profit rate of marx the "ricardo effect" of hayek and model du pont.pdf

7/29/2019 profit rate of Marx the "Ricardo Effect" of Hayek and model Du Pont.pdf

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Parallels between the profit rate ofMarx, the "Ricardo Effect" of Hayek,

and model Du Pont

by: Carlos E. Pascuali

Universidad Nacional de Rosario - 2009

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1 S u m m a r y

This paper attempts to make use of the statement by Paul Samuelsonthe existence of analogies between the basic structures of different theo-ries: ... Implies the existence of a general theory to underpin to indivi-duals and one with respect to these central characters. It attemptsto explain the symmetries and parallels between different approachesto determining the rate of profit. To demonstrate these parallels betweenparticular approaches, is the first step toward finding of what Samuelsoncalled the general theory, which would unify the analysis considereddifferent theories. The approaches discussed here are: the determina-tion of the rate of gains in the price level of production that Marx madein the Book III of Capital. Determination that is going to take place,inter alia, the problem called transformation of values into prices ofproduction. The called Du Pont model system or the return on equity

companies, widely used system in the world of corporate finance andfinally the model used by F. Hayek in his article The Ricardo effect.

Equal the rate of profit according to the approaches is trivial, butwhat is not a triviality when we define the rate of gain as a functionof the spin yield multiplied by the number of turns taken in the year.First we will present briefly the three approaches and then analyze theirequivalents, and possible theoretical linkages, holding that lead to thesame results and, more significantly, the same view of the situationsunder analysis. Moreover be discussed considering that such modes of

determining the rate of gain, fall in conflict with the neoclassical produc-tion function within certain limits and if certain units of measurement.They try to emphasize that analysis approaches in the emphasis placedin the variable CAPITAL TURNOVER.Or average product of capital(PMEK) and analytical importance has failure limit, or homogenization,the duration of the production processes equal to a period of time,considering different durations of cycles productive. Moreover significantnumerical problems should be taken in the theoretical, as employed bythese authors and by Ricardo and Wicksell , And apply the formulationsin question analysis.

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Keywords: Symmetry theoretical parallels between different approa-ches, determination the rate of profit, Du Pont, Marx, Hayek, Ricardoeffect, Ricardo, Wicksell. Capital turnover. Temporal duration of pro-

duction cycles. rate profit (g) as a function of turnover rate (r) and thenumber of turnover annual capital (n):G(r, n) = rn.

Summary 3


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ndice1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Justification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Historical introduction to the subject . . . . . . . . . . . . . 93.1 The development of the concepts in the area of finance . . . 9

3.1.1 What concept of capital used in financial theory . . . 103.1.2 Hamilton Macfarland Barksdale. A mental revolution: thehistorical origin of the Du Pont formula . . . . . . . . . . . . 113.1.3 The concepts of flow and rotation in the paradigm Du Pont

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 The notion of a capital in the Austrian theory . . . . . . . 17

3.2.1 The background: W. S. Jevons and the average period ofproduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.2 Analysis of K. Wicksell average period of production. . 243.2.3 Wicksell to Hicks and capital measurement within the Aus-trian approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Hayeks model on the Ricardo effect . . . . . . . . . . . . . . 293.3.1 Hayek Model Assumptions . . . . . . . . . . . . . . . . . 293.3.2 Conclusion on Hayek model . . . . . . . . . . . . . . . . 33

4 The rate of profit in Marx . . . . . . . . . . . . . . . . . . . . . 34

4.1 Background: David Ricardo. . . . . . . . . . . . . . . . . . . . 344.2 Capital and time in Karl Marx . . . . . . . . . . . . . . . . . 394.3 Some conclusions on the model of Marx of rate of profit. . 50

5 Comparative of formulations. . . . . . . . . . . . . . . . . . . 50

5.1 Comparative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2 Application of the formulas compared . . . . . . . . . . . . . 54

5.2.1 Wicksells problem and the rate of profit. . . . . . . . 555.2.2 The problem of Ricardo and the issue of machinery . 57

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5.2.3 On the transformation of values of commodities into pricesof production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.3 The formula "M-DP-H" and the production function . . . 69

6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7 Bibliographic references . . . . . . . . . . . . . . . . . . . . . . 78

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2 Introduction

Among the different formulations for the determination and ex- com-

plication rate of corporate profitability are the denominado Du Pontsystem [66], the formulation made by C. Marx in Book III of Capital[35] and arising from the article by Professor F. Hayek called Ricardoeffect [19] which relates variations in the rate of return with variations inthe periods of rotation of capital. When comparing the same are certainparallels form and the use of similar variables.

Thus, for example, three are characterized by giving a marked- phasisto the category of rotation, giving relevance to the spin cycles assets,

sales, etc., which enter as variables in the three forms formulations. Marxwill develop his famous expression DMD 1, in which incorporatesthe time of rotation and on which its sits formulation of the gain, theDu Pont system relies on the consideration of the company as a systemof fund flow, and the Hayek article used as one of the key variables tospeed of capital.

However, these formulations belong to or are part of theoreticalapproaches that are often considered different and even contra- posts,and they are used in different dimensions of analysis: while the deve-

lopment of Marx and Hayek they have been used in preference to levelof economic aggregates, Du Pont system it uses micro economically. Inaddition to comparing and analyzing whether the variables em- ployedare the same conceptually, and fulfill the same roles in the three for-mulations, one wonders whether the use of the three formulas- mules,starting from the same business data, lead to equal explanations andpredictions. In short: to analyze the cycle D M D as a pro-cess that occurs over time and highlight fundamental variable mentalnumber of rotations the capital, or assets are in a period of time, is what

will provide the foundation of the proposed relationship between thehypothesized gain formula Marx, the Du Pont and the article by Hayek.

2.1 Hypothesis

The hypothesis is that when you try to prove Marx says:

1. Spanish nomenclature is preserved:D M D

, rather than money-commodities-money; M C M.

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The sum of the values (plus values) is determined, the-refore, the value set in rotation multiplied by the numberof rotations in a given period. Rotation of capital is = the

production time + circulation time.

Is implying, in terms of values, so the system Du Pont, price level,noted in the expression:

ROE = ROS ATO

Where:

ROE return over equity

ROS return over sales profit

sales

ATO assets turn over sales

capital

And what Hayek expressed in the formula:

i=mt

i profit rate on capital

m profit rate per cycle

t annual turnover rate of assets

It is argued that the proper use of any of the three expressions describedabove, can reach the same conclusions, ie they have the same explana-

tory and predictive capacity. This is because the conceptual frameworkto see the production process as cycle or rotation of funds:

DMD+ D=D

constitutes the foundation and is behind the three formulations asinsight into the production process as feedback loop or reproductionof capital. As a secondary hypothesis arises to talk about D M D

as Marx and see the enterprise as a system of fund flow, the wayconsidered by modern financial management is the same.

Introduction 7


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2.2 Justification

This is a significant problem because it involves explicitly linking an

empirical and based on accounting data, which has become part of theFinancial Administration - the model ROE / ROI or Du Pont system -conceptual frameworks belonging to the economic theory: the RicardoEffect of Hayek and the approach made on the rate of profit in Book IIIof The Capital, belonging to Marx.

One hypothesis that attempt to demonstrate, as we noted, is thethree formulations have the same conceptual framework. Holding whichapplies the same conception, in case the hypothesis posed must be veri-fied, it would unify under one umbrella three different developmentsand considered non relacionados. In case is proved that the hypothesisproposed in advance knowledge of the differences of the three theoreticalschemes and what behind the appearance of similarity. Clearly thiswould a theoretical advance in the one case as in another.

Consider apply theoretical analytical tools such as the system DuPont, tried to explain and predict success at the micro level allow anefficient explanatory power of phenomena at macro. This is possible ifevidence theoretical relations existing. It is considered important for

employees to three developments determine the rate of return, whichnow run by lifts different and which is treated as belonging to com-partments watertight and not interconnected, they are related expresslywhich highlight the contact points which have in common.

It believes that this is going to generate mutual enrichment bet-ween theory and practical developments, the Du Pont system may haverelationships theoretical frameworks from which today lacks, while themodel called The Ricardo effect of Hayek and formulation on the

rate of gain made in Book III of The Capital by Marx, they can earnempirical applicability. Despite all the imperfections theory that mayarise regarding the use of variables in the mode used, by the Du Pontsystem, the majority of the authors considered relevant to the field offinancial management recognized to their best advantage the type ofdata used, which in practice business are those obtained with lower costand greater ease.

It believes that showing the proposed relationships can be shownthe impact on the relative prices movement along the cycle economic,because of variations in the rate of capital turnover. The important

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thing is that it could make from accounting data. The technical termfeedback loop. The characteristic of a feedback loop is that presents a setof causally connected elements in the that an initial cause propagates

cycle through the elements returning to the origin point at a time diffe-rent from initiation, and in which the end of a cycle giving rise to a newprocess.

3 Historical introduction to the subject

The basic concept in this analysis is the capital, many sometimes given

to it by sitting or not yet clear what is meant by it, or comparing con-cepts used by the authors with different meanings beyond the commonname occasionally used. Lets clarify under which senses applied theconcept of capital, Marx 2, prevailing financial theory and Hayek. Webegin by the area of finance and the Du Pont formula.

3.1 The development of the concepts in the area of

financeWhile financial theory began to emerge in late not until the nineteenthcentury marked the period between 1950 and 1970 that defined many ofits key concepts, tools and theories. Selecting a few authors hypothesizedthat the same founding authors and are basing this assumption on therelevance of work in the field of finance for the purpose of taking themDu Pont and the system as presented.

The authors chosen are: Ezra Solomon, Miller, Merton, Modigliani,

Alchian, Robicheck, Anthony, J. Fred Weston, J.C. Van Horne, allcontributions linked to an article significant in the field of financial eco-nomics. As we shall see Du Pont formula is developed in the corporatepractice in the end nineteenth century, but is institutionalized acade-mically and is reported on all for the work of these authors since 1950.but before entering the actual history should be clarified as were usedor still used in financial theory concepts, mainly the capital.

2. Not repeat hereinafter, in the context of this work, we understand the talk about

the categories used by Karl Marx (rate of profit, turnover, capital, etc.). the expressed andused in Book III of The Capital, unless otherwise indicated otherwise expressed.

Historical introduction to the subject 9
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3.1.1 What concept of capital used in financial theory

According to E. Solomon 3 assessing the return on investment orROI can be determined by evaluating the performance of every dollarinvested. This performance can be calculated in various ways. Someare based on accounting standards and other streams in discounted cash.The first way that explains [55] is that of accounting standards, wewill focus on this item because it is valid within the context of thiswork. ROI evaluations grounded in accounting standards is to mea-

sure some extent of utility, performance or profit on some measure ofexpenditure or investment, taking accounting data. The result is a rategenerally shown as percentages and therefore used both the denomi-nator and the numerator amounts expressed in the same type of units.

This "RATE" as is based on accounting data of the amount activitiesexpressed in the numerator and denominator, thus often called accoun-ting rate of return. And the same, how is it calculated?

Solomon notes that there are several ways to measure and all are

corstraight as each responds to different questions. There were at leastin the decades of the 50 , 60 or 70 generally accepted standards resultsto calculate the ROI4 and states that all are correct or valid, what isrequired is to specify clearly the method of calculation. this healthygeneral recommendation is ignored today. Ultimately argues that for-mula is simply a convention used in a professional practice.

In the second term in the field of concrete practice financial mana-gement in large corporations, from start twentieth century, took forma system of calculation and measurement of the rate corporate profitcalled ROE, acronym for: return over equity. The academic theory offinancial management in the sixties named in this development as DuPont system and incorporated it as a tool - sometimes unnamed - inmost of the relevant academic literature. Such as the works of F. Weston,Van Horne, Merton, and so on.

3. [Page 92 et seq]

4. Ibidem.Pgina 939.

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3.1.2 Hamilton Macfarland Barksdale. A mental revolution:

the historical origin of the Du Pont formula

The development of administrative and financial management paralleled

the historical formation of large corporations. Especially in the U.S.between 1880 and 1935 are developing guidelines for managing signifi-cant normally used in present. By taking large corporations relevance inthe collection of savings through issues of shares, bonds, etc.., and theconsequent development of markets and financial instruments; begin torequire certain information, primarily intended for the investing public.The information required, such as financial reports, etc.. involve a newform of management, management that will be characterized by relyingon quantitative data that allow vision of business progress. Within thatperiod of design administrative systems Barksdale said Hamilton Mac-farland ( 1861 to 1918). Lets look in detail at this point.

In the early twentieth century a group of executives: Pierre Du Pont,Amory Haskell and Barksdale were dedicated to making what wouldnow be called a re-engineering in the chemical company Du Pont deNemours. This process, which was analyzed in detail by Alfred Chan-dler, pioneer in the history of business in the U.S., began operating in thehigh explosives department of the company and consisted of application

of the concepts developed by Frederick W. Taylor on The Principles ofScientific Management in a premeditated manner.

H. M. Barksdale, who had just assumed as a manager general of thecompany, piloted this mental revolution, as has sometimes been referredto by authors such as John C. Rumm. Regardless of the particular issueat hand should be noted that this process of Du Pont is a milestonein the history of the administration and has been studied as a casetype of conflict management and organizational resistance to change, forexample by Professor Christiane history Diehi-Taylor of the University

of Minnesota.

Barksdale was who reorganized and led to positions featured on themarket at the Du Pont de Nemours, organized the systematic way ofmanaging that company who then was transferred its mode to GeneralMotors and through it, what is usually known as the Sloan system, themajority of U.S. corporations Among some administrative innovationsmade are the following:

coding in an internal manual of the "how-to" administrative ofDu Pont,



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establishing the Department of Product Development,

start analyzing purchases and set the workflow as tool,

inventory analysis and its rotation,

establish the market analysis department in 1906!!

hire economists to estimate the progress of the national economy,which implemented perhaps the first macroeconomic analysisdepartment in a private company,

placing technical services within customer! (which in sometimestakes it as an invention of the 80s),

all this was done successfully before 1910.

For Barksdale mode control business was measuring the return oninvestment of capital. Under his leadership a group of young executivesdevised a measurement system for this purpose.

This system was baptized, years later, as system Du Pont in honorof the corporation in which Donaldson Brown in 1903 (Disciple and sonof Hamilton Macfarland Barksdale), who occupied the role of SeniorExecutive Accounting, built the ROI model: the profitability of salesmultiplied by the annual turnover of assets. Later other Du Pont exe-cutives discovered the importance of another variable: the leverage orleverage: Total assets divided by equity capital and formed the ROEformula as it is known today day

Newton Fowler, citing a 1990 article in Selling & Sticney F. considersDonaldson Brown was the creator of the formula Du Pont , though someauthors interpret the inspiration was Hamilton Macfarland Barksdale,father-in-law, teacher and head of Donaldson Brown, as discussed above.The latter in his memoirs seem to support this interpretation as recog-nizing Barksdale great strategist of the managerial revolution createdby the Du Pont and after the first Great War would be continued in theGeneral Motors which extend to almost all large corporations5.

5. [3, pg.:151- 153]

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Anyway although Donaldson Brown can be considered as the creatorof the ROI formula, which is the basis of the system, who was notdrafted ROE mode, as noted earlier.Based on the analysis of Russell B.

Read on Return on investment. A guide to management decisions 6

and picture published in [54, page 203] was standardized in the mannerformula which can be displayed in the following figure 2.1:

The financial control system called Du Pont used accounting data,being the administrative department of the company data supplier. Thisled to consider Solomon Esra these charges as accounting rates of return7, as noted earlier. While there is much literature review of such feesas the pioneer accounting article Solomon & Laya, Measuring the pro-ductivity of the company: some systematic errors cos committed in the

rate of return in general all, even Solomon end up recognizing thepracticality, not easily suplantable of work down with accounting data8.

Figura 1. Du Ponts scheme

6. [NAA; June, 1954]

7. [55, page 92-93]

8. Solomon & Laya say: the ratio of net income to net assets per books, not a reliablemeasure, to estimate the overall performance of an investment. Furthermore this analysis

requires a certain amount of return on investment and No other way to measure thisconcept in a division or company.[49]

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Almost 40 years after the articles of Joel Dean Measuring the Pro-ductivity of Capital and The payoff period and the rate of profit of

M.J. Gordon, 19559

who initiated the critical accounting data usedin the formula Du Pont, Richard S. Teitelbaum [60] in an article inFortune April 1996 states that the largest U.S. industries still employDu Pont model, it is built with one of the indices of S & P 400, anddespite attempts to implement replacements to date no substitutes thathave neither the simplicity, elegance and practicality of the Du Pontformula.

9. [54, pages 21 to 31/48 to 56]

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With the development of computerized administrative systems suchSAP or equivalent, in which transactions are recorded in real time, thisformula has better support data. Beyond the problems of measurement

data is real time, the Current computerization reinforces the value ofDu Pont formula.

3.1.3 The concepts of flow and rotation in the paradigm Du

Pont

It is also important to note that Erich Helfert 10developed, amongothers, detail the concept of the company as a circulation system inthe form of funds usually represented today. The focus of the companyand fund flow system is closely linked to the model Du Pont and is anestimate of said formulation.

COMPANY

The Bell Telephone Co. of Pennsylvania

The Coca-Cola Company

Eli-Lilly

Ford Motors Company

Merck & Co.

Vick Chemical

Union Carbide

West Virginia Pulp and Papers Co.

COMPANY

Campbell Soup Company

Du Pont de Nemours

Federal-Mogul

General Electric Company

Rheem Manufactoring

The Timken Roller

Westinghouse Electric Corp

and so on

Tabla 1. List N.A.A

Du Pont system is generally used in two versions: Weighing the gainon equity - ROE - or pondering on Total Capital invested in the businessin question: ROI (return over investment). Both modalities, according tothe objective of the proby: posal, remain in daily use tools most corpo-rations to date11. The flow of funds approach is based on the recognitionof the next cycle.

10. [23]

11. [60]



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cash purchases production sales collection cash + cash

Rotation cycle or time consuming. Each of the above categories:cash, purchases, etc., Represents a stadium employee by moneycapital in successive transformations until reversion to the originalform.

For description of Du Pont formula used the publication of theNational Association of Accountants [41] intended for assessment ofhistorical and projected profitability of companies. This work was madeby the NAA with participation of 44 companies belonging different sec-tors or activities of these three preferred not to give to know his name,the 41 were named companies as listed in Table 1.

As you can see in the sample of companies in Table 1, companiesare not only globally but significant belonging to various productivesectors, the total interviewed 42 Du Pont system used to evaluate theirperformance.From the authors concerned and the work of the Du Pontformula NAA in version used is constructed as:

roe = (utility sales) (sales assets)

Of course the above expression assumes that no debt or passive, incase of considering the effect thereof include leverage constructing theformula as follows:

roe = (utility sales) (sales assets) (assets equity)

In this work, as Hayek and Marx did not consider the debts or liabi-lities since they vanish at the macro level, consider the equation given inaddition to first disregard liabilities assuming that there are the same,the same as the capital asset and roe roi.

What is the concept that gives NAA categories or variablesthat make up the formula at work mentioned above, such ascapital,equity, etc?. The answer is simple: The forty-two com-companies that use the return on equity to evaluate performance beenbased both profits and capital, in the figures in financial statements12.

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This has a logic beyond the theorethe above formulatical discussionthe quality of the figures, which should be the quantities to be used,that the ideal is to use the category of Capital goods and analyze

physical drives profitability and more beyond the problems of homoge-nization of the categories, companies using available data, with all itsflaws, are a reasonable guide for decision making. No class companiesworking with global production functions, marginal productivity themarginal productivity of capital and production factors. the decisionsand analyzes of what happened or what may happen - About decisionsinvolving capital and profitability-are taken with other tooling which themodel called Du Pont is the paradigm. Of course this does not meanthat is invalidated to production functions, etc., here arises only comfort

operational availability based on the figures of tooling that is widely usedand, moreover, that this model Du Pont with other denominations,has been used in economic theory.

3.2 The notion of a capital in the Austrian theory

Hayek was part of the so-called Austrian school of economy. Will

see below what they meant by capital and for that try to outline brieflythe line genetic concept from Jevons, Bohm-Baweck, Wicksell andHayek finally. Will attempt to show as authors like Jevons and Wicksellincorporated and used in its notion of capital in the Austrian theory ofcapital, the time variable, in the form of average of production period.

3.2.1 The background: W. S. Jevons and the average period

of production.

Jevons developed the theme of capital in his The Theory of PoliticalEconomy published in 1871 - with a second edition in 1879 - there pre-sented his concept of the average period of production Austrian schoolthen became famous. Capital defined as:

12. [41, pg.:11].Emphasis not on the rise.



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the set of commodities which are required to maintainmaintenance workers of any class or kind committed toworking13

practically defined as a wages fund but with the characteristic of notlimiting it to one year. For Jevons the time between the start and end ofan activity - understanding as to productive activity product realization- is supported by the capital. He considered this support function asintended:

...main but not only unique, of the capital...14

That is the word time constitutes significant variable. Expressedtwo concepts that the Austrian school will maintain over use of itsfamous triangular schemes:

the volume of invested capital (K), amount of a single dimension:capital.

and the volume of investment (I): amount of two dimensions: thecapital and time (t) which is applied during an activity specific.

The volume of invested capital (K) is expressed by the value of theordinate of the function F(t) = K(t) =kt where K =k, in continuousterms:

K

t=k. The capital investment volume is determined by multipl-

ying each increment of capital or investment for the period of time (ti)that this increase is invested:

K i=1

i=n

ti= volume of capital investment (1)

or when there is a flow reversal process, continuous or discrete, we have:

K

i=0i=n

tit0

tnK(t)dt

13. [26]

14. [26]

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This gives a well-known example, that if you are building a machineand everyday work is done at a salary equivalent four dollars daily forone year will be:

4 364 + 4 363+ 4 362+ + 4 1 = 265,720

however, in which units are measured 265,720 , following Jevons, arelbs / day and are applying the above formula (1). It can represent thevolume of capital investment in a diagram in which on the x-axis is timedto duration of investment and on the vertical axis K or volume amountof capital invested by time unit. If we have a function that representsthe investment flow rate continuously F= K(t) the resulting surface areaor under the curve F, measures the volume of investment during time t.

The value of the ordinate at each sample point of the absisa thevolume of capital (K ti) while the area under the curve shows thevolume of investment. In the example, the volume of capital after 364days is: 1456 equals the value of the ordinate of the straight by day 364for 4 pounds daily investment.

Indeed Jevons approaches the concept of numeral. the numeral is acategory used to calculate average account balance current bank, creditcards, savings, checking accounts commercial, etc.., and is not nothingbut the sum of the daily balances divided by the number of days. In our

example, the numeral is:

numeralN =I t =

t0

tn

K(t) dt

t (2)

To determine the amount of investment, in your example, Jevons willemploy the following methods, which give the same result. One is givesthe detailed above 265,720 lbs / day, but this sum is equivalent to:

surface=S=(base height) 2 = (364 4 364) 2=264,992 (3)

which is nothing else than the surface of the triangle formed by theunion of the plane with the maximum time and the value of ordinatefull time investment. The area of the triangle is equal to: 264,992, ifwe make the calculation of the definite integral of the line between 0and 364 his is equal to: 264,991.99. The discrepancy (265, 720 Vs 264,992) between formulas (2) and (3) or the surface S of the triangle is theknown difference between the surface of the rectangles making up thecalled Riemann sum and the area under the curve or straight.



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Definitely try to calculate what Jevons (t 2) or period meansof implementation of capital, which involves determining tacitly nowcalled numeral or average capital applied for a period of time. The

numeral, as noted above is the method employed by financial institutionsin America and Europe at least, to calculate average daily balancesfor a period of time, today. Both methods allow to obtain, given aninterest rate, the same amount of interests, have a fixed time and use theaverage capital of a lapse of time or use the middle period is thesame for calculating interest. Well see how the building gets its famousperiod means.

Taking the example gives the building a house, which the Jevonsused, will have noted that if:

W= total wagesT= total time investment

N = workerss= wage per workers= Total daily wages = average investment period

where:

s= s N =K =I (4)

W= s T= K (5)

=1

2 T (6)

W=s T W

T= s

K

T=I (7)

If work continues for n +1 days:If work continues for n +1 days:s+s2+s3+ + s(n+1) = K

In terms continuous the average period is deducted by:T0

Tn

s TdT= s

1

2 T2

(8)

Replacing in (8) by (7):

1

2 W T =K T

2 = investment volume = VI (9)

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The total investment volume VI is constructed as the product totalvolume of the wages or ordered at the time Tn (or K) by "Middle period"or:

12 W T =K T

2 = K =VI

Wand:

VI

W=

W

1

2 T

W

=1

2 T= (10)

We will see this more clearly following the example Blaug15 offers toaddress the issue 15 and see how you mix the concepts of average capital(K) to total capital K. Suppose that in a single-sector economy are:

=VI

W=

1

2 t

where:N = system number of workerI

=flow input= rate of investment per day =N W

w = daily wages

K = capital=

t=0t=n

Nt w

T= Total time

K =k= average capital

then:

I=N w

= VIK

= VII T

= VIT N w

= K 1

2 T

T N w= (11)

=T N w

1

2 T

T N w

=1

2 T (12)

15. [7] Blaug, in his extraordinary book points out that the production period through

a single-sector economy can be expressed as: =K

I, where K is the amount of real

capital, as shown by (4), (5) and (8/9) this is not so, this ratio is the production timewhich, in the examples is 2 .(pag.552-4).

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Consider a numerical example that will allow us to clarify whatabove:

N: 60 workersw: 2 wage unitsT: Total investment period of 10 days

by (11) and (12):

VI

K=

VI

I T=

VI

T N w

1

2 T2 =

VI

I=

VI

N w

1

2 T2 (N w) =VI (13)

Substituting (13) for the values assigned in the example:

VI=1

2 102 (602) =6000

Obviously this value of 6000 does not match what Jevons calledvolume of capital invested. Since this is the value of ordinate the lastday of the investment period (in the example the 10th) or as he calledthe height of the triangle in the charts above, for Jevons is:

K=t(N w)

Substituting the values of the previous example:10(60 2) = 1,200

That is, the value of the ordinate at t=10. We deepening do in thisarid exercise since the peculiar nomenclature used by Jevons has led tosome confusion. For example with the balance capital through, amongothers seem to Blaug, [7, p. 554] incurs this.

Now we can write the basic equation model Bohm-

Bawerk to develop Wicksell: = 12 t =k

N w

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or k=1

2 N w t. As a collection of physical elements,

capital is the cumulative result of1

2 N t man-years

of work. the total value of work tied up in the stock of

capital is precisely half the amount invested in the totalproduct an investment period 16

Applying the example gets values K = k= 600 ; ie average capital.It is obvious that the equality indicated by Blaug, paragraph afore-mentioned, performed using the average capital value of which has todifferentiate the physical heritage and it is this form that Jevons applied.

in the text quoted above, he says, wrongly:

The total value of work tied up in the stock of capital isprecisely the HALF of the amount invested in the totalproduct of an investment period

Clearly that is used in the passage quoted average capital and notcapital Total employee. It is the first concept, the average capital, whichwill used for determining the interest rate and put a system again

the importance of the time factor in the Austrian model. Caracteristicshared with Marxist models and formula Du Pont as we shall see. Butthe total value of work tied up in the stock of capital (not half) isequal the value invested in a period investment.

For Jevons the volume of capital is the total capital accumulatedor integral investment rate. The average balance of capital, or capitalenvironment, which today is used in the Most financial institutions, usedin the production time period or considered is:

k=[(s1 t1) +(s2 t2) + + (sn tn)]

i=1i=n ti

Where:

s = balance

t = time

i=1i=n

ti = T

The middle period or average period, , can also be seen as thearithmetic mean of the period time considered17.

16. [7,pag.554]



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3.2.2 Analysis of K. Wicksell average period of production.

We have analyzed how Jevons works implicitly with the averagebalance of capital, category, calculated in the same way, today is usedto determine the interests of savings banks, cards credit, etc.., worldwideWestern Financial. Well see Wicksells work and how it will discoverwhat is now called Wicksell effects (real and price) and the problem ofthe reversal of the techniques. But most significant of Swedish authorsanalysis, in the context of this thesis, is its capital concept and approach,in which the marginal productivity of capital is equal to the interest, so

you can not sustain a distribution theory based on marginal producti-vities.

Points out one aspect of the problem of capital, perhaps for the firsttime: the problem of measurement units. When measured at capitalamounts of exchange value performance - interest - is the species thus

constitutes a pure number. Unlike the above, the relationshipwages

workor

income

productf the earth, are heterogeneous quantities relations. Wicksell in

his analysis will use a production function Cobb and Douglas before.The form gives this function is as follows:

F= F(A , B , l , r) = A l+B r (14)

Where:A: number entry workersB: Acreage

l: wage per worker F

A

r: rent per acre F

B

It takes into account the timing of capital as follows:

F= F(A , B , At, Bt, l , r , lt, rt) F(A , B , l , r , t) (15)

Where:F

Atis partial derivative of the production function with respect

to the work of the year t: lt and so on. For the first time highlights,and this fact has been generally neglected in theoretical work, there isa validity to the individual entrepreneur in a context of perfect compe-tition is not maintained at a macro level18

17. In the above scenario we assume zero depreciation, and processes such as invest-ment in a stream and product at a point.

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This theory applies only to capital .... if seen from thepoint of view of the individual employer for whom wagesand rents are market-dependent data. If we start from

an increase (or perhaps decrease) of the total capital ofthe country, this will not be true if the correspondingincrease (or decrease) of the social product is the gover-ning interest rate19.

This is to take care with aggregate production functions that aregenerally ignored, and is a point that has relevance in our analysis. Butthe big difference with modern treatment of production function is thesignificance that gives the time. Wicksell temporal stratification timelyanalyzes of capital structure, and linking the interest rate and incomedistribution. Lets follow the example he gives himself in words Wicksellthis author methodology aims to:

The method that we will expose the interest will empha-size the importance of the time element, which is reallythe core of the concept of capital20

Wicksell taking a simple case in which factors production are usedonly once and then the product needs a period of storage, parking and

or maturation, as given in forestry, viticulture, cheese production, etc.,states the following. The function is capital, working capital, on a bac-kground of maintenance workers. If you know the total labor supplyand the total supply of land the only variable dimension of capital willtime.Assuming that: we have a closed economy, and occurs a singleproduct, the wine, which are exchanged with other countries remaininggoods, assuming it is determined by the market price parked wine, resul-ting in a time-dependent rate of aging (Pt) we have21:

Pt = P0 t Pt

P0 = t (16)

18. The emphasis is not on the original.It employs the same nomenclature that Wic-ksell.

19. [62. pag.133-4].

20. [62.pag.134] el resaltado no est en el original.

21. The fact consider a single product is not exclusive to Wicksell, the Swan and Solowmodels that gave rise to intensive macro production functions added (and subsequentdiscussion from the work of J. Robinson) are functions of a single product - the meccano as

Swan-still called in recent texts as the renowned Advanced Macroeconomics by Roemeror Economic Growth by Barro & Sala-i-Martin, used this type of functions.



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Supposed an annual production of one million hectoliters inputsbeing the only land and labor, and the price of wine P0 = wagest0 +

rentt0; the Wickselsample values are:P0 = 67P1 = 74P2 = 81P3 = 90P4 = 100P5 = 110

If we take the value of the must and multiply again by the rate of

price growth, given the values of the example, we to sell a wineVt=4,with four years of aging, it is necessary capital the following:

V0 V1 V2 V3 V4

K = 67[1.1050 + 1.1051 + 1.1052 + 1.1053] = 313.24

or what amounts to the same, for four periods:

K4 = 67 (1.1054 - 1 ) 0.105 = 313.24

But after a year, the entire stock of wine will be aged (aged) andincorporates a class K5 , the total value of the stock will be:

K5 = 67 (1.1055 - 1.105 ) 1.105 = 346.1327

The difference between these two amounts (K5 - K4)E 32.89 E 33.0represents annual accumulation (for fifth year) of stock in units currency.It adds a utility or performance of 33 monetary units or what is thesame: wine sales price then parked the fourth year wort year originalprice (100-67) = 33 monetary units. The difference between these

amounts, the 33 monetary units, is the annual remuneration of capitalof 313.24 currency units.

K4 67 (1.1054 - 1 )0.105=

99.89 67.

313.24=0.10499

313.24

0.105= 32.99

But if he enters another year of storage, fruit of the savings of thepopulation, Wicksell shows that the interest rate falls and can give thefollowing relationship:

profit

capital = PmgK r

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capital =K = Km - Knm = n + 1

In short: with his numerical example, which was followed verbatimas to the amounts, aims to highlight the importance of the time factor

in the analysis of capital and not necessarily marginal productivity ofcapital coincides with the rate of interest, at the macro level. Essentiallystates that the theory of D. Ricardo on capital and profit is correctand criticizes Walras theory by losing sight of the time factor. In facthighlights the link between distribution of income and profit rate, thus:

profit rate =profit

income

income

social capital(17)

=P

I I

K (18)

on this point, and continuing with the example of Wicksell, return later,specifically on the period of rotation () or average period of production.Previously first need to introduce other topics.

3.2.3 Wicksell to Hicks and capital measurement within the

Austrian approach.

In the preface of Capital and Time Hicks says the evolution of histhinking from Value and Capital in which while applying a Walrasianmethod, it does on problems similar to those that Keynes sought tounravel. In Capital Growth basically tries clarified himself approachpossible modes of economic dynamics or time evolution of the variablesof a model. for Directions in Capital and time to guide their thinking

about measurement capital in the same approach, Hicks called neo Aus-trian.

Hickss model is based on a key opposition: the difference betweencapital and capital goods 22. This is a very important distinction ineconomic theory and has not resulted in very few confusions. In generalneoclassical production functions work implicitly on the assumption ofa single class of capital good in physical terms.

22. His distinction is not unique to Hicks and is the dominant mode of neoclassicalsthinking.

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The controversy over capital theory in the words of Hicks is moreabout two different concepts of capital, according to this author, areuseful in different contexts: the capital to see a list of capital goods or

equipment and see the capital as an amount in monetary terms. Thecontroversy appears from the fact, accepted from Wicksell who firstmade explicit that the subject, that as soon as you leave the world ofmicroeconomics of capital appears the problem in all its dimensions.

In macroeconomics or global level requires a unique value capitalthrough which to represent the acquis. Those who think that capital isa list of physical goods: capital goods, accept the need to homogenize avalue only. And this is the root of the problem. In the words of Hicks[25;pags.158-159]:

Whatever one might expect from physical goods is a list- so much of this that -; macroeconomics should be ableto have aggregation. This is an obvious added in termsof value added ..... The capital must always be estimatedin terms of something, money ..... If a concept as thereason product/capital, which is part of this approach, hasto make sense, capital and output must be measured in thesame terms

The reason capital

output or

K

Qis the inverse of the rate capital tur-

nover. But the solution beyond that accorded to capital measurementissues important thing is the perspective you look at the problem. Hicks,in a way that coincides with the continued focus in this work, says:

The concept of production as a process over time, withcapital (accountant equity) as the report is done inthis on the state of the process, not specifically Austrian.

Is the same concept that underlies The Theoryof the British classical economists, and is

older still ... is the typical view of manbusiness currently standpoint of accounting

and formerly the viewpoint of traders ..... Canaddress a short period ... but of course, is impos-sible to deal with a sequence of such periods withoutreinstituting accounting discipline 23

23. The highlight certain words not in the original,[25;pags.21-22]

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From the point of view of capital Hicks treated as accountantequity is the common view of the classical economists, Austrian andbusinessmen, this interpretation is consistent with the assumption made

in this work. All three models: that of Marx, Von Hayek and model DuPont, as we shall see, are characterized by accepting the unreliability ofthe measuring accountant, the accepted for its practicality and availa-bility. In fact, companies around the world and whatever their size makedecisions based on this type of capital measurement, as noted earlier.

3.3 Hayeks model on the Ricardo effect

Von Hayek published in London, in the February issue of 1942 Eco-nomic, an article entitled The effect of Ricardo and from whichhave emerged articles and comments Hicks, Kaldor, Haberler, Blaug andothers. The same relates, essentially, on the thesis Ricardian competi-tion between labor and machinery, as set forth in the famous ChapterXXXI of the Principles of Political Economy and Taxation. Hayekattempts to show that the Keynesian thesis that an increase in finaldemand induces an elevation of the level of investment is not is valid,

we will focus our discussion on this point but on methodological instru-ments employing Hayek, who is the subject relevant to this work 24.

3.3.1 Hayek Model Assumptions

Hayek defines Ricardo effect as that proposition states that ageneral alteration of wages in relation to Prices of consumer goods,revised profit rates on capital in proportion to the different speeds of

rotation capital. It will take the following as basic proposition: a generaldecline real wages relative to prices of consumer goods, rise over therate of return on the capital of companies, proportionally higher speedhave its capital.

to lower (or raise) real wages should be interpreted from the pointof view or companies from which the product has, from risingprices, a higher purchasing power.

24. Our comments are guided by the publication of the article as an appendix to

[20] pages XVI Appendix IV and pages 390-422. Appointments are made all of thispublication.

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The rise in prices is due to increased demand caused by increasedconsumption of rents collected ... in the production of capitalgoods[19,pags.303]

The increased demand for consumer goods that exceeds levelbeyond which it is not easy to increase the production of con-sumer goods.

Wages and interest rate of loanable funds market remain cons-tant. The invariance of the price of loanable funds equivalent toassuming that ... no cash loans of any kind during the periodin question ....

The rates of return on capital are the same for all companies at

baseline and in the long run. The restriction on the loan market is not only basic used to

facilitate exposure, Hayek actually going to analyze the impactof imperfect credit markets in the model. We assume that thereare no liabilities of any kind, whether it is simple to include andtake into account the impact of different levels of leverage thatcompanies can get, do not consider it to focus on the essentials.

Hayek believes that Ricardo effect although ... is funda-mental to the examination of the interest in the work of Bohm-Bawerk, Wicksell, Mises, none of these authors develops someextension .. [19;pags.390]

Hayeks basic proposition is synthesized with the following expres-sion:

We have yet to introduce a measure that is clear, anduncontroversial as possible, in the proportions in whichthey combine capital and labor in different companies andin Different production methods. For our purposes, themost convenient, and it also has the advantage of beingwell-known businessmen, is the concept of turn rateapplied to all or part of the capital of a company. .....When it is remembered that the rotation rate expressesthe number of times the total sales value exceeds capitalof the company.[19;pags;394-395]

From the above the basic variables are:

m profit margin on sales (or the output)

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t rate of rotation of capital or rotational speed or turnover

i rate of return on equity

m=

product-cost

product =

profit

producto

t=product

equity

i=profit

product

product

equity=

profit

equity=m t

And builds a formula of the rate of profit on capital which is

expressed as follows:

i = m t (19)

That is, the rate of return on capital is equal to the profit margin onthe product (or sales in the course all that occurs sold) by the speed ofrotation of equity. It should be noted that two aspects Hayek explicitly,t determines the number of times, whole or fractional, that capitalor assets total result in sales during the period. We assume that the

unit of time is one year. Therefore the reciprocal of tor 1

t 360 = n

where n is the number of days it takes to rotate once the equity or thefamous period average (). As the assets of a firm does not constitute ahomogeneous whole, not all asset classes rotate at the same speed. Thisis easy to visualize taking stock of any company that inventories turnover fast production machines, etc. While analysis of Hayek performedby taking the equity as a quantity of monetary value such as men-tioned above, can be expressed in units of company product:

cm = average cost in product units

p = unit priceQ = physical quantity productK= capital in physical units ProductC= monetary capital

then:

mr=(p Q) (cm Q)

p Q= Q

p cmp Q

=1cm

p=

tr=p Q

C=

p Qp R

=Q

R

ir=m t= Q

R



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Considering the capital in terms of product25 recall that theinverse relationship

Q

Ris another way of expressing the average period

of production26: =1Q

R

=R

Q. Lets see how the model works pro-

posed by Hayek, we use different numbers for the purpose of highlightingsome aspects in which Hayek does not stop.

Taking four companies, a, b, c, d and data have monetary quantitiessold, prices, costs and volume of capital means money employee is partof an initial situation in which there different values of m and t for

each company except c and d having equal values but different productprices, as seen in Table 4. Hayek assuming that demand will increase forthese products for the reason given in the course of increased consumerdemand, will come to a final situation in which rates of return on capitali, are different in rising industries in those with higher turnover rateto what is, less average period of production.

Company

ABCD

Capital

1000250800800

Sales

100050020002000

Cost

90047619201920

Tabla 2. Initial situation

Hayek is a net increase in the selling price and sales of 5%, with novariability in cost or valuation of capital

m t i10% 1 10%5% 2 10%4% 2,5 10%4% 2,5 10%

Tabla 3. Initial rate of return on the capital

25. mr,tr, ir ; are expressed in terms of the product.

26. Consider the year (360 days) as the unit of measurement.

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There are different returns on sales and capital speeds different, butequal rates of return on capital

Company Capital Sales CostA 1000 1050 900B 250 525 476C 800 2100 1920D 800 2100 1920

Tabla 4. Net increase of 5% in sales price

With the net change in price changes the value of sales remainingconstant the rest

m t i14% 1.05 15%9% 2.1 20%9% 2.625 22%9% 2.625 22%

Tabla 5. Final rate of return on the capital

3.3.2 Conclusion on Hayek model

It makes the goal of this paper the description of the effectRicardo27 we highlight the model, what their variables, their condi-

tions assumed for purposes of comparison with the known formula thenDu Pont and analysis of Marx and try to prove that are structurallythe same. Yes it is important to note that in building the model,Hayek,is based on :

1. The concept of rate of rotation - t - noting that it has theadvantage of being well-known businessmen [19, p.: 394]. It isimportant to emphasize that Hayek, like Hicks, is fully aware thatthis category applies and knows in business.

27. In [43] is analyzed and described the Ricardo effect and its operation.

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2. Considers the profitability or sales margin m is different fromthe return on capital i, which is the key issue since the modelsmatching rate of return on sales the rate of return on capital

directly exclude the impact of time to analyze problems. Theexcluded because the rates match no sense to speak of rotation.Furthermore, equalization implies that soften or disappear thedifferent composition of capital structures28. This is not an issuelower by 1972 Monza Alberto stated: Instead of conceiving theidea production function in a historical context, it began to beused in one timeless instant or [39, p.: 22].

3. His notion of rate of rotation as a significant variable continuesthe focus of Ricardo, Jevons and Wicksell.

4 The rate of profit in Marx

Before digging into the construction of the determination of the rateof profit that Marx uses in Book III of Capital, see David Ricardoanalysis on the subject. Ricardo makes his soliciting on capital andprofitability highlighting the variable rotation.

4.1 Background: David Ricardo.

David Ricardo tried to set the economy and basic problem as thedetermination of the laws governing product distribution between diffe-rent social classes, linked to the rate overall benefit of the economy withthe distribution and thus the value capital with that. Without enteringinto the debate about the value of this hypothesis, it is necessary toexpose the role that Ricardo gives the time and their relationship withcapital.

28. In the best case is considered a capital turnover rate equal to 1.

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Ricardo expressly raised, perhaps for the first time, the problem ofcapital measurement. The Essay on profits of 1815 to analyze thedetermination of the rate of profit and relation to the accumulation

of capital defending the thesis that the rate of profit will decline ifthere progress in agriculture. One of the methodological decisions takenRicardo, Sraffa and will stand out in his comments on the completeworks of this author, is the tacit assumption that the input and outputof agriculture are physically identical 29. As noted Cartelier [12, p.: 242]:

Ricardos conception, based on the idea that the cost pro-duction .... is the basis of price, it only makes sense if thecost of production of wheat is determinable independentlyof the price of the goods .... In short, Ricardo develops

propositions in the Essay on PROFIT require theassumption of homogeneity of inputs and outputs

The problem posed by Ricardo on capital measurement in the 60nd 70 of the nineteenth century and generated reappeared calledcapital controversy or both Cambridge. The subjects consisted ofbasic theoretical discussion on the possibility of achieving a unit sepa-rate capital and distribution prices at the aggregate level or productionof macro function.

Ricardos analysis of Sections III, IV and V of chapter On thevalue of the Principles incorporates the impact of time30 but holdingthe principle that relative prices are independent of income distribution.The tool tries to use is that of "dating" tacitly work, especially in sectionIV, and transform the capital into homogeneous units of work originatedin different time. Which is going to take note Cartelier following:

...another way to say the same is to emphasize thateverything happens as if the date of the expenditure of

labor did play a paper the side of the your quantity ...(if the quantities of labor remain constant and only itstemporal distribution changes) ... The importance of thisphenomenon, sometimes called today days Ricardo effect

is the greater in that the process of capital accumula-tion progresses ...31.

29. Wicksell model discussed earlier about wines from different years is metodolgi-camente equal to the raise of Ricardo in the Essay.

30. As pointed out by Pasinetti referring to Ricardo and Principles: All exceptions- as explained later in a letter - re reduced to one, which refers to the time.[44, p. 15-16]

The rate of profit in Marx 35


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In the first edition of the Principles chapter On the value pre-sents the subject in a clearer manner, within the framework of this work,and mark how the general principle of independence of relative pricesrelative to capital structure presents exceptions.

If between fixed and circulating capital different propor-tions exist, or if the fixed capital had a different duration,the relative value of goods produced would be altered as aresult of increased wages.

The example he adds 32, after the text referred to in the above quote,

to prove what they say is: comparing the hunter and fisherman and whilethe hunter has a capital structure such that fixed capital formation (FC)is pounds L150 and the capital circulating (CV) of L 50 a fishermanpresents FC L50 and CV L150, prices determined based on a 10% profiton total capital. The calculations used to show that Ricardo huntermust sell assets in pounds L79 and 8s, while the fisherman must sellL173 pounds and 7d 2s are not shown and only highlights the result.We will make explicit tar calculations, because the way to make themis linked to the issue we are trying to clarify and are illustrative of theimpact of different rotation periods. Employ for this purpose the measu-rement system sterling, which is obviously the employee by Ricardo, thatNewton, whenever the Director of House of the Currency of England,designed and which is based on the following conversions:

1L = 20s1s = 12d

the previous relationship between pounds, shillings and pennies trans-

form it in the following example, in decimal. Except this transformationit does not affect the result, as it is a change of scale, the numbers areused by Ricardo. Take the concept of annuities and present value of itexplicitly in his example, consider the following example built with thedata given in the 1st. edition of the "Principles" of 1817. First raisesthe capital structure for the hunter and fisherman

31. The Ricardo Effect as Hayek so renamed it, is one of the thematic our main focus onthe rate of profit, and we agreed to link their way (of Cartelier) to issue temporary capital.

32. In the first edition, the third this example is not found.

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sector FC CV price profithunter 150 50 L79s8 10%fisherman 50 150 L173s2d7 10%

Tabla 6. capital structure

To interpret the justification for these prices [Table 2] and the follo-wing is important to note that Ricardo calculates compensation circula-

ting capital with direct rate of 10% per year (5 and 15 respectively)but the remuneration of the fixed capital obtained by applying:

The hunter .... To replace your capital with 10%fixed profit, the present value of an annuity of L24.4

at 10% per annum for ten years will be to 150lbs ................................. L 24.42

Now, as it integrates the current value of the annuities used byRicardo for compensation of fixed capital of the hunter and the fis-herman?

hunter

year FC interest amortization annuities

0 150 0 0 01 140.5884 15 9.4116 24.4116

fisherman

0 50 0 0 01 46.8627 5 3.1372 8.1372

Tabla 7. Annuities to 10%



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The interest component in the value of the respective Annuities inyear zero, L24.4 and L13.8 , respectively, in addition to the replacementsof CV (50 and 150 respectively) over the relevant interest needed to form

prices in each sector. From here applies the same criterion, that Hayeklater used in his article, noting that:

... if wages increase, will alter the relative value of theproperty, although none of them requires more work forproduction ... .

What if these values, we apply the same method to the problem ofthe transformation of values into prices of production? We apply theanalysis scheme C. Marx made the show the relationship between values

and prices of production in the transformation problem.

sector FC CV profit amortization cost price

hunter 150 50 20 9.4116 59.4116 79.4116fisherman 50 150 20 3.1372 153.1372 173.1372

total 200 200 40 12.5488 212.5488 252.5488

Tabla 8. Ricardos problem according to the scheme of Marx

The table above displays the price structure implemented by D.

Ricardo. El component amortization is key, without that amountdoes not integrate the Ricardian example price, but also does not employthe full amount of the annuity. Here is the price as a decimal, we willfor L79s79 , d8 out of 20 shillings make one pound thus constitute0.4 in decimal form:

L79.4116 E L79s8

Now and raised the price differs of labor value. If we apply the criterionof Marx has global totals of price and value, must be equal, plus

valor and values are determined. For the determination of surplus value,L40 or profit system, are distributed in proportion to the CV, with thehypothesis of equal value plus rate for all sectors. See table below.

sector FC CV value plus amortization cost value

hunter 150 50 10 9.4116 59.4116 69.4116fisherman 50 150 30 3.1372 153.1372 183.1372

total 200 200 40 12.5488 212.5488 252.5488

Tabla 9. Example values

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Place column amortization the value of depreciation of the sharecapital for the perpetuity [see Table 7], is curious but in this example

of the first edition of the Principles all hypotheses are verified thatMarx analyzed in his famous chapter on the transformation of valuesinto prices of produccin. In Marxian terms the amounts of the pro-ducts of hunting and fishing that determines Ricardo: L79.4 and L173.13respectively are producer prices and values are: pounds L69.4116 andL183.1372 respectively33.

In this example from the first edition of the Principles we empha-size that:

as Marx pointed out on several occasions, but does not prove,Ricardo uses values and prices of production. As exemplified inthe preceding tables made with data from the example of the firstedition of the Principles.

that there is a temporal distribution of capital strongly markedand evidenced by the ratio

CV

FC.

in the sectors, there is a different rate of rotation of capital: 0.397

and 0.866 in the hunter and fisherman, respectively .

The above points put us in the context of the transformation pro-blem and allow us to state that the issue is already implicit Ricardo,as evidenced by the previous example and as Marx pointed out withoutproof. We will leave in this instance, momentarily, the development ofthis example and, like the previous Wicksell, deepen it by applying themodel of the Ricardo effect later.

4.2 Capital and time in Karl Marx

33. The fact that Ricardos example, of the first edition, applies the model used by

Marx in the transformation problem and is evidenced in the course prices and values ??aredifferent, we know that has arisen prior to this work.

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In Book II of Capital, first published in 1885, Marx will performa careful analysis of the circuit of money capital ,in other words, theturnover time and number of turnovers of capital. And anticipating in

decades to works management financial, to study the effect of rotationtime investment in capital-money or more precisely: cash requirementsthat are determined by the magnitude of the turnover time or type ofbusiness cycle in question. this aspect leads to recognition Blaug, whonotes commenting on the Marxian analysis of capital turnover in BookII:

The facts of the time consuming nature of the productionprocess have never been better described, even by Bohm-Bawerk. [7, p.: 305]

In Chapter VII of Book II entitled The turnover time andnumber of turnovers, considers and defines the total turnover timeas the period of time it takes the process D M D , making itclear that the year as a unit of measure logic to quantify the numberof rotations. Marx explains the cycle D M D = D + Dcommenting three phases:

1. its company appears on the market as a buyer, investing theirfunds in the purchase of goods, starting with the existencecapital money or D.

2. the production process or create a value added to the companyinternal process, which consists of the use of production time, Mgenerator.

3. the company returns to the market as a seller and you need toconvert its products into cash to restart the cycle. Turn yourproducts into money within a period of time called the circulationtime, which makes the appropriation of value added produced in

(2), in the form of D = D + D

One paragraph more clear as to how to calculate the rotation andthat is particularly important in the context of this work is in ChapterIX The aggregate turnover of the capital advanced. Cycles ofturnover. Here then is taken to explain why the cycle D D and givea series of examples will point:

On the way to calculate the turnovers, give the word toa American economist[34, p.: 165]

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To mention later a extensive paragraph of Principles of Political

Economy of Poulet Scrope 34, the shape of this author to arrive at therotation of 16 months is linking annual sales and capital total 35.InChapter XVI, the same volume II, introduces the fact that the annualrate of surplus is equal to the quota of rotation or cycle multiplied bythe number of rotations in the year. After noting:

Economists tell us that there never unclear aboutthe mechanism of rotation, pass continually ignorethis fundamental factor, namely the production processactually can only absorb a portion of the capital indus-trial.[34;pag:237]

This refers to the need to considertime of production+time of circulating or marketing. In Chapter XVIThe turnover of variable capital. Showing numerical example defi-ning the rotation like the ratio of annual output and the value of thecapital advanced, [34, page. :262-263]. Really the capital advanced is aflow concept and refers to the capital investment made in the period (theannual expenditure of Scrope cited) and not the stock of capital. Marxconsidered the annual cost price equal to capital expenditures cons-tant and variable capital, like the amount related to the total capital.

34. by Google is consige Longmans English edition. This is collated with the abovein E L CAPITAL. Marx cites rigor Potter book Political Economy: its Objects, Uses,and Principles, New York, 1841. It appears that much of this work is essentially a slightlymodified reprint of the first ten chapters of Scrope Principles of Political Economy,

published in England in 1833. On the other hand Scrope was English and not American.35. In his book Poulet Scrope; [ 1943: 156-159]. take annual expenditure + profit

= annual sales and it is this latter concept that divides the total capital:capital

annualsales

12 = month rotation. And it is this latter concept that divides the total capital-monthrotation give 16 and 9 months respectively for rotation thereby. According to the editionmade by Siglo XXI of Capital: In Werke and TI this includes the following note: Inthe manuscript, Marx points out that this way of calculating the rotation time capitalis false. The average time of rotation shown on the appointment (16 months) has beencalculated taking into account a gain of 7 1/2% on the total capital of 50,000 dollars.Regardless of profit, turnover time of this capital amounts to 18 months.. A Marx gives18 months because rotation calculated based on the cost price instead of using annual

sales: capitalcostprice

12=month rotation.



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The capital is defined like value that includes both capital constantas the variable. Marx after studying the process of circulation of capitalin Book II, Volume III appeared in 1894, and in reality like the Volume

II, compiled from drafts by F. Engels, proceedings opened to researchthe....

The various forms of capital, as evolved in this book,thus approach step by step the form which they assume onthe surface of society, in the action of different capitalsupon one another, in competition, and in the ordinaryconsciousness of the agents of production them-

selves.[35;pags:45] 36

Is important the point of view adopted of: ... habitual conscious-ness of the agents of production, which coincides with the selectedand emphasized by Hayek and Hicks, of seeking common categories ofanalysis to businessmen. Marx introduces the category of quota profitin the following terms:

The rate of surplus-value measured against the variablecapital is called rate of surplus-value. The rate of surplus-value measured against the total capital is called rate of

profit. These are two different measurements of the sameentity, and owing to the difference of the two standardsof measurement they express different proportions or rela-tions of this entity.... The transformation of surplus-valueinto profit must be deduced from the transformation ofthe rate of surplus-value into the rate of profit, not viceversa. And in fact it was rate of profit which was the histo-rical point of departure. Surplus-value and rate of surplus-value are, relatively, the invisible and unknown essence

that wants investigating, while rate of profit and thereforethe appearance of surplus-value in the form of profit arerevealed on the surface of the phenomenon[35;pags.,58]

In the third book of Capital, presents his formula of the rate of profitor quote of profit from the surplus value p, or simply for the profit,as follows:

g =p

C=

p

CC+ CV(20)

36. The highlight is not in the original.

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Where:

g profit rate

p value plus

C total capital

CC constant capital

CV variable capital

But then the above expression, indicates two aspects that influence

the formula:

a) the value of money that must be assumed constant,

b) turnover, noting that the above formula only...

...is strictly correct only for one period of tur-nover of the variable capital.[35, p.: 65]

In the Grundrisse also explains its way to analyze the capital turnover

and its impact on the process. Very clearly exposes each cycle of repro-duction of capital is equal to a rotation:

The number of reproductions is = to the number of tur-nover. So the plus-value total = p n R 37 [36, p.: 187]

To continue with a clear numerical example which calculates the rateof turnover or n, as Marx called dividing the annual product by totalcapital. [36, p. :243-254] In Chapter IV of Book III of E L C APITAL,analyzes the impact of rotation on the rate of profit and gives exampleson pages 86-87, which begins in calculating the rate of return on theinvested capital and arrives at a formulation follows:

g = p n V

C(21)

Where:

37. R is rotation, are respected the symbols the text quoted.

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p surplus of a rotation

n annual number of rotations

P annual surplus P = p n

C total capital

V annual variable capital

g profit

g profit rate =

i=1i=n

pi

C=

P

C i=rotations

k variable capital cycle

p surplus of a rotation=p

k

P annual rate of surplus value=P

C

Replacing in (21):

g =

pk

k n

V

V

C=

p n

C=

P

C(22)

That is: surplus value of a cycle,p, multiplied by the annual number ofturns in the cycle ,n, divided by total capital,C; is equal to the annualrate of return on capital,

P

C. This going to allow you to emphasize that

equal terms the profit rate of two capitals :

the rates of profit of the two capitals are related inverselyas their periods of turnover.:

adding:

The amount of variable capital invested in his businessis something the capitalist himself does not know in mostcases. We have seen in Chapter VIII of Book II, and shallsee further along, that the only essential distinction withinhis capital which impresses itself upon the capitalist is thatof fixed and circulating capital.[35, p.: 88]

After the foregoing uses, returning to it, an example of a textileplant with 10,000 spindles Mule. This example is developed in the firstvolume of Capital and assumed that the figures given for one week of

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april 1871 are valid for every week of the year (raises a stationary state).This development is at the end of the symbol FE, which is likely thatthe author is Engels, in any case is the interpretation of Engels on the

rate of profit and this is significant for our hypothesis.Beyond this particular will reproduce this example because showsthe determination of the rate of profit, as Marx understood it, andexpose the same result by reaching our author, otherwise. It can be seenin Table 10 , built by example and numbers used by Marx, thatthe profit rate per cycle multiplied by the number of turns gives the totalcapital in the year determines the annual profit rate equal to 33.28%(33.27% Marx placed a calculation and 33.28% with the mode used here,indicating the difference below). The key is what specifically says:

p n = P p n = P (23)

Where P is the annual quantity of surplus value in Table 10 this is4160 = 80 surplus value of a period 52 cycles. Take the example ofMarx:

weekly product

C amortization CC per cycle CV Surplus Product12.500 20 358 52 80 510

Year 52 weeks - Annual values

12.500 1.040 18.616 2.704 4.160 26.520

profit per cycle

Cycle Cycle Profit rate

profit product cycle80 510 0.1568

Profit Rotation Annual rateon the product of profit on capital

P

product=

4.160

26.520

product

C=

26.520

12.500

P

C=

4.160

12.500

0.1568627 2.1216 0.3328

Tabla 10. Example of Marx, cap.IV of Volume III



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On the basis of preceding example is understood, therefore, that (23)can be expressed as:

P

V

V

C= g

P

C= g

profit cycle

product cycle n = g

g = annual profit rate

In:P

V V

C = g , the first term is the annual rate of surplus value andsecond rotation number gives the total capital in the period annually

through V. The expressionV

CMarx once used at least

to indicate the so-called organic composition of capital, butalso indicates turnover. Clearly, the annual mass surplus value equalsthe the annual mass of profit at the macro level, but in spite of theemphasis our author gives this point, this equality of masses of surplusvalue and profit, Marx emphasizes again and again, is not respected by

either Borkiewitz or others known attempted solution to the problem oftransformation.

Marx noted above will say that the mass of surplus value measuredby the variable capital is the rate of surplus value and measure the massof surplus value by the total capital, is the rate of profit. The mass ofsurplus value coincides with the profit, at company level and or sector,in terms of values but do not production prices, but globally in a closedeconomic system mass aggregate surplus value must be equal to the

mass of profit aggregate to the same period of time:

n= number of cycles in the yearp= a cyclesurplus valueg= annual profit

t=1t=n

pt=P= g

Chapter VIII of the third book will reiterate, leaving well clear, theincidence of different rotations of capital [35, p.: 158].

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We demonstrated in the preceding chapter that, assu-ming the rate of surplus-value to be constant, the rateof profit obtaining for a given capital may rise or fall

in consequence of circumstances which raise or lower thevalue of one or the other portion of constant capital,and so affect the proportion between the variable andconstant components of capital. We further observed thatcircumstances which prolong or reduce the time of tur-nover of an individual capital may similarly influence therate of profit. Since the mass of the profit is identicalwith the mass of the surplus-value, and with the sur-plus-value itself, it was also seen that the mass of the

profit - as distinct from the rate of profit - is not affectedby the aforementioned fluctuations of value....Aside fromdifferences in the organic composition of capitals, and the-refore aside from the different masses of labour - andconsequently- other circumstances remaining the same,

from different masses of surplus-labour set in motion bycapitals of the same magnitude in different spheres of pro-duction, there is yet another source of inequality in ratesof profit. This is the different period of turnover ofcapital in different spheres of production. We haveseen in Chapter IV that, other conditions being equal, therates of profit of capitals of the same organic compositionare inversely proportional to their periods of turnover. Wehave also seen that the same variable capital turned overin different periods of time produces different quantities ofannual surplus-value. The difference in the periods ofturnover is therefore another reason why capitals

of equal magnitude in different spheres of produc-tion do not produce equal profits in equal periods,and why, consequently, the rates of profit in these dif-

ferent spheres differ.

You can see, in the following example -Table 11 - also extracted fromMarx, that the profit rate per cycle multiplied by the number of turnsgives the total capital in the year, determines the annual profit rate,which is the same for all three companies, despite the different capital



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structure. The data is taken from pages 86-87 of Volume III.

company fixed variable totalcapital capital capital

I 10000 500 11000II 9000 1000 11000III 0 5000 11000

company amortization cc cv(d) advance

I 100 500 500

II 200 1000 1000III 0 6000 5000

surplus product annualper cycle product

p x D

I 500 1600 16000II 1000 3200 32000III 5000 16000 16000

Turnover rate annualper cycle profit rate

D

total capital= T

p

d + cc + cv + p=g T g = g

I 1.454545 0.3125 0.4545II 1.454545 0.3125 0.4545III 1.454545 0.3125 0.4545

Tabla 11. with data from Marx

The profit rate is the same for our author arrives 45.45% and theformulation in this example, which rigorously follows the method ofScrope, is:

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g =

i=1i=t

pi

i=1i=t (di+ cci+ cvi+ pi)

T=

i=1i=t

(di+ cci+ cvi+ pi)

total capital

annual rate of profit= g =g T

What is interesting in this example is that Marx assumed thatvariable capital turns are different:

Company turnovers per yearof the variable capital

I 10II 5

III 1

Whereupon also be expressed Table 7 with the formula38:

n CV

C= g ifp = 1, 00 (24)

Where Cis total capital, and the rate of surplus is 100%.

Company nCV

Cn

CV

C

I 10 0,04545 45.45%II 5 0,09090 45.45%III 1 0,45454 45.45%

38. The quantity of surplus-value appropriated in one year is therefore equal to thequantity of surplus-value appropriated in one turnover of the variable capital multipliedby the number of such turnovers per year. Suppose we call the surplus-value, or profit,appropriated in one year S, the surplus-value appropriated in one period of turnover s, th

profit rate of marx the "ricardo effect" of hayek and model du pont.pdf

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