Welcome

I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Wages, Employment Not Determined By Supply And Demand

1.0 Introduction

I do not think I have presented an introductory example in a while in which an increased wage is associated with firms wanting to employ more labor, given the level of net output. This example is presented as a matter of accounting for a vertically integrated firm.

Exact calculations with rational numbers are tedious in this example. I expect that if anybody bothers to check this, they would use a spreadsheet. As far as I can tell, Microsoft Excel uses double precision floats.

2.0 Technology

The managers of a competitive, vertically-integrated firm for producing corn know of the four production processes listed in Table 1. Corn is a consumption good and also a capital good, that is, a produced commodity used in the production of other commodities. In fact, iron, steel, and corn are capital goods in this example. The first process produces iron, the second process produces steel, and the last two processes produce corn. Each process exhibits Constant Returns to Scale (CRS) and is characterized by coefficients of production. Coefficients of production (Table 1) specify the physical quantities of inputs required to produce the specified unit output in the specified industry. All processes require a year to complete, and the inputs of iron, steel, and corn are all consumed over the year in providing their services so as to yield output at the end of the year. The data on technology are taken from a larger example.

Table 1: Technology

Input	Process
	a	d	e	f
Labor	1/3 person-year	7/20 person-year	1 person-year	3/2 person-year
Iron	1/6 ton	1/100 ton	1 ton	0 tons
Steel	1/200 ton	3/10 ton	0 tons	1/4 ton
Corn	1/300 bushel	0 bushel	0 bushels	0 bushels
Output	1 ton iron	1 ton steel	1 bushel corn	1 bushel corn

The managers of the firm have available two techniques for producing corn from inputs of labor, with intermediate inputs being constantly replaced. The iron-producing, steel-producing, and first corn-producing processes are operated in the Gamma technique. The second corn-producing process, as well as the iron and steel-producing processes, are operated in the Delta technique. Iron, steel, and corn all enter, either directly or indirectly, into the production of corn in both techniques. Vertically-integrated firms can also operate a linear combination of the Gamma and Delta technique.

3.0 Quantity Flows

One can consider various levels of operations in each of the processes for each of the technique. I consider two examples of snychronized production, in which inputs of labor simultaneously produce a net output of corn for consumption. A structure of production, consisting of specific capital goods, intervenes between the inputs and output. The labor input reproduces that structure, as well as producing the output.

3.1 Gamma Quantity Flows

Suppose 14,000/11,619 ≈ 1.205 tons iron are produced with the first process, 100/11,619 ≈ 0.0086 tons steel are produced with the second process, and 34,997/34,857 ≈ 1.004 bushels corn are produced with the third process. Then the quantity flows illustrated in Table 2 result. 14,000/11,619 tons iron are used as inputs among the three industries. These inputs are replaced by the output of the iron-producing process. 100/11,619 tons of steel are used as inputs among the three industries, and these inputs are replaced by the output of the steel-producing process. 140/34,857 bushels of corn are used as inputs among the three industries, leaving a net output of one bushel corn. In short, these quantity flows are such that 49,102/34,857 ≈ 1.409 person-years produce one bushel corn net. Obviously, I did not pick a very good set of coefficients for this example to support exact calculations in rational numbers.

Table 2: Vertically-Integrated Production with the Gamma Technique

Input	Process
	a	d	e
Labor	14,000/34,857 person-year	35/11,619 person-year	34,997/34,857 person-year
Iron	7000/34,857 ton	1/11,619 ton	34,997/34,857 ton
Steel	70/11,619 ton	30/11,619 ton	0 tons
Corn	140/34,857 bushel	0 bushel	0 bushels
Output	14,000/11,619 ton iron	100/11,619 ton steel	34,997/34,857 bushel corn

3.2 Delta Quantity Flows

Suppose 100/23,331 ≈ 0.00429 tons iron are produced with the first process, 25,000/69,993 ≈ 0.3572 tons steel are produced with the second process, and 69,994/69,993 ≈ 1.00001 bushels corn are produced with the fourth process. By the same logic as above, these quantity flows are such that 1807/1111 ≈ 1.626 person-years produce one bushel corn net.

Table 3: Vertically-Integrated Production with the Delta Technique

Input	Process
	a	d	f
Labor	100/69,993 person-year	1,250/9,999 person-year	34,997/23,331 person-year
Iron	50/69,993 ton	250/69,993 ton	0 ton
Steel	1/46,662 ton	7,500/69,993 ton	34,997/139,986 tons
Corn	1/69,993 bushel	0 bushel	0 bushels
Output	100/23,331 ton iron	25,000/69,993 ton steel	69,994/69,993 bushel corn

4.0 Prices

Which technique will the managers of the firm choose to adopt? By assumption, they take the price of corn and the wage as given on the consumer and labor markets. For simplicity, assume that price of a bushel corn is unity. That is firms treat the price of the consumer good as numeraire. At the end of the year, firms own a stock of iron, steel, and corn. They sell some of the corn to consumers. They retain the iron, steel, and enough corn to continue production the next year.

In a consistent accounting scheme, the price of iron and steel are such that:

• The same (accounting) rate of profits is obtained in all operated processes.
• The cost of the inputs, per bushel corn produced gross, for the corn-producing process not operated for a technique does not fall below that for the operated process.

The first condition specifies prices of intermediate goods and the rate of profits the accountants register. The second condition states that no pure economic profits can be obtained. Under these conditions, the managers of the firm can price their capital stock at the end of any year.

4.1 Prices at a Low Wage

Suppose the wage is w = 19,296/352,547 ≈ 0.05473 bushels per person-year. The accountants set the price of iron at p₁ = 6,860/27,119 ≈ 0.2530 bushels per ton iron and the price of steel at p₂ = 76,454 ≈ 2.819 bushels per ton steel. Table 4 shows the cost per unit output for each process and the resulting rate of profits obtained by operating each process. In constructing the tables for price systems, wages are assumed to be advanced. Under these assumptions, the rate of profits is 9/4, that is 225 percent, in each process comprising the Gamma technique. A lower rate of profits is obtained in the remaining corn-producing process, and it will not be operated. This is a consistent accounting system for the vertically-integrated firm, given the wage.

Table 4: Costs and the Rate of Profits at a Low Wage

Process	Cost	Rate of Profits
a	(1/6)p1 + (1/200)p2 + (1/300) + (1/3)w = 27,440/352,547	225 percent
d	(1/100)p1 + (3/10)p2 + (7/20)w = 305,816/352,547	225 percent
e	p1 + w = 2,308/7,501	225 percent
f	(1/4)p2 + (3/2)w = 554,839/705,094	≈ 27.1 percent

4.2 Prices at a Higher Wage with the Original Technique

Now suppose the wage is higher, namely w = 1,332/5,197 ≈ 0.2563 bushels per person-year. Consider prices of p₁ ≈ 0.2622 bushels per ton iron and p₂ ≈ 0.4167 bushels per ton steel. Table 5 shows cost accounting for these prices.

Table 5: Costs and the Rate of Profits at a High Wage (Incomplete)

Process	Cost	Rate of Profits
a	0.141 Bushels per ton iron	85.9 percent
d	0.2241 Bushels per ton steel	85.9 percent
e	0.5379 Bushels per bushel	85.9 percent
f	0.5178 Bushels per bushel	93.1 percent

Notice the same rate of profits is obtained in operating the first three processes. But the cost of producing a bushel corn with the last process is lower than in producing corn with process e. A larger rate of profits is obtained in operating that process. The managers of the firm will realize that their accounting implies that the Delta technique should be operated. If this firm were not vertically integrated and iron and steel were purchased on the market, a market algorithm would also lead to the Delta technique being adopted at this wage.

4.3 Prices at the Higher Wage with the Cost-Minimizing Technique

Continue to consider a wage of w = 1,332/5,197 ≈ 0.2563 bushels per person-year. The accountants report prices of p₁ = 1,420/5,197 ≈ 0.2732 bushels per ton iron and p₂ = 2,402/5,197 ≈ 0.4622 bushels per ton steel. Table 6 shows costs per unit output for the five processes under these prices.

Table 6: Costs and the Rate of Profits at a High Wage

Process	Cost	Rate of Profits
a	710/5,197	100 percent
d	1,201/5,197	100 percent
e	2,752/5,197	≈ 88.8 percent
f	1/2	100 percent

With this set of prices, the Delta technique is operated, and a rate of profits of 100 percent is obtained. The cost of operating the first corn-producing process exceeds the cost of operating the corn-producing process in the Delta technique. With a higher wage, the managers of a cost-minimizing firm will choose to operate a corn-producing process that requires more labor per bushel corn produced gross. (3/2 person-years is greater than 1 person-year.) More labor will also be hired per bushel corn produced net.

5.0 Conclusion

Table 7 summarizes these calculations. The ultimate result of a higher wage in the range considered is the adoption of a more labor-intensive technique. If this firm continues to produce the same level of net output and maximizes profits, its managers will want to employ more workers at the higher of the two wages considered. So much for the theory that, given competitive markets, wages and employment are determined by the interaction of well-behaved supply and demand curves on the labor market.

Table 7: A More Labor-Intensive Technique at a Higher Wage

Wage	Technique	Labor Intensity
0.05473 bushels per person-year	Gamma	1.409 person-years per bushel
0.2563 bushels per person-year	Delta	1.626 person-years per bushel

This example can be generalized in many ways. Different types of labor can be introduced. More intermediate produced capital goods can be included. Any number of processes can be available for producing each good, including an uncountable infinity. The use of fixed capital introduces more complications. The introductory marginalist textbook story about wages and employment in competitive markets is without foundation.

Why do so many economists teach nonsense?

Alienation And Commodity Fetishism

Marx, in Theories of Surplus Value, quotes James Stuart writing about 'profit upon alienation'. When one sells a good one owns, one has alienated it from oneself. In the typical work relation under capitalism, the managers of firms, that is, the representatives of capitalists, sell the product or services that workers produce. Workers do not own the goods they produce, for they have previously sold their labor-power. That is, they have agreed that their product is not owned by themselves, and neither is their labor.

But alienation means something more in Marx's Paris Manuscripts. The work of Ludwig Feuerbach is important background here. (By the way, this post is based mostly on secondary and tertiary literature, I forget which. I have not read most of the Marx and Engels' works cited here in some time.)

Feuerbach's criticism of Christianity is of some importance for Marx's concept of alienation. According to Feurbach, God's human-like qualities of knowledge, wisdom, and power are projections of extensions of human qualities. We impose them on God. This result of the projection of human qualities is then taken as ruling over us.

Capital goods are themselves the result of human labor. But, in capitalism, the alienated worker is then ruled by these products of human labor. In both cases, human do not usually understand that they are ruled by an entity created collectively by themselves.

The word 'alienation' never appears in the three volumes of Capital as I understand it. Instead, Marx writes about commodity fetishism. I guess the continuity I am claiming is debated among scholars of Marx. But the following sounds like alienation, as developed from the ideas of Feuerbach, to me:

"A commodity is therefore a mysterious thing, simply because in it the social character of men's labour appears to them as an objective character stamped upon the product of that labour; because the relation of the producers to the sum total of their own labour is presented to them as a social relation, existing not between themselves, but between the products of their labour. This is the reason why the products of labour become commodities, social things whose qualities are at the same time perceptible and imperceptible by the senses... with commodities... existence of the things qua commodities, and the value relation between the products of labour which stamps them as commodities, have absolutely no connection with their physical properties and with the material relations arising therefrom. There it is a definite social relation between men, that assumes, in their eyes, the fantastic form of a relation between things. In order, therefore, to find an analogy, we must have recourse to the mist-enveloped regions of the religious world. In that world the productions of the human brain appear as independent beings endowed with life, and entering into relation both with one another and the human race. So it is in the world of commodities with the products of men's hands. This I call the Fetishism which attaches itself to the products of labour, so soon as they are produced as commodities, and which is therefore inseparable from the production of commodities.

The religious analogy suggests, perhaps, that this supposed relation between things appears as a independent being. That is, capital is an entity with seeming agency and its own logic. Marx uses such metaphors as zombies, vampires, and table-turning for this spectral creature. "Capital comes dripping from head to foot, from every pore, with blood and dirt." In a longer exposition, I would also want to go the formal and real subsumption to capital.

It may seem odd to talk about capital as a creature with agency. Many human beings, following certain protocols, can implement a Turing machine, unbeknowest to themselves. The analogy of markets to a computer is harly novel. More prosaically, every manager or firm owner who justifies layoffs; the closure of factories, stores, and offices; or the abandoment of one line of business and the start up of another is appealing to some such logics of capital. Whatever you may think of such people, they are not wrong in claiming to be ruled by an overarching entity.

Capital is not the only supra-personel entity, discussed among Marxists, that seems to have agency. Hardt and Negri's Empire also seems to be such an entity.

I think that Marx condemns capitalism, inasmuch as he does, because he objects to the rule of capital as a supra-personel entity. This creature is constructed by human beings, and we should be able to rule ourselves without such illusions. The rule of this creature hardly seems consistent with a society in which "the free development of each is the condition for the free development of all."

Precursors Of The Modern Revival Of Classical Political Economy

A revolution occurred in price theory about two-thirds of a century ago. Several scholars independently developed components of this revolution. This post merely lists selected literature. I have previously tried to briefly describe why some of these authors are precursors.

• Ladislaus von Bortkiewicz (1907) On the correction of Marx's fundamental theoretical construction i the third volume of Capital. Translated and reprinted by Sweezy.
• David G. Champernowne (1945-1946) A note on J. V. Neumann's article on "A model of economic equilibrium". Review of Economic Studies 13 (1): 10-18.
• Georg von Charasoff (2010) Das System des Marxismus: Darstellung und Kritik. Berlin: H. Bondy.
• V. K. Dmitriev (1974) Economic Essays on Value, Competition, Utility. English Trans.
• Walter Isard (1951) Interregional and regional input-output analysis: A model of a space economy. Review of Economics and Statistics 33 (4): 318-328.
• Wassily Leontief (1928). The economy as a circluar flow.
• Maurice Potron (2010) The Analysis of Linear Economic Systems: Father Maurice Potron’s Pioneering Works (ed. by Christian Bidard and Guido Erreygers). Routledge.
• Jacob Schwartz (1961). Lectures on the Mathematical Method in Economics. New York: Gordon & Breach.
• Piero Sraffa (1960) Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory Cambridge
• John Von Neumann (1945-1946) A model of economic equilibrium. Review of Economic Studies 13 (1): 1-9.

Elsewhere

• Prof. Rowena Ball teaches a course on indigenous mathematics at Australian National University.
• Prof. Caroline Fohlin, an economics professor at Emory University, is arrested for being assaulted by rioting police.
• Prof. Tim Garrett questions the units of measurement in aggregate production functions. Aggregate production functions are not laws of nature, and those not in a broken discipline should not be thrown by questions about units of measurement. Maybe some production functions make sense as limit cases of linear combinations of Leontief production functions.
• Daniel Kahneman has died.
• Deirde McCloskey asserts, without cogent argument, that the labor theory of value is wrong. In what units do you imagine the marginal product of capital is measured?
• Andy Merrifield has an article, "Gramsci and his friend 'S'", in Monthly Review.
• Branko Milanović reminisce about a neo-Ricardian study group in communist Yugoslavia.

Update on 1 May: Added link to Andy Merrifield essay,

Marxian Political Economy As Forward-Looking

Every child knows a nation which ceased to work, I will not say for a year, but even for a few weeks, would perish. Every child knows, too, that the masses of products corresponding to the different needs required different and quantitatively determined masses of the total labor of society. That this necessity of the distribution of social labor in definite proportions cannot possibly be done away with by a particular form of social production but can only change the mode of its appearance , is self-evident. No natural laws can be done away with. What can change in historically different circumstances is only the form in which these laws assert themselves. And the form in which this proportional distribution of labor asserts itself, in the state of society where the interconnection of social labor is manifested in the private exchange of the individual products of labor, is precisely the exchange value of these products. -- Karl Marx to Dr. Kugelmann, 11 July 1868

The above quotation is a pithy statement of a pre-analytical vision. The ideas underlying this vision are interesting, independently of what you may think about the details of Marx's theory of value.

One can start to explicate these ideas with a one-commodity model. Accordingly, consider an economy in which one commodity, corn, is produced. Suppose production takes one year. Let a₀ be person-years of labor needed to produce a bushel corn. Let a be the bushels of seed corn needed to produce a bushel corn. Assume labor is necessary to produce corn:

a₀ > 0

Assume that a surplus product is produced, in that more than a bushel corn is produced for every bushel of seed that is planted:

0 < a < 1

The table below shows how each person-year of workers hired by the capitalists are allocated.

Distribution of a Work in the Current Year

Labor Time	Purpose
1 - a	To produce (1 - a)/a0 commodities to consume at the end of the current year.
a (1 - a)	To produce capital-goods to be used to produce (1 - a)/a0 commodities to consume at the end of the next year.
a2 (1 - a)	To produce capital-goods to be used to produce capital goods to produce (1 - a)/a0 commodities to consume at the end of two years hence.
a3 (1 - a)	To produce ... (1 - a)/a0 commodities to consume at the end of three years hence.
. . .	. . .

Recall the sum of a geometric series:

1 + a + a² + a³ + . . . = 1/(1 - a)

So some algebra shows that the labor expended at a moment of time for the purposes shown in the table is indeed one person-year.

This is very simple, of course. The heterogenous nature of capital goods is not shown, even though such heterogeneity is essential for the full articulation of these ideas. In a capitalist economy, nobody is in charge of ensuring that the labor force is allocated so as to produce commodities for consuming now and in the future. The social division of labor comes about through participants responding to prices, orders, contracts, and so on, as they perceive them. A structure of production exist at any moment of time, refracting (not necessarily consistent) plans and expectations about what can be sold in the future.

Even in this simple example, variations can be introduced. Suppose the economy is expected to grow. And suppose that one expects technical progress to reduce one or both coefficients of production at some rate. Then the allocation of labor would not be as in the table. Pasinetti's vertically hyper-integrated sectors help in the analysis here.

Another question is if the plans implicit in the allocation of labor at a moment in time will be realized in the years to come. This realization depends on the mix of decisions to consume and save, now and in time to come. But those decisions are constrained by income, which depends on the decisions to hire workers for wages today. An independent equilibrium does not exist that is just being followed by agents in the economy. Instead, possible and actual future paths are being laid down, tile by tile, plank by plank. Thus, as Paul Davidson has argued, Post Keynesians have an appreciation of the distinction between uncertainty and risk that economists of the Austrian school lack.

Austrian School Claims About The Period Of Production And Capital

1.0 Introduction

Economists of the Austrian school generally retain some concept that lower interest rates incentivize capitalists or entrepreneurs to adopt more lengthy production processes, in some sense, while still rejecting aggregate physical measures of roundaboutness or capital intensity. This post collects some quotations of economists of the Austrian school or Austrian-adjacent saying such or saying something confused about the Cambridge Capital Controversy. I want to recall this post.

2.0 Hayek on the Mythology of Capital

Hayek's 1936 paper is, I think, often cited by Austrian economists. I can agree with the following:

"The basic mistake – if the substitution of a meaningless statement for the solution of a problem can be called a mistake – is the idea of capital as a fund which maintains itself automatically, and that, in consequence, once an amount of capital has been brought into existence the necessity of reproducing it presents no economic problem. According to Professor Knight, 'all capital is normally conceptually, perpetual,' 'its replacement has to be taken for granted as a technological detail,' and in consequence 'there is no production process of determinate length, other than zero' or 'all history,' but 'in the only sense of timing in terms of which economic analysis is possible, production and consumption are simultaneous.'" Hayek 1936: 201-202.

I think Bohm-Bawerk has a metaphor of capital as like a lake, with a stream flowing in and another one out. The streams may have the same volume of water flowing at the same rate, but the depth of the lake still matters.

Here is a less well-posed objection Hayek has to Knight:

"it is asserted that 'making an item of wealth more durable' or 'using a longer period of construction,' i.e. lengthening the time-dimension of investment in either of the two possible ways, is only one among an 'accurately speaking, infinite number' of possible ways of investing more capital, which are later even described as 'really an infinite number of infinities.'" Hayek 1936: 202

And here Hayek clearly makes a mistake:

"An increase of capital will always mean an extension of the time dimension of investment, that capital will be required to bring about an increase of output only in so far as the time dimension of investment is increased." Hayek 1936, p. 204

Hayek is considering the analysis of the choice of technique in a given state of technical knowledge:

"It should be quite clear that the technical changes involved, when changes in the time structure of production are contemplated, are not changes in technical knowledge." Hayek 1936: 205

And here Hayek rejects Böhm Bawerk's measure of the period of production:

"It is not proposed, and is in fact inadmissible, to reduce the description of the range of periods for which the different factors are invested to an expression of a single time dimension such as the average period of production." Hayek 1936: 206

3.0 de Soto on Reswitching

I skip ahead to this century. Here is a deeply confused quotation:

"growth in voluntary saving always causes, in prospective terms, a ‘lengthening’ of the productive structure, irrespective of whether techniques which were only profitable at higher interest rates are readopted in certain new investment processes - all initial factors (land, labor, and existing capital goods) are subjectively deemed to be 'original means of production' which merely determine the starting point of the production process. It is therefore irrelevant whether or not the new investment process incorporates techniques which, considered individually, may have been profitable at higher rates of interest." de Soto (2006)

Considering which techniques are cost minimizing at different rates of interest is an analysis conducted in a comparision of long period positions. It is questionable if it even makes sense to talk about an interest rate on money in an intertemporal equilibrium, that being the model in which initial quantities of capital goods are given. Some fans of Austrian economics have recently injected confusion into the entry on the Cambridge Capital Controversy. De Soto is certainly a 'reliable source', though, in Wikipedia terms.

4.0 Yeager on the CCC

Leland Yeager was, at least, sympathetic to the Austrian school. He re-introduced something like a period or production, where that period depends on prices:

"The paradoxes dissolve when we recognize that the amount of that factor required in a physically specified production process does indeed depend on its own price." (Yeager 1976)

I do not think his definition is clear. He calls this measure 'waiting':

"We have to recognize waiting as a factor of production—the tying-up of value over time." (Yeager 1976)

And he is clear about how it is dependent on prices:

"the amount of waiting required in accomplishing a physically specified purpose does depend on its own price." (Yeager 1976)

In their response to comments on their retrospective, Cohen and Harcourt say, as I recall, that Yeager misunderstood the issues. Traditional marginalist theory is about the allocation of given resources. Those given resources are land, labor, and capital. What does it mean to talk about a given quantity of capital in the theory? Yeager's waiting does not help answer this question.

At any rate, Yeager recognizes consumption-reversal remains a challenge:

"One paradox not cleared up to my full satisfaction concerns consumption... It seems inadequate to reply that labor is not the only factor of production and that the higher output per man in [a] technique ... does not, at all interest rates, mean higher output in relation to labor and waiting together." (Yeager 1976)

Yeager claims that not fully specifying a traverse limits the CCC:

"Standard theory need not be embarrassed by stories that do not even say how the interest rate is determined and changed, why one economy might be in a steady state employing one technique and an otherwise similar economy in a steady state employing another, or how an economy might make a transition between such states." (Yeager 1976)

I conclude with one more quotation:

"the concept of an aggregate of physical capital is inherently fuzzy. Some capital goods are always being worn out and scrapped, and new ones are always being constructed. Whether the aggregate is growing or shrinking or staying unchanged may be hard to say, especially since unforeseen changes in technology and tastes are always occurring and raising or lowering the market values and the genuine usefulness of particular capital goods." (Yeager 1976)

5.0 Cachanosky and Lewin

Cachanosky and Lewin champion an old measure of the period or production:

"It is the (present-) value-weighted amount of time involved in the investment. As such, it is a money-value of time measure. It can be easily show that it is also the elasticity of the NPV with respect to the discount factor f. Therefore, Duration (D) can be interpreted as a measure of 'roundaboutness' and also of the sensitivity of the value of the investment to changes in the interest rate." (Lewin and Cachanosky 2019b)

I know this measure from Hicks' Value and Capital. They also cite Macaulay, a researcher in finance about contemporary with Hicks' work. Duration depends on prices. Fratini recalls that this measure requires a division of zero in an equilibrium. I have noticed a lack of appreciation of the wage-rate of profits frontier in some literature from Austrian school economists.

Anyways, they present Duration in the context of Austrian business cycle theory:

"In its most generic form, the ABCT posits a scenario in which, because of an unsustainably low discount rate, many investors mistakenly invest in unsustainable (ultimately unprofitable) ventures. A surge of investments characterized by higher Durations as a result of the lower rate of discount, is followed eventually by a surge of business failures reversing this trend, bouncing back to lower Duration, safer, investments. Regardless of whether the Duration of some investments rise more or less than others, thus changing the ranking of ventures in terms of their Durations, investors are in general choosing higher duration investments." (Lewin and Cachanosky 2019b)

I am not sure quite what is being claimed in that last sentence, especially with the phrase, "in general".

Anyways, they resist explicitly equating Duration to a measure of the quantity of capital, although I thought that was the point:

"our definition of capital does not suggest that more capital and less labor is implied by an increase in Duration. These are the very aggregate concepts that are rejected by our approach." (Lewin and Cachanosky 2019b)

Consumption reversal might still be an issue for Cachanosky and Lewin.

6.0 Conclusion

I do not know how much more literature I want to look at. Above, I have nothing to say about Hayek's triangles or Hayek (1941). I skip over Roger Garrison's more recent book, too, and much more. Apparently, Cachanosky and Lewin have an even more recent book where they might have a response to Fratini.

References

• Cachanosky, N and P. Lewin. (2018). The role of capital structure in Austrian business cycle theory. Journal of Private Enterprise, 8(2): 268–280.
• de Soto, J. H. (2006). Money, Bank Credit, and Economic Cycles, 1st English ed. (trans. by M. A. Stroup) Auburn: Ludwig von Mises Institute.
• Fratini, S.M. (2019a) A note on re-switching, the average period of production and the Austrian business-cycle theory. Review of Austrian Economics. 32 (4): 363-374
• Fratini, S.M. (2019b) Re-switching and the Austrian business-cycle theory: A rejoinder. Review of Austrian Economics. 32 (4): 368-389.
• Hayek, Friedrich A. (1936). The mythology of capital. Quarterly Journal of Economics 50: 199-228.
• Hayek, Friedrich A. (1941). The Pure Theory of Capital. Chicago: University of Chicago Press.
• Lewin, P. and Cachanosky, N. (2019a) Austrian capital theory: A modern survey of the essentials. Cambridge: Cambridge University Press.
• Lewin, P. and Cachanosky, N. (2019b) Re-switching, the average period of production and the Austrian business-cycle theory: A comment on Fratini. Review of Austrian Economics. 32 (4):375-382.
• Yeager, Leland B. (1976). Capital paradoxes and the concept of waiting. In Time, Uncertainty, and Disequilibrium: Exploration of Austrian Themes (Ed. by Mario Rizzo). Lexington: D. C. Heath.