departures from, or imperfections in, the latter. To it there was an easy answer from the liberal economists and free traders: namely, 'join with us in demanding really free trade and then there can be no "unequal exchanges" and exploitation.'" -- Maurice Dobb, "Introduction" in K. Marx, A Contibution to the Critique of Political Economy, Progress Publishers, 1970, pp. 12-13.

Interestingly enough, the great Austrian economist Eugen Böhm-Bawerk's account of capitalism arguably does not challenge Marx's claim that the workers are exploited.

"Whoever is the owner of a capital sum is ordinarily able to derive from it a permanent net income which goes under the scientific name of interest in the broad sense of the term.

This income is distinguished by certain notable characteristics.

It arises independently of any personal act of the capitalist. It accrues to him even though he has not moved a finger in creating it, and therefore seems in a peculiar sense to arise from capital, or, to use a very old metaphor, to be begotten by it...And, finally, it flows without ever exhausting the capital from which it arises, and therefore without any necessary limit to its continuance. It is, if one may use such an expression in mundane matters, capable of everlasting life.

And so the phenomenon of interest presents, on the whole, the remarkable picture of a lifeless thing, capital, producing an everlasting and inexhaustible supply of goods. And this remarkable phenomenon appears in economic life with such perfect regularity that the very concept of capital has often been founded on it. Thus Hermann, in his Staatswirtschaftiche Untersuchungen defines capital as 'wealth which produces a constant flow of income without suffering any diminution in exchange value.'

Whence and why does the capitalist receive this endless and effortless flow of wealth? -- Eugen von Böhm Bawerk, Capital and Interest, "Volume 1: History and Critique of Interest Theories", p. 1.

Notice that attempts to change the conditions don't attack the logic of the above story. I don't see how the ability for some workers to save to become capitalists or attempts to justify some highly paid personnel as being paid for the labor of supervision threatens the logic of the story. If you want to criticize the logic, show that it's not reasonable within its own assumptions. But this cannot be done. On the other hand, those that understand, say, the John von Neumann model of growth know how to generalize the story to make it much more realistic.

Blissex said...

«“The problem for Marx was not to prove the existence of surplus value and exploitation by means of a theory of value: it was, indeed, to reconcile the existence of surplus value with the reign of market competition and of exchange of value equivalents.”»

I claim as usual that Marx never expressed a "theory of value": he simply *defined* "value" as "labour", rather than "weight", "time", "rarity", "beauty" etc.; with this definition it is a *tautology* rather than a theory that if "value" *is defined as* labour, those who contribute no labour to production yet consume its outputs are exploiting others.

«As he himself expressed it: 'To explain the general nature of profits, you must start from the theorem that, on an average, commodities are sold at their real values»

That exchange prices "converge" to hours of labour is not a theorem, it is a “supposition” as more properly stated below:

«and that profits are derived from selling them at their values ... If you cannot explain profit upon this supposition [the "theorem" that, on an average, commodities are sold at their real values], you cannot explain it at all.'»

If “on an average, commodities are sold at their real values” is a mere supposition and not a theorem then he cannot explain profit :-).

But my understanding of his argument here however is that it is an explanation of profit, but a proof that the “supposition” is indeed a “theorem”: since profit is an observable fact, the only way to explain it is the premise that “exchange prices "converge" to hours of labour” that is the existence of profits *proves* that exchange prices converge to labour values.

Quite an interesting argument, but one that not really explain much, because what needs explaining before that is not exchange prices of commodities converge to labour values, but why the exchange price of labour power *does not* converge to the labour value of the commodities that of the labour delivered by that labor-power.

«the importance which Marx attached to his distinction between 'labour' and 'labour-power':»

here is is very important to note that (IIRC Marx does this) labor-power has its own labor value, which is the labor needed to reproduce that labour power, that is the labour needed for subsistence. So actually there are two things to explain:

* Why the exchange-price of labor-power does not converge down to the subsistence wage (lower bound, usually).
* Why the exchange-price of labor-power does not converge up to the labor-value of the commodities the labor it can deliver can produce. (upper bound, usually).

Stating that since profit is a fact it can only be explained by the “supposition” that “commodities are sold at their real values” does not answer either question.

Blissex said...

«the school of writers to whom the name of the Ricardian Socialists has been given (such as Thomas Hodgskin, William Thompson and John Bray), who can be said to have held a 'primitive' theory of exploitation, explained profit on capital as the product of the superior bargaining power [...] This was the kind of explanation that Marx was avoiding rather than seeking.»

But my impression is that is also the theory of profit of Marx! Why would workers sell their labour-power for an exchange price less than the labour such labour-power can provide to the buyer? Because of the "reserve army of labour" giving the buyer superior negotiation power:

https://www.marxists.org/archive/marx/works/1867-c1/ch06.htm
“He, who before was the money-owner, now strides in front as capitalist; the possessor of labour-power follows as his labourer. The one with an air of importance, smirking, intent on business; the other, timid and holding back, like one who is bringing his own hide to market and has nothing to expect but — a hiding.”

Consider the reverse case: the plusvalue of production is less than the wages, that is the exchange price of labour-power is higher than that of the labour that the buyer can get our of that labour-power. That is entirely compatible with my understanding of Marx's arguments.

In case of a glut of capital it is the “possessor of labour-power” who “strides in front”, with an “air of importance, smirking”, while the the “money owner” “follows”, “timid and holding back”, because the “money owner” brings his owned “hide [capital] to market and has nothing to expect but — a hiding.”

Cases of capital glut have happened in the past, for example after the Black Plague, and the consequences have been that owners have had to accept to either leaving a portion of their capital fallow for lack of workers, or to use it at negative profit, that is to liquidate part of it to pay workers the difference (negative surplus) between the higher exchange-price of the labour-power and the lower plusvalue of the product.

Blissex said...

«Why would workers sell their labour-power for an exchange price less than the labour such labour-power can provide to the buyer? Because of the "reserve army of labour" giving the buyer superior negotiation power:»

Here this is well described be Bernard de Mandeville (whose works Marx was well aware of and cites):

http://oll.libertyfund.org/titles/mandeville-the-fable-of-the-bees-or-private-vices-publick-benefits-vol-1
Bernard de Mandeville “The fable of the bees" (1724): “The Plenty and Cheapness of Provisions depends in a great measure on the Price and Value that is set upon this Labour, and consequently the Welfare of all Societies, even before they are tainted with Foreign Luxury, requires that it should be perform’d by such of their Members as in the first Place are sturdy and robust and never used to Ease or Idleness, and in the second, soon contented as to the necessaries of Life; [...] From what has been said, it is manifest, that, in a free nation, where slaves are not allowed of, the surest wealth consists in a multitude of laborious poor”

«labor-power has its own labor value, which is the labor needed to reproduce that labour power, that is the labour needed for subsistence.»

And precisely as to this Marx quotes Bernard de Mandeville (another work but similar):