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.