Nancy Kress On Global Inequality And Poverty

I picked up the novel that the following quotation is from because I think I recall Kress participating in conversations on Usenet years ago. This novel ended up more a political argument than I expected. It is for Genetically Modified Organisms (GMOs), done right. We should rather strive for plants for food resistant to insects, not resistant to pesticides, for example. I assume that Kress agrees with her heroine.

"He had spent the two-week winter vacation from school, which somehow got extended to nearly another week, with Jake in Los Angeles...

He left an eleven-year old nerd, dress in Levi's, a tee that said CHESS PLAYERS HAVE GREAT MOVES, and a baseball cap. He returned looking like a thirty-two-year-old investment banker trying to be cool, dressed in a $300 Ferragamo zip-front polo, designer jeans, and sockless shoes that cost more than my weekly salary. He carried a state-of-the-art laptop that could probably have moved satellites in orbit. Jake had invested in an independent production company that had struck movie gold with two wildly popular films about aliens who battled Earth. Jake was rich.

'Wow, look at you,' I said, not approvingly.

Ian could always read me. 'You don't like it. Dad said you wouldn't. But just because some of the world isn't blessed doesn't mean that we shouldn't enjoy the facts that through our own efforts, we are.'

I stared at him. No way that was Ian talking, or even Jake. I asked, 'Who is she?'

'Who's who?' But he shifted from one foot to the other as we faced each other at the SeaTac arrival gate. Passengers streamed past.

'Your dad's new girlfriend. It's okay, Ian, he's an adult. So am I.'

He turned sulky. 'Sage Scott.'

I blinked. She was a huge international star with more beauty than talent. 'Well,' I said heartily, 'that's fine. But -'

'Mom,' Ian blurted out, 'don't hassle me because I like money, okay.'

'Money is useful,' I said, and hugged him again.

But it wasn't that easy. With almost-teenagers, it never is. There were times during the next week when I wanted to apologize to my lone-dead parents for my own teen years.

Ian was disdainful of his old school and wanted to transfer to one that had a good lacrosse team.

Ian was disdainful of his old clothes.

Ian refused to go with me to the soup kitchen where once a week for years now, we'd helped feed the homeless.

When Ian said, 'People can always feed themselves if they just try, just like the rest of the world could if it got its act together. All you have to do is grow food,' I'd had enough. Arguments weren't going to do it here. He needed immersion learning.

'Pack up your designed duds,' I said. 'We're taking a field trip.'

'Where?'

'Overseas.'

'I don't want to. Mom, I missed enough school already.'

'Like you really mind that. And we'll only be gone for a long weekend, so pack up.'

He was eleven, and eleven-year-olds don't have household veto. Not in my house. Ian went with me. Sulky, barricaded during the long flight behind laptop and earbuds and resentment, he went.

Chennai was a huge, prosperous commercial and cultural center in southern India. A tourist draw, it had the gorgeous Kapaleeswarar Templd, museums, parks, a British fort dating from the Raj, the Tamil film industry. That was not the Chennai I took Ian to.

I'd arranged for a guide who, along with an armed bodyguard, took us to outlying slums, to coastal villages flooded by the rising sea, to fields so ravaged by inland drought or coastal salt water that they could grow nothing. Ian saw ragged, starving children living in tin boxes, beggars whose bones stuck out sharp as chisels, a fight over food on an aid truck that left two people lying bloody in the road. Each night I brought him back to Chennai to eat rich food in expensive restaurants. I spent the money from my divorce freely, and I didn't have to say a word.

Sweating in the heat, Ian said, 'Sage was wrong. Those people - they can't grow enought food.'

'No. Each year, childhood deaths from malnutrition rise sharply, and it's only going to get worse. The need for food is projected to rise 70 percent over the next thirty years. And as to poverty - well, a handful of super-rich people have as much money as the whole bottom half of the world's population put together.'

'That can't be right.'

'It's not right.'

'I mean, that can't be correct.'

'It is.'

He said nothing more, staring at a child digging through a stinking garbage dump for something to eat. Back at the hotel, after a shower, I saw him checking statistics on his laptop. At dinner he stared at the exquisitely cooked food on his plate.

'Mom, what can we do?'

'Donate. Understand the situation. Care.'

He picked up his fork, put it down again, scowled. But not, this time at me. I thought I saw down beginning on his upper lip - could that be true? So soon?

'I can sell a lot of my stuff,' Ian said, 'and donate the money.'

'That's your choice, honey,' I said. 'But keep what you really need. The trick is to decide what that is.'" -- Nancy Kress, Sea Change, Tachyon Publications, 2020.

Where Do Prices Come From In Marginalist Economics?

1.0 Introduction

Where do prices come from in mainstream economics? As far as I know, some hard questions were raised half a century ago. They still have not been answered, I gather.

2.0 No Agent Makes Prices

Consider competitive markets, as defined in marginalist economics for most of the twentieth century. This implies that agents in the market take prices as given.

From Steve Keen, I know that if only a countable infinity of consumers and firms exist, the agents are systematically mistaken. Despite their beliefs, they are not atomic, and their actions in varying quantities bought or sold affect prices. For agents not to be systematically mistaken, an uncountable infinity of consumers and firms must exist.

I have noted Emmanuelle Benicourt making similar points before.

Classical political economy provides another concept of competitive markets. This concept is that no barriers to entry or exit exist. This concept has been taken into mainstream economics under the rubric of contestable markets.

If all agents take prices as given, who makes prices?

"How can equilibrium be established? ... Do individuals speculate on the equilibrium process? If they do, can the disequilibrium be regarded as, in some sense, a higher-order market process? Since no one has market power, no one sets prices; yet they are set and changed. There are no good answers to these questions." -- Kenneth Arrow (1987)

Franklin Fisher did some work here which he agrees is not a fully satisfactory answer. In his investigation of disequilibrium, convergence to an equilibria requires the ad-hoc assumption of 'No favourable suprise'. Furthermore, the equilibrium that is found will generally not correspond to the initial data. The disequilibrium process changes the data, for example, the initial distribution of endowments.

3.0 Equilibrium Paths?

Suppose one wants to model production. Many economists turned away from long run theory, towards analyzing intertemporal equilibrium paths. Even though I have done work in signal processing, I do not not feel comfortable with optimal control theory.

Some general objections can be raised to this whole approach. For example, initial endowments are among the givens. If some were previously produced, a failure to fulfill expectations is possible. But an equilibrium position is one in which all expectations are fulfilled in the future.

As I understand it, markets always clear at all moments in time along an equilibrium path. For given initial conditions, typically an uncountable infinity of such paths exist. Some of these paths result in the economy eventually reaching a point in which capital goods needed to keep the economy going are just not produced. Other paths approach a path for steady-state growth, from which they will eventually diverge. Frank Hahn argued that, given multiple capital goods, an infinite number of steady-state growth paths exist. How one of these paths is picked out is the 'Hahn problem'. Some paths neither lead to the economy collapsing or a steady state. Instead, they lead to cycles.

I am not clear what is typically assumed about expectations. I guess myopic expectations are needed, in some sense, for the existence of equilibrium paths that end up with the economy crashing.

Reswitching appears in this literature. Michael Bruno has a paper in Shell (1967) that has equilibrium paths just skipping over a reswitching regime. Rosser identifies this possibility with a cusp catastrophe. Maybe an issue arises here with how an equilibrium path can approach a steady state. Is this what Hahn refers to in the closing paragraphs of Hahn (1982).

I guess economists typically assume that the economy will not follow a path in which the economy cannot continue to be sustained. And initial prices are such that one unique path is picked out. Typically this path converges to a steady state growth path which has the stability of a saddle poing.

4.0 Conclusion

My references are not recent. Maybe I want to read something by William Brock. As far as I know, marginalist economic theory still has these problems. I guess mainstream economists just assume transversality conditions, with no theory of how equilibrium is reached or why the equilibrium path that is found does not lead to collapse.

References

• Kenneth J. Arrow. 1987. Economic theory and the hypothesis of rationality, The New Pagrave: A Dictionary of Economics.
• Robert Aumann. 1964. Markets with a continuum of traders. Econometrica, 32 (1-2): 39-50.
• Emmanuelle Benicourt. 2016. Is the core e-Book a possible solution to our problems?, Real-World Economics Review, 75: 135-142
• Robert Dorfman, Paul Samuelson, and Robert Solow. 1958. Linear Programming and Economic Analysis.
• Franklin M. Fisher. 1983. Disequilibrium Foundations of Equilibrium Economics, Cambridge University Press.
• Harvey Gram and G. C. Harcourt. 2017. Joan Robinson and MIT, History of Political Economy 49(3): 437-450.
• Frank Hahn. 1982. The neo-Ricardians, Cambridge Journal of Economics 6(4): 353-374.
• Frank Hahn. 1987. 'Hahn problem', The New Pagrave: A Dictionary of Economics.
• J. Barkley Rosser Jr. 1983. Reswitching as a cusp catastrophe, Journal of Economic Theory 31(1): 182 - 193.
• Karl Shell (ed.). 1967. Essays on the Theory of Economic Growth, MIT Press.

Reswitching Pattern In Corn-Tractor Model

Figure 1: Variation in the Cost-Minimizing Technique with Selected Coefficient of Production

This post reports on some work with Steedman's corn-tractor model. I have yet to find an instance of triple-switching. I have found a case of reswitching, though.

Figure 1 above and Table 1 below show how switch points vary with perturbations of the labor needed to produce a bushel of corn in the corn industry with Type I tractors. Only one switch point exists in region 1. Around this switch point a lower rate of profits is associated with the production and use of Type I tractors, an increase in consumption per labor-year, and a decrease in labor inputs in the corn industry per bushel produced. In other words, this switch point conforms to obsolete marginalist intuition.

Table 1: Regions

Region	Description
1	Around switch point, Type I tractors are cost-minimizing at a lower rate of profits, higher wage.
2	Reverse labor deepening. Around switch point, Type I tractors are cost-minimizing at a lower rate of profits, higher wage. Increased wage is associated with more labor employed in corn industry.
3	Reswitching. Type II tractors are cost-minimizing at high and low rates of profits.
4	Type II tractors are cost-minimizing throughout.

A single switch point exists in region 2 as well. This switch point is like that in region 1, except a lower rate of profits around the switch point is associated with an increase in labor inputs in the corn industry. This is a case of the reverse substitution of labor.

Region 3 is an example of reswitching. In region 4, both switch points have disappeared. Figure 2 below is much like Figure 1, but the wage is graphed on the ordinate.

Figure 2: Variation in Wage at Switch Points

I also graphed two of my fluke switch points. Figure 3 is for a switch point on the wage axis. It is at the partition between regions 2 and 3 in the above graphs. Figure 4 is for what I call a reswitching pattern. It is at the partition between regions 3 and 4.

Figure 3: Pattern over Wage Axis

Figure 4: Reswitching Pattern

Consider the switch point at the higher rate of profits in region 3. Around this switch point, a lower rate of profits is associated with adoption of the technique in which Type I tractors are produced and used. Consumption of corn per employed worker is decreased. Suppose, incoherently, that a lower rate of profits is an indication that consumers are more patient and supply more capital. The example clarifies that identifying a type of machine as more capital-using or labor-saving cannot be seen from a physical characterization of machinery alone.

I am still seeking parameters in which triple-switching occurs. To find the above case, I needed to find the roots of a fourth degree polynomial. I am looking for a case in which all roots are real, and three are positive and less than the maximum rate of profits.

It also would be nice to find reswitching in the special case in which the following is true for each type of tractor:

a/b = alpha/beta

Reswitching in this special case contradicts Samuelson's 1962 account of surrogate production functions. He claims that reswitching is impossible here. The difference is that Steedman analyzes depreciation rigorously, not with an approximation of radioactive decay.

Ludwig Von Mises, Male Chauvinist

Ludwig Von Mises expanded his erroneous 1920 essay into a book, Socialism: An Economic and Sociological Analysis. The first edition was published in 1922 and the second edition in 1932.

Since Von Mises is attempting to be more comprehensive, he treats the socialist advocacy of free love in an early chapter. Being au courant, he writes about Freud. He argues that the bourgeois idea of marriage as a contract, binding on both husband and wife, is an improvement on what came before.

But I find it hard to get beyond passages like those below. Here, Von Mises confines women to her supposed role in propagating the human race, as in Margaret Atwood's The Handmaid's Tale:

"The radical wing of Feminism, which holds firmly to this standpoint, overlooks the fact that the expansion of woman's powers and abilities is inhibited not by marriage, not by being bound to man, children, and household, but by the more absorbing form in which the sexual function affects the female body. Pregnancy and the nursing of children claim the best years of a woman's life, the years in which a man may spend his energies in great achievements. One may believe that the unequal distribution of the burden of reproduction is an injustice of nature, or that it is unworthy of woman to be child-bearer and nurse, but to believe this does not alter the fact. It may be that a woman is able to choose between renouncing either the most profound womanly joy, the joy of motherhood, or the more masculine development of her personality in action and endeavor. It may be that she has no such choice. It may be that in suppressing her urge towards motherhood she does herself an injury that reacts through all other functions of her being. But whatever the truth about this, the fact remains that when she becomes a mother, with or without marriage, she is prevented from leading her life as freely and independently as man. Extraordinarily gifted women may achieve fine things in spite of motherhood; but because the functions of sex have the first claim upon woman, genius and the greatest achievements have been denied her." -- Ludwig von Mises, Socialism, pp. 100-101

Here, Von Mises suggests that women are not capable of the intellectual contemplation possible for men:

"It is clear that sex is less important in the life of man than of woman. Satisfaction brings him relaxation and mental peace. But for the woman the burden of motherhood begins here. Her destiny is completely circumscribed by sex; in man's life it is but an incident. However fervently and whole-heartedly he loves, however much he takes upon himself for the woman's sake, he remains above the sexual. Even woman are finally contemptuous of the man who is utterly engrossed by sex. But woman must exhaust herself as lover and as mother in the service of the sexual instinct. Man may often find it difficult, in the face of all the worries of his profession, to preserve his inner freedom and so to develop his individuality, but it will not be his sexual life which distracts him most. For woman, however, sex is the greatest obstacle.

Thus the meaning of the feminist question is essentially woman's struggle for personality. But the matter affects men not less than women, for only in co-operation can the sexes reach the highest degree of individual culture. The man who is always being dragged by woman into the lower spheres of psychic bondage cannot develop freely in the long run. To preserve the freedom of inner life for the woman, this is the real problem of women; it is part of the cultural problem of humanity." -- L. von Mises, op. cite., pp. 102-103

Here, Von Mises says that it does not matter that women cannot vote or hold elected office, as well as a lot of other vicious nonsense:

"...And now man and woman are equal before the law. The small differences that still exist in private law are of no practical significance. Whether, for example, the law obliges the wife to obey her husband is not particularly important; as long as marriage survives one party will have to follow the other and whether husband or wife is stronger is certainly not a matter which paragraphs of the legal code can decide. Nor is it any longer of great significance that the political rights of women are restricted, that women are denied the vote and the right to hold public office. For by granting the vote to women the proportional political strength of the political parties is not on the whole much altered; the women of those parties which must suffer from the changes to be expected (not in any case important ones) ought in their own interests to become opponents of women's sufferage rather than supporters. The right to public office is denied women less by the legal limitations of their rights than by the peculiarities of their sexual character. Without underestimating the value of the feminists' fight to extend woman's civil rights, one can safely risk the assertion that neither women nor the community are deeply injured by the slights to women's legal position which still remain in the legislation of civilized states.

The misconception to which the principle of equality before the law is exposed in the field of general social relationships is to be found in the special field of relations between those sexes. Just as the pseudo-democratic movement endeavours by decree to efface natural and socially conditioned inequalities, just as it wants to make the strong equal to the weak, the talented to the untalented, and the healthy to the sick, so the radical wing of the woman's movement seeks to make women the equal of men. [Footnote: To examine how far the radical demands of feminism were created by men and women whose sexual character was not normally developed would go beyond the limits set to these expositions.] Though they cannot go so far as to shift half the burden of motherhood on to men, still they would like to abolish marriage and family life so that women may have at least all that liberty which seems compatible with childbearing. Unencumbered by husband and children, woman is to move freely, act freely, and live for herself and the development of her personality.

But the difference between sexual character and sexual destiny can no more be decreed away than other inequalities of mankind. It is not marriage which keeps woman inwardly unfree, but the fact that her sexual character demands surrender to a man and that her love for husband and children consumes her best energies..." -- L. von Mises, op. cite., pp. 104-105

Von Mises' praise for Mussolini's fascism appears to be more well-known that his stated indifference to women not being allowed to vote.

Goal: Perturb Special Case Of Steedman's Corn-Tractor Model

1.0 Introduction

I would like to illustrate triple switching, in the corn-tractor model, with one of my one-dimensional diagrams. I have a triple-switching example, from Bertram Schefold, but the wage-rate of profit frontier is not visually striking in it. Such an example would not be worthy of a research paper. But perhaps I could modify a section of my recent working paper to submit somewhere. Besides, posing a new problem might motivate me to update my computing technology.

2.0 Technology

The corn-tractor model is a fixed capital model, an adaption of the Samuelson-Gargenani model. Labor and tractors are used to produce new tractors. Labor and tractors are also used to produce corn. Corn is the consumption good and the numeraire. Table 1 shows the coefficients of production for a particular type of tractor.

Table 1: Inputs for The Technology

INPUTS	Industry
	Tractor	Corn
Labor	b person-years	beta person-years
Tractors (of any age)	a tractors	alpha tractors
Corn	0	0
OUTPUTS	1 new tractor	1 bushel corn

Tractors last n years in the tractor industry and v years in the corn industry. Although not apparent in the table, this is an example of joint production. Every process for producing a new tractor also produces tractors one year older than the tractors used as inputs, except for the process using (n - 1)-year old tractors as an input. Similarly, every process for producing corn also produces tractors one year older, except for the process using (v - 1)-year old tractors. Tractors operate with constant efficiency for their physical life, albeit with different efficiencies in the two industry. As assumed in pure fixed capital models, old tractors cannot be transferred between industries.

With these assumptions, no choice of the economic life of a machine arises. The tractor will be used for its full physical life in each industry. Only three coefficients need to be specified for each type of tractor: a, beta, and (alpha b). The last is a matter of scaling, of selecting units of measure for labor or tractors, I guess. Without loss of generality, one can set alpha to unity throughout.

3.0 A Special Case

To find a triple-switching example, it is apparently sufficient to set n = v = 2. Tractors last for two years in both the tractor and the corn industry. Eventually, I want to consider two types of tractors. The choice of technique is a matter of choosing the type of tractor to produce and use. (I always find it mysterious how Steedman and his co-authors find their examples. One might think this model was thoroughly analyzed decades ago and did not have anything new to tell us.)

The remainder of this post specifies the solution, in a stationary state, for this special case.

4.0 Quantity Flows

Consider a stationary state in which employment is one person-year, across the four operated processes. Let q₁ be the number of new tractors produced in each process in the tractor industry. Let q₂ be the bushels corn produced in each process in the corn industry. These quantities are as follows:

q₁ = alpha/{2 [2 beta + (alpha b - a beta)]}

q₂ = (2 - a)/{2 [2 beta + (alpha b - a beta)]}

One can check this solution. Total employment, L, is:

L = 2 b q₁ + 2 beta q₂ = 1

The number of new tractors produced is (2 q₁), and the number of new tractors used in production processes is the sum of (a q₁) and (alpha q₂). The new tractors used as inputs replace, at the end of the year, the one-year old tractors used in each industry. So this is a stationary state with employment of one person-year.

The gross output of corn is also the net output, since corn is not used as an input in production. That is, consumption per person-year in a stationary state, c, is:

c = 2 q₂ = (2 - a)/[2 beta + (alpha b - a beta)]

5.0 Prices of Production

The system of equations for prices of production are set out in terms of five price variables:

• p₀: The price of a new tractor.
• p₁: The price of a one-year old tractor used in the tractor industry.
• p₂: The price of a one-year old tractor used in the corn industry.
• w: The wage, in units of bushels per person-year, paid to the workers at the end of the year.
• r: The rate of profits, assumed to be the same in each of the four production processes.

Sraffa shows how to eliminate the prices of old tractors from the system. This analysis derives the price of an annuity. The following variable is convenient in setting out the solution of the price equations:

denom(r) = [(alpha b - a beta) r²

+ [beta + 2 (alpha b - a beta)] r

+ 2 beta + (alpha b - a beta)

The wage, as a function of the rate of profits, is:

w = [-a r² + (1 - 2 a) r + (2 - a)]/denom(r)

I call the above function the wage curve. The price of a new tractor, also as a function of the rate of profits, is:

p₀ = b (r + 2)/denom(r)

The price of a one-year old tractor is:

p₁ = p₂ = b (r + 1)/denom(r)

I think that, in this model, as long as the life of a tractor is the same in producing tractors and corn, the price of an old tractor of a given age does not vary between the two industries.

The wage curve is also the tradeoff for consumption per worker and the steady state rate of growth. Accordingly, the wage at a rate of profits of zero is the same as consumption per worker, c, found as a result of the solution of the quantity equations.

6.0 Conclusion

I guess I should create a spreadsheet for this special case, but with a choice of two types of tractors. My problem is to find a set of six coefficients of production, three for each type of tractor, such that the two wage curves intersect at three points, with positive rates of profits but below the maximum. Finding such is probably tedious. Then, I would like to consider perturbations of the coefficients, maybe exponential decreases with time in labor inputs. And finally, I would like a diagram of, say the wage, for switch points and the maximum, graphed against time.

Update 9/9/2024: Added calculation and comment about price of old tractors.

Elsewhere

• Louis-Philippe Rochon on Paul Davidson.
• James Galbraith, Thomas Palley, and Matias Venengo on Paul Davidson.
• The Economist on Donald Harris. Response in letters to the editor (Both behind paywall).
• A blog post from Matias Vernengo commenting on the above.
• The Washington Post on policy advice from Donald Harris for Jamaica (Behind paywall).
• Maybe I want to read Vanessa Wills' Marx's Ethical Vision, which may be in tension with views I have set out.
• Gordon Katic on the insidious elitist upshot of behavioral economics.

Austrian And Marginalist Capital Theory Without Foundation: A Summary

A mistaken theory claims prices convey information about relative scarcities. Friedrich Hayek uses an example of tin. According to this theory, a higher wage incentivizes investments in less labor-intensive techniques and to shifting production towards less labor-intensive commodities. Likewise, a lower interest rate incentivizes investments toward more capital-intensive techniques and to shifting production towards more capital-intensive commodities.

A number of attempts have been made to elaborate this theory and to formalize this vision:

1. One can measure capital-intensity by aggregating the prices of capital goods used, per person-year of labor employed, in producing a commodity. Around switch points, a lower interest rate is associated with the adoption of a more capital-intensive technique. This approach can be seen in the mainstream economist Edwin Burmeister's work with David Champerowne's chain-index measure of capital.
2. One can measure capital-intensity by the period of production, which is a weighted sum of the prices of dated unproduced inputs (labor and land). The weights, in Eugen Böhm-Bawerk's approach are based on a simple interest model. A lower interest-rate is associated with an increase in the period of production.
3. Capital goods include machines that operate with constant efficiency over their physical life. Lower interest rates are associated with the adoption of techniques with longer-lived machines. Ian Steedman's corn-tractor model provides a framework to investigate this approach.
4. Capital goods include machines that operate with variable efficiency over their physical life. Lower interest rates are associated with the lengthening of the economic life of machines.
5. One can measure the period of production by a financial approach, as in the work of Nicolás Cachanosky and Peter Lewin. Their Duration is a rediscovery of J. R. Hicks' average period of production.

The lack of foundation of these approaches can be seen by the existence of numeric counter-examples. These counter-examples are set in a framework in which market prices are attracted by prices of production.

Examples of negative real Wicksell effects show, as acknowledged by Burmeister, that the first approach is, at best, an arbitrary special case. The existence of price Wicksell effects invalidates the second approach. Steedman shows that the third approach is, again, an arbitrary special case. Numeric examples from Bertram Schefold and others show the fourth approach relies on another special case. I have demonstrated that the issues with the fourth approach are independent of the issues with the first approach.

Saverio Fratini has shown that the fifth approach is compatible with reswitching. A more roundabout technique of production, by the measure of Duration, can result in less net output per worker. This result seems contrary to what those formalizing measures of capital-intensity intend.

One could respond to above with mysticism, maintaining the doctrines of Austrian capital theory, while refusing to state anything clearly. As I understand it, this is the approach of Jésus Huerta de Soto and others.

Ludwig Von Mises Being Wrong On Economic Calculation

I have demonstrated that Von Mises fails to identify problems with central planning. This post merely documents Von Mises being mistaken. He erroneously says that an economic decision cannot be made over alternative methods of producing a given good, without market prices for capital goods and resources.

"The director wants to build a house. Now, there are many methods that can be resorted to. Each of them offers, from the point of view of the director, certain advantages and disadvantages with regard to the utilization of the future building..; each of them requires other expenditures of building materials and labor... Which method should the director choose; He cannot reduce to a common denominator the items of various materials and various kinds of labor to be expended. Therefore he cannot compare them... In short, he cannot, in comparing costs to be expended and gains to be earned, resort to any arithmetical operation. The plans of his architects enumerate a vast multiplicity of various items in kind; they refer to the physical and chemical qualities of various materials and to the physical productivity of various machines, tools, and procedures. But all their statements remain unrelated to each other. There is no means of establishing any connection between them.

Imagine the plight of the director when faced with a project. What he needs to know is whether or not the execution of the project will increase well-being, that is, add something to the wealth available without impairing the satisfaction of wants which he considers more urgent. But none of the reports he receives give him any clue to the solution of this problem.

We may for the sake of argument at first disregard the dilemmas involved in the choice of consumers' goods to be produced. We may assume that this problem is settled. But there is the embarrassing multitude of producers' goods and the infinite variety of procedures that can be resorted to for manufacturing definite consumers' goods. The most advantageous location of each industry and the optimum size of each plant and of each piece of equipment must be determined. One must determine what kind of mechanical power should be employed in each of them, and which of the various formulas for the production of this energy should be applied. All these problems are raised daily in thousands and thousands of cases. Each case offers special conditions and requires an individual solution appropriate to these special data. The number of elements with which the director's decision has to deal is much greater than would be indicated by a merely technological description of the available producers' goods in terms of physics and chemistry. The Iocation of each of them must be taken into consideration as well as the serviceableness of the capital investments made in the past for their utilization. The director does not simply have to deal with coal as such, but with thousands and thousands of pits already in operation in various places, and with the possibilities for digging new pits, with the various methods of mining in each of them, with the different qualities of the coal in various deposits, with the various methods for utilizing the coal for the production of heat, power, and a great number of derivatives. It is permissible to say that the present state of technological knowledge makes it possible to produce almost anything out of almost everything. Our ancestors, for instance, knew only a limited number of employments for wood. Modern technology has added a multitude of possible new employments. Wood can be used for the production of paper, of various textile fibers, of foodstuffs, drugs, and many other synthetic products.

Today two methods are resorted to for providing a city with clean water. Either one brings the water over long distances in aqueducts, an ancient method long practiced, or one chemically purifies the water avaiIable in the city's neighborhood. Why does one not produce water synthetically in factories? Modern technology could easily solve the technological problems involved. The average man in his mental inertia is ready to ridicule such projects as sheer lunacy. However, thc only reason why the synthetic production of drinking water today - perhaps not at a later day - is out of the question is that economic calculation in terms of money shows that it is a more expensive procedure than other methods. Eliminate economic calculation and you have no means of making a rational choice between the various alternatives.

The socialists, it is true, object that economic calculation is not infallible. They say that the capitalists sometimes make mistakes in their calculation. Of course, this happens and will always happen. For all human action points to the future and the future is always uncertain. The most carefuIly elaborated plans are frustrated if expectations concerning the future are dashed to the ground. However, this is quite a different problem. Today we calculate from the point of view of our present knowledge and of our present anticipation of future conditions. We do not deal with the problcm of whether or not the director will be able to anticipate future conditions. What we have in mind is that the director cannot calculate from the point of view of his own present value judgments and his own present anticipations of futurc conditions, whatever they may be. If he invests today in the canning industry, it may happen that a change in consumers' tastes or in the hygienic opinions concerning the wholesomeness of canned food will one day turn his investment into a malinvestment. But how can he find out today how to build and equip a cannery most economically?

Some raiIroad lines constructed at the turn of the century would not have been built if people had at that time anticipated the impending advance of motoring and aviation. But those who at that time built railroads knew which of the various possible alternatives for the realization of their plans they had to choose from the point of view of their appraisements and anticipations and of the market prices of their day in which the valuations of the consumers were reflected. It is precisely this insight that the director will lack. He will be like a sailor on the high seas unfamiliar with the methods of navigation, or like a medieval scholar entrusted with the technical operation of a railroad engine.

We may admit that in its initial period a socialist regime couId to some extent rely upon the experience of the preceding age of capitalism. But what is to be done later, as conditions change more and morc? Of what use could the prices of 1900 be for the director in 1949? And what use can the director in 1980 derive from the knowledge of the prices of 1949?

The paradox of 'planning' is that it cannot plan, because of the absence of economic calculation. What is called a planned economy is no economy at all. It is just a system of groping about in the dark. There is no question of a rational choice of means for the best possible attainment of the ultimate ends sought. What is called conscious planning is precisely the elimination of conscious purposive action." -- Ludwig Von Mises, 1963. Human Action: A Treatise on Economics, Third revised edition. Yale University Press. (Emphasis added)

The above is from Human Action, presumably after Von Mises has had time to consider arguments about his 1920 essay. Since I do not want to argue the errors of Austrian capital theory in this post, I have elided errors on that topic in the above quotation.

Joan Robinson On Dual Labor Markets

In re-reading Robinson, I often find her succinctly summarizing a theory, often developed later. Here is a quotation from one of my favorite books by her:

"The argument is sometimes advanced that evidence shows that, in reasonably prosperous countries, the percentage of unemployment is never seen to vary very much, averaging good times with bad, over the long run ... But even for prosperous countries the evidence is largely an optical illusion. Capitalist industry does not employ the whole work force in any country. Domestic service, paid or unpaid, jobbing work and small-scale trade, and, in most countries, agriculture, hold a reservoir of labour which fills up when regular employment is not expanding as fast as the population. The question of whether people are happier in these occupations than they would be in regular employment is not to the purpose. The point at issue is that there is no justification for putting an assumption into the model to make the rate of growth of the labour force set a minimum to the rate of accumulation." -- Joan Robinson, Normal prices, republished in Essays in the Theory of Economic Growth, Macmillan: 1962.

In this article, Robinson distinguishes between economic models of the allocation of scare resources and models focused on the conditions for the reproduction of the economy.

Maybe her comment looks back on W. Arthur Lewis' 1954 article, Economic development with unlimited supplies of labour. One might also draw connections to Marx's concept of the reserve army of labor and to Rosa Luxemburg's insistence that capitalist reproduction arises only with a background of less-developed non-capitalist markets.

This comment also looks forward to Michael Reich, David Gordon, and Richard Edwards' theory of dual labor markets. In the formal or corporate sector, you can expect to have a standard work week, weekends off, benefits, some asurance that your job will exist next week, and so on. In the informal sector, not so much.

Monopoly Capitalism Is Inefficient

The title claim is not surprising. But it occurs to me that it follows from how I model prices of production, given stable relative profit rates among industries. I am not original with this modeling. My contribution is analying the choice of technique and exploring how this analysis varies with perturbations of relative markups.

In the price equations, s₁ r, s₂ r, s₃ r, and so on are the rate of profits in the various industries. I call r the scale factor for the rate of profits. Given the technique and a given wage in terms of a given numeraire, one can find prices and the scale factor for the rate of profits. The scale factor is a declining function of the wage. The cost-minimizing technique at a given wage is the technique for the wage curve on the outer frontier at that wage. At a switch point, more than one technique is cost-minimizing.

In the case of competitive markets, 1 = s₁ = s₂ = s₃ = ... The analysis of the choice of technique reduces to the usual analysis in the literature.

The cost-minimizing technique, at a given wage, varies, in general, between the competitive case and the case with with relative markups varying among industries. The cost-minimizing technique is efficient, in some sense, in the competitive case. The outer frontier is sometimes called the efficiency frontier. (I could stand to review what efficiency means in this case.)

Anyways, the above outlines an argument for the title claim based on the analysis of the choice of technique in models of the production of commodities by means of commodities.

Von Mises Wrong On Economic Calculation (Update)

1.0 Introduction

This post is an update, based on suggestions from a user on reddit. I have explained this before. Suppose one insists socialism requires central planning. In his 1920 paper, 'Economic calculation in the socialist commonwealth', Ludwig Von Mises claims that a central planner requires prices for capital goods and unproduced resources to successfully plan an economy. The claim that central planning is impossible without market prices is supposed to be a matter of scientific principle.

Von Mises was mistaken. His error can be demonstrated to follow from the theory of linear programming and duality theory. This application of linear programming reflects a characterization of economics as the study of the allocation of scarce means among alternative uses. This post demonstrates that Von Mises was mistaken without requiring, hopefully, anything more than high school mathematics to understand what is being claimed.

2.0 Technology, Endowments, and Prices of Consumer Goods as given

For the sake of argument, Von Mises assumes the central planner has available certain data. He wants to demonstrate his conclusion, while conceding as much as possible to his supposed opponent.

Accordingly, assume the central planner knows the technology with the coefficients of production in Table 1. Two goods, wheat and barley are to be produced and distributed to consumers. Each good is produced from inputs of labor, land, and tractors. The column for Process I shows the person-years of labor, acres of land, and number of tractors needed, per quarter wheat produced. The column for Process II shows the inputs, per bushel barley, for the first production process known for producing barley. The column for Process III shows the inputs, per bushel barley, for the second process known for producing barley. The remaining two processes are alternative processes for producing tractors from inputs of labor and land.

Table 1: The Technology

Input	Process I	Process II	Process III	Process IV	Process V
Labor	a1,1	a1,2	a1,3	a1,4	a1,5
Land	a2,1	a2,2	a2,3	a2,4	a2,5
Tractors	a3,1	a3,2	a3,3	0	0
Output	1 quarter wheat	1 bushel barley	1 bushel barley	1 tractor	1 tractor

A more advanced example would have at least two periods, with dated inputs and outputs. I also abstract from the requirement that only an integer number of tractors can be produced. A contrast between wheat and barley illustrates that the number of processes known to produce a commodity need not be the same for all commodities.

Von Mises assumes that the planner knows the price of consumer goods. In the context of the example, the planner knows:

• The price of a quarter wheat, p₁.
• The price of a bushel barley, p₂.

Finally, the planner is assumed to know the physical quantities of resources available. Here, the planner is assumed to know:

• The person-years, x₁, of labor available.
• The acres, x₂, of land available.

No tractors are available at the start of the planning period in this formulation.

3.0 The Central Planner's Problem

The planner must decide at what level to operate each process. That is, the planner must set the following:

• The quarters wheat, q₁, produced with the first process.
• The bushels barley, q₂, produced with the second process.
• The bushels barley, q₃, produced with the third process.
• The number of tractors, q₄, produced with the fourth process.
• The number of tractors, q₅, produced with the fifth process.

These quantities are known as 'decision variables'.

The planner has an 'objective function'. In this case, the planner wants to maximize the objective function:

Maximize p₁ q₁ + p₂ q₂ + p₂ q₃

The planner faces some constraints. The plan cannot call for more employment than labor is available:

a_1,1 q₁ + a_1,2 q₂ + a_1,3 q₃ + a_1,4 q₄ + a_1,5 q₅ ≤ x₁

More land than is available cannot be used:

a_2,1 q₁ + a_2,2 q₂ + a_2,3 q₃ + a_2,4 q₄ + a_2,5 q₅ ≤ x₂

The number of tractors used in producing wheat and barley cannot exceed the number produced:

a_3,1 q₁ + a_3,2 q₂ + a_3,3 q₃ ≤ q₄ + q₅

Finally, the decision variables must be non-negative:

q₁ ≥ 0, q₂ ≥ 0, q₃ ≥ 0, q₄ ≥ 0, q₅ ≥ 0

The maximization of the objective function, the constraints for each of the two resources, the constraint for the capital good, and the non-negativity constraints for each of the five decision variables constitute a linear program. In this context, it is the primal linear program.

The above linear program can be solved. Prices for the resources do not enter into the problem. So I have proven that Von Mises was mistaken.

4.0 The Dual Problem

But I will go on. Where do the prices of resources and of capital goods enter? A dual linear program exists. For the dual, the decision variables are the 'shadow prices' for the resources and for the capital good:

• The wage, w₁, to be charged for a person-year of labor.
• The rent, w₂, to be charged for an acre of land.
• The cost, w₃, to be charged for a tractor.

The objective function for the dual LP is minimized:

Minimize x₁ w₁ + x₂ w₂

Each process provides a constraint for the dual. The cost of operating Process I must not fall below the revenue obtained from it:

a_1,1 w₁ + a_2,1 w₂ + a_3,1 w₃ ≥ p₁

Likewise, the costs of operating processes II, and III must not fall below operating them:

a_1,2 w₁ + a_2,2 w₂ + a_3,2 w₃ ≥ p₂

a_1,3 w₁ + a_2,3 w₂ + a_3,3 w₃ ≥ p₂

The cost of producing a tractor, with either process for producing a tractor, must not fall below the shadow price of a tractor.

a_1,4 w₁ + a_2,4 w₂ ≥ w₃

a_1,5 w₁ + a_2,5 w₂ ≥ w₃

The decision variables for the dual must be non-negative also:

w₁ ≥ 0, w₂ ≥ 0, w₃ ≥ 0

In the solution to the primal and dual LPs, the values of their respective objective functions are equal to one another. The dual shows the distribution, in charges to the resources and the capital good, of the value of planned output. Along with solving the primal, one can find the prices of resources.

5.0 Conclusion

One could consider the case with many more resources, many more capital goods, many more produced consumer goods, and a technology with many more production processes. No issue of principle is raised. Von Mises was simply wrong.

One might also complicate the linear programs or consider other applications of linear programs. Above, I have mentioned introducing multiple time periods. How do people that do not work get fed? One might consider children, the disabled, retired people, and so on. Might one include taxes somehow? How is the value of output distributed; it need not be as defined by the shadow prices.

Or one might abandon the claim that socialist central planning is impossible, in principle. One could look at a host of practical questions. How is the data for planning gathered, and with what time lags? How often can the plan be updated? Should updates start from the previous solution? What size limits are imposed by the current state of computing? The investigation of practical difficulties is basically Hayek's program.

Von Mises Wrong On Economic Calculation

1.0 Introduction

I have explained this before. Suppose one insists socialism requires central planning. In his 1920 paper, 'Economic calculation in the socialist commonwealth', Ludwig Von Mises claims that a central planner requires prices for capital goods and unproduced resources to successfully plan an economy. The claim that central planning is impossible without market prices is supposed to be a matter of scientific principle.

Von Mises was mistaken. His error can be demonstrated to follow from the theory of linear programming and duality theory. This application of linear programming reflects a characterization of economics as the study of the allocation of scarce means among alternative uses. This post demonstrates that Von Mises was mistaken without requiring, hopefully, anything more than high school mathematics to understand what is being claimed.

2.0 Technology, Endowments, and Prices of Consumer Goods as given

For the sake of argument, Von Mises assume the central planner has available certain data. He wants to demonstrate his conclusion, while conceding as much as possible to his supposed opponent.

Accordingly, assume the central planner knows the technology with the coefficients of production in Table 1. Two goods, wheat and barley are to be produced and distributed to consumers. Each good is produced from inputs of labor and land. The column for Process I shows the person-years of labor and acres of land needed, per quarter wheat produced. The column for Process II shows the inputs, per bushel barley, for the first production process known for producing barley. The column for Process III shows the inputs, per bushel barley, for the second process known for producing barley.

Table 1: The Technology

Input	Process I	Process II	Process III
Labor	a1,1	a1,2	a1,3
Land	a2,1	a2,2	a2,3
Output	1 quarter wheat	1 bushel barley	1 bushel barley

Von Mises assumes that the planner knows the price of consumer goods. In the context of the example, the planner knows:

• The price of a quarter wheat, p₁.
• The price of a bushel barley, p₂.

Finally, the planner is assumed to know the physical quantities of resources available. Here, the planner is assumed to know:

• The person-years, x₁, of labor available.
• The acres, x₂, of land available.

3.0 The Central Planner's Problem

The planner must decide at what level to operate each process. That is, the planner must set the following:

• The quarters wheat, q₁, produced with the first process.
• The bushels barley, q₂, produced with the second process.
• The bushels barley, q₃, produced with the third process.

These quantities are known as 'decision variables'.

The planner has an 'objective function'. In this case, the planner wants to maximize the objective function:

Maximize p₁ q₁ + p₂ q₂ + p₂ q₃

The planner faces some constraints. The plan cannot call for more employment than labor is available:

a_1,1 q₁ + a_1,2 q₂ + a_1,3 q₃ ≤ x₁

More land than is available cannot be used:

a_2,1 q₁ + a_2,2 q₂ + a_2,3 q₃ ≤ x₂

Finally, the decision variables must be non-negative:

q₁ ≥ 0, q₂ ≥ 0, q₃ ≥ 0

The maximization of the objective function, the constraints for each of the two resources, and the non-negativity constraints for each of the three decision variables constitute a linear program. In this context, it is the primal linear program.

The above linear program can be solved. Prices for the resources do not enter into the problem. So I have proven that Von Mises was mistaken.

4.0 The Dual Problem

But I will go on. Where do prices of resources enter? A dual linear program exists. For the dual, the decision variables are the 'shadow prices' for the resources:

• The wage, w₁, to be paid for a person-year of labor.
• The rent, w₂, to be paid for an acre of land.

The objective function for the dual LP is minimized:

Minimize x₁ w₁ + x₂ w₂

Each process provides a constraint for the dual. The cost of operating Process I must not fall below the revenue obtained from it:

a_1,1 w₁ + a_2,1 w₂ ≥ p₁

Likewise, the costs of operating processes II and III must not fall below operating them:

a_1,2 w₁ + a_2,2 w₂ ≥ p₂

a_1,3 w₁ + a_2,3 w₂ ≥ p₂

The decision variables for the dual must be non-negative also:

w₁ ≥ 0, w₂ ≥ 0

In the solution to the primal and dual LPs, the values of their respective objective functions are equal to one another. The dual shows the distribution, in payments to the resources, of the value of planned output. Along with solving the primal, one can find the prices of resources.

5.0 Conclusion

One could consider the case with many more resources, many more produced consumer goods, and a technology with many more production processes. No issue of principle is raised. Von Mises was simply wrong.

One might also complicate the linear programs or consider other applications of linear programs. How do people that do not work get fed. One might consider children, the disabled, retired people, and so on. Might one include taxes somehow?

Or one might abandon the claim that socialist central planning is impossible, in principle. One could look at a host of practical questions. How is the data for planning gathered, and with what time lags? How often can the plan be updated? Should updates start from the previous solution? What size limits are imposed by the current state of computing? The investigation of practical difficulties is basically Hayek's program.

Visualizing Variations In The Analysis Of The Choice Of Technique

I have another working paper, Visualizing variations in the analysis of the choice of technique, at the Centro Sraffa. The abstract follows.

Abstract: This article describes a diagram that depicts how the analysis of the choice technique varies with perturbations of selected parameters in models of the production of commodities. Fluke switch points partition the graph. Three examples are provided, of circulating capital with markup pricing, of fixed capital with structural economic dynamics, and of intensive rent with markup pricing.

How Ownership Obtains A Return According To Marx

1. Introduction

Elsewhere on the internet, I have been explaining my understanding of some rudiments of the political economy of Karl Marx.

Marx's concept of surplus value is a generalization of the concept of profit, in some sense. Surplus value takes in all returns to ownership, whether they be profits, interest, rent, and so on. Surplus value arises from the distinction between the use value and the exchange value of labor power, a peculiar commodity. Because capitalists own the means of production, they can ensure through their domination of the workers, that laborers work longer than the time needed to reproduce their means of subsistence.

2. A Simple LTV as the Setting of Marx's Theory

Marx explains the generation of surplus value in volume 1 of Capital. For the sake of argument, he assumes a special case in which a simple labor theory of value holds. Market prices tend towards prices of production. When the organic composition of commodities does not vary among industries, prices of production are proportional to labor values. Marx knows this is a special case.

Why assume the labor theory of value? It was a dominant theory at the time. Marx can take it over from Ricardo, albeit he modifies it and critiques it. It also accords with what some socialists think is fair. Marx wants to explain surplus value when nobody is cheating anybody:

"This sphere [of simple circulation or of exchange of commodities] that we are deserting, within whose boundaries the sale and purchase of labour-power goes on, is in fact a very Eden of the innate rights of man. There alone rule Freedom, Equality, Property and Bentham. Freedom, because both buyer and seller of a commodity, say of labour-power, are constrained only by their own free will. They contract as free agents, and the agreement they come to, is but the form in which they give legal expression to their common will. Equality, because each enters into relation with the other, as with a simple owner of commodities, and they exchange equivalent for equivalent. Property, because each disposes only of what is his own. And Bentham, because each looks only to himself. The only force that brings them together and puts them in relation with each other, is the selfishness, the gain and the private interests of each. Each looks to himself only, and no one troubles himself about the rest, and just because they do so, do they all, in accordance with the pre-established harmony of things, or under the auspices of an all-shrewd providence, work together to their mutual advantage, for the common weal and in the interest of all." -- Karl Marx, Capital, volume 1, chapter 6.

This emphasis on fairness in exchange also justifies a lack of focus on market prices. Marx does not want to explain surplus value as 'profits on alienation', on cleverness in buying low and selling high. He is looking for a system-wide explanation, not an explanation arising from lucky transactions.

3. Labor-Power as a Commodity

According to Marx, what workers sell is the capacity to labor under the direction of the capitalist and with materials and equipment provided by the capitalist. Like all commodities, labor-power has an exchange-value and a use-value. The exchange value is its labor value, that is, the amount of labor-time needed to produce the commodities needed to sustain the worker.

The value of labor-power depends on social conventions about what is needed for consumption. Marx, unlike Ferdinand Lassalle, does not hold an 'iron law' of wages. In chapter 25 of volume 1 of Capital, Marx describes how the wage varies with the increase and decrease of the 'industrial reserve army'. Richard Goodwin has a formal model of this aspect of Marx's theory.

The use-value of the commodity of labor power is the expenditure of labor in production. It is the realm of production that we are arriving at after leaving the realm of exchange above. But, before discussing this commodity and its use-value further, I want to note one more statement of Marx's problem domain:

"In order to be able to extract value from the consumption of a commodity, our friend, Moneybags, must be so lucky as to find, within the sphere of circulation, in the market, a commodity, whose use-value possesses the peculiar property of being a source of value, whose actual consumption, therefore, is itself an embodiment of labour, and, consequently, a creation of value." -- Karl Marx, Capital, volume 1, chapter 6.

4. On The Existence of Labor-Power

Marx is searching for the preconditions of capitalism and of political economy. He wants his reader to realize that some properties of a commodity-producing economy are not eternal natural-laws, but have a history and a start. They thus might also have an end.

The availability of labor-power for purchase on the market is one aspect of capitalism that has a history. For labor-power to be a commodity, workers must have a double freedom:

"In themselves money and commodities are no more capital than are the means of production and of subsistence. They want transforming into capital. But this transformation itself can only take place under certain circumstances that centre in this, viz., that two very different kinds of commodity-possessors must come face to face and into contact; on the one hand, the owners of money, means of production, means of subsistence, who are eager to increase the sum of values they possess, by buying other people's labour power; on the other hand, free labourers, the sellers of their own labour power, and therefore the sellers of labour. Free labourers, in the double sense that neither they themselves form part and parcel of the means of production, as in the case of slaves, bondsmen, &c., nor do the means of production belong to them, as in the case of peasant-proprietors; they are, therefore, free from, unencumbered by, any means of production of their own. With this polarization of the market for commodities, the fundamental conditions of capitalist production are given. The capitalist system presupposes the complete separation of the labourers from all property in the means by which they can realize their labour. As soon as capitalist production is once on its own legs, it not only maintains this separation, but reproduces it on a continually extending scale. The process, therefore, that clears the way for the capitalist system, can be none other than the process which takes away from the labourer the possession of his means of production; a process that transforms, on the one hand, the social means of subsistence and of production into capital, on the other, the immediate producers into wage labourers. The so-called primitive accumulation, therefore, is nothing else than the historical process of divorcing the producer from the means of production. It appears as primitive, because it forms the prehistoric stage of capital and of the mode of production corresponding with it." -- Karl Marx, Capital, Volume 1, Chapter 26 (my emphasis)

For surplus value to exist, workers must be constrained to work longer than needed to reproduce their wage. The division of the working day into the time to replace wage goods and the time that produces surplus value is not obvious in looking at a single industry. Many workers are producing capital goods, not goods that they consume. Here too one must look at the economy as a whole.

Capitalists can constrain workers to work long enough to produce surplus value because they own the means of production. Production requires labor to work with produced capital goods. These were previously produced by other workers. Because of the products of labor are alienated from the workers, capitalists are able to use their domination of the production process to acquire surplus value. Under this domination, productivity increases and it becomes even more difficult for a group of workers to go into business for themselves.

5. An Exception

In his first draft for Capital, Marx explicitly recognizes that some workers can escape having to sell their labor power. But this cannot be true for workers in general:

"When we look at social relations which create an undeveloped system of exchange, of exchange values and of money, or which correspond to an undeveloped degree of these, then it is clear from the outset that the individuals in such a society, although their relations appear to be more personal, enter into connection with one another only as individuals imprisoned within a certain definition, as feudal lord and vassal, landlord and serf, etc., or as members of a caste etc. or as members of an estate etc. In the money relation, in the developed system of exchange (and this semblance seduces the democrats), the ties of personal dependence, of distinctions of blood, education, etc, are in fact exploded, ripped up (at least, personal ties all appear as personal relations); and individuals seem independent (this is an independence which is at bottom merely an illusion and it is more correctly called indifference), free to collide with one another and to engage in exchange within this freedom; but they appear thus only for someone who abstracts from the conditions, the conditions of existence within which these individuals enter into contact (and these conditions, in turn, are independent of the individuals and, although created by society, appear as if they were natural conditions, not controllable by individuals). The definedness of individuals, which in the former case appears as a personal restriction of the individual by another, appears in the latter case as developed into an objective restriction of the individual by relations independent of him and sufficient unto themselves. (Since the single individual cannot strip away his personal definition, but may very well overcome and master external relations, his freedom seems to be greater in case 2. A closer examination of these external relations, these conditions, shows, however, that it is impossible for the individuals of a class etc. to overcome them en masse without destroying them. A particular individual may by chance get on top of these relations, but the mass of those under their rule cannot, since their mere existence expresses subordination, the necessary subordination of the mass of individuals.) These external relations are very far from being an abolition of 'relations of dependence'; they are rather the dissolution of these relations into a general form; they are merely the elaboration and emergence of the general foundation of the relations of personal dependence. Here also individuals come into connection with one another only in determined ways. These objective dependency relations also appear, in antithesis to those of personal dependence (the objective dependency relation is nothing more than social relations which have become independent and now enter into opposition to the seemingly independent individuals; i.e. the reciprocal relations of production separated from and autonomous of individuals) in such a way that individuals are now ruled by abstractions, whereas earlier they depended on one another. The abstraction, or idea, however, is nothing more than the theoretical expression of those material relations which are their lord and master. Relations can be expressed, of course, only in ideas, and thus philosophers have determined the reign of ideas to be the peculiarity of the new age, and have identified the creation of free individuality with the overthrow of this reign. This error was all the more easily committed, from the ideological stand-point, as this reign exercised by the relations (this objective dependency, which, incidentally, turns into certain definite relations of personal dependency, but stripped of all illusions) appears within the consciousness of individuals as the reign of ideas, and because the belief in the permanence of these ideas, i.e. of these objective relations of dependency, is of course consolidated, nourished and inculcated by the ruling classes by all means available." -- Karl Marx. Grundrisse (my emphasis)

I am not sure where I should have cut the above quotation. I need some reference for "case 2" in the highlighted part. As far as I can see, the Grundrisse reads mostly like the above. By contrast, Capital mostly reads as if it is positivist social science.

Back in the 1960s, one might have thought that the exception would become the rule over a worker's lifetime. If retirement were universal, a group of elderly people would be living off surplus value, so to speak, generated by working-age population. But that is only true for those in the 'formal' part of the economy, and maybe not even always then.

6. Conclusion

Surplus value, according to Marx, is generated by the use value of labor power being potentially a longer time to work than the time needed to reproduce the labor value of labor power. Because of the separation of the means of production from the workers, the capitalists can constrain the workers to generate surplus value. This explanation relies on institutions needed to sustain capitalism.

Is The Labor Theory Of Value Compatible With Automation?

Automation Of Chinese Ports

With automation, many processes for production and distribution now execute with minimal human oversight. How can the labor theory of value, as in volume 1 of Capital, be compatible with this?

Marx has some comments on this subject in the Grundrisse:

The exchange of living labour for objectified labour – i.e. the positing of social labour in the form of the contradiction of capital and wage labour – is the ultimate development of the value-relation and of production resting on value. Its presupposition is – and remains – the mass of direct labour time, the quantity of labour employed, as the determinant factor in the production of wealth. But to the degree that large industry develops, the creation of real wealth comes to depend less on labour time and on the amount of labour employed than on the power of the agencies set in motion during labour time, whose 'powerful effectiveness' is itself in turn out of all proportion to the direct labour time spent on their production, but depends rather on the general state of science and on the progress of technology, or the application of this science to production. (The development of this science, especially natural science, and all others with the latter, is itself in turn related to the development of material production.) Agriculture, e.g., becomes merely the application of the science of material metabolism, its regulation for the greatest advantage of the entire body of society.

Real wealth manifests itself, rather – and large industry reveals this – in the monstrous disproportion between the labour time applied, and its product, as well as in the qualitative imbalance between labour, reduced to a pure abstraction, and the power of the production process it superintends. Labour no longer appears so much to be included within the production process; rather, the human being comes to relate more as watchman and regulator to the production process itself. (What holds for machinery holds likewise for the combination of human activities and the development of human intercourse.)

No longer does the worker insert a modified natural thing as middle link between the object and himself; rather, he inserts the process of nature, transformed into an industrial process, as a means between himself and inorganic nature, mastering it. He steps to the side of the production process instead of being its chief actor. In this transformation, it is neither the direct human labour he himself performs, nor the time during which he works, but rather the appropriation of his own general productive power, his understanding of nature and his mastery over it by virtue of his presence as a social body – it is, in a word, the development of the social individual which appears as the great foundation-stone of production and of wealth. The theft of alien labour time, on which the present wealth is based, appears a miserable foundation in face of this new one, created by large-scale industry itself. As soon as labour in the direct form has ceased to be the great well-spring of wealth, labour time ceases and must cease to be its measure, and hence exchange value [must cease to be the measure] of use value. The surplus labour of the mass has ceased to be the condition for the development of general wealth, just as the non-labour of the few, for the development of the general powers of the human head. With that, production based on exchange value breaks down, and the direct, material production process is stripped of the form of penury and antithesis. The free development of individualities, and hence not the reduction of necessary labour time so as to posit surplus labour, but rather the general reduction of the necessary labour of society to a minimum, which then corresponds to the artistic, scientific etc. development of the individuals in the time set free, and with the means created, for all of them.

Capital itself is the moving contradiction, [in] that it presses to reduce labour time to a minimum, while it posits labour time, on the other side, as sole measure and source of wealth. Hence it diminishes labour time in the necessary form so as to increase it in the superfluous form; hence posits the superfluous in growing measure as a condition – question of life or death – for the necessary. On the one side, then, it calls to life all the powers of science and of nature, as of social combination and of social intercourse, in order to make the creation of wealth independent (relatively) of the labour time employed on it. On the other side, it wants to use labour time as the measuring rod for the giant social forces thereby created, and to confine them within the limits required to maintain the already created value as value. Forces of production and social relations – two different sides of the development of the social individual – appear to capital as mere means, and are merely means for it to produce on its limited foundation. In fact, however, they are the material conditions to blow this foundation sky-high. 'Truly wealthy a nation, when the working day is 6 rather than 12 hours. Wealth is not command over surplus labour time' (real wealth), 'but rather, disposable time outside that needed in direct production, for every individual and the whole society.' (The Source and Remedy etc. 1821, p. 6.)

Nature builds no machines, no locomotives, railways, electric telegraphs, self-acting mules etc. These are products of human industry; natural material transformed into organs of the human will over nature, or of human participation in nature. They are organs of the human brain, created by the human hand; the power of knowledge, objectified.

The development of fixed capital indicates to what degree general social knowledge has become a direct force of production, and to what degree, hence, the conditions of the process of social life itself have come under the control of the general intellect and been transformed in accordance with it. To what degree the powers of social production have been produced, not only in the form of knowledge, but also as immediate organs of social practice, of the real life process. -- Karl Marx, Grundrisse, Contradiction between the foundation of bourgeois production (value as measure) and its development. Machines etc.

I take the paragraphing above from David McLellan's severely abridged version. I think I need a hard-copy version if I am ever going to fully read the Grundrisse. For what it is worth, John Von Neumann has a theory of value for a fully automated economy.

Marx above seems to offer one story of how capitalism will end. An issue exists with finding supposed anti-Marxist arguments echoed in writings unpublished in Marx's lifetime. It is not clear how to working class has a role in the above story. Is this story consistent with what Marx says in Capital, as quoted in Section 4 here? Sundry observations do not neccessarily add up to a consistent theory.

Adam Smith's 'Effectual Demand'

"There is in every society or neighbourhood an ordinary or average rate, both of wages and profit, in every different employment of labour and stock...

There is likewise in every society or neighbourhood an ordinary or average rate of rent...

These ordinary or average rates may be called the natural rates of wages, profit and rent, at the time and place in which they commonly prevail.

When the price of any commodity is neither more nor less than what is sufficient to pay the rent of the land, the wages of the labour, and the profits of the stock employed in raising, preparing, and bringing it to market, according to their natural rates, the commodity is then sold for what may be called its natural price...

The actual price at which any commodity is commonly sold, is called its market price. It may either be above, or below, or exactly the same with its natural price.

The market price of every particular commodity is regulated by the proportion between the quantity which is actually brought to market, and the demand of those who are willing to pay the natural price of the commodity, or the whole value of the rent, labour, and profit, which must be paid in order to bring it thither. Such people may be called the effectual demanders, and their demand the effectual demand; since it maybe sufficient to effectuate the bringing of the commodity to market. It is different from the absolute demand. A very poor man may be said, in some sense, to have a demand for a coach and six; he might like to have it; but his demand is not an effectual demand, as the commodity can never be brought to market in order to satisfy it...

When the quantity brought to market is just sufficient to supply the effectual demand, and no more, the market price naturally comes to be either exactly, or as nearly as can be judged of, the same with the natural price. The whole quantity upon hand can be disposed of for this price, and can not be disposed of for more. The competition of the different dealers obliges them all to accept of this price, but does not oblige them to accept of less...

The natural price, therefore, is, as it were, the central price, to which the prices of all commodities are continually gravitating. Different accidents may sometimes keep them suspended a good deal above it, and sometimes force them down even somewhat below it. But whatever may be the obstacles which hinder them from settling in this centre of repose and continuance, they are constantly tending towards it.

The whole quantity of industry annually employed in order to bring any commodity to market, naturally suits itself in this manner to the effectual demand. It naturally aims at bringing always that precise quantity thither which may be sufficient to supply, and no more than supply, that demand." -- Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations, Book I, Chapter VII.

I prefer the term 'prices of production' to Smith's 'natural price'. Smith calling something 'natural' does not mean he approves of it, but I prefer to avoid the argument.

I wish I had access to Alex M. Thomas' 2021 article in The European Journal of the History of Economic Thought.

Adam Smith speaks of supply and demand in the above quotation. These are levels of quantities. Neither is a schedule showing how the quantity quantity supplied and demand varies with prices. These supplies and demands are thus not the curves graphed in introductory courses in contemporary mainstream economics.

I think of 'effectual demand' as being dependent on income distribution. It depends on how landlords, for example, divide up their income among savings, consumption on luxury commodities, and consumption of staples.

Some literature builds on and critiques Smith's metaphor of market prices gravitating towards or around prices of production.

Anyways, suppose all industries are producing at the level of effectual demand. Market prices match prices of production. In this situation, the total labor force of the country is distributed among industries in definition proportions. "The masses of products corresponding to the different needs require[s] different and quantitatively determined masses of the total labor of society."

Karl Marx described these quantities of labor being expended in each industry as "socially necessary".

A Personal Note: My Mind Is Going. I Can Feel It.

So my computer crashed. I hadn't backed it up in a while. But, even so, my backup failed, too. I am currently paying for some specialist organization to restore the data, and they are on their third attempt. The cost seems a lot for an individual, but I feel like I need a lot that is on it.

I am going to buy a new computer, and I have been slow about this. Until I do this, I will not be able to post any mathematical examples. I think that I have posted enough that I can recreate these examples. But I have lost draft introductions and conclusions not in posts. This is always my difficulty, and what I had should probably have rewritten those parts anyways.

I have also lost code, some for applications I do not recall. I have lots of PDFs, some for works I have also in books. I had downloaded PDFs for collected works of Ricardo, Marx & Engels, and Lenin. I am not sure whether these are still freely available.

Anyways, maybe I will post less frequently for quite a while.