Marx, , ch. XXI , which provide a theory of the relationship between quantities, or sectoral proportions, and the rate of growth of the economic system as a whole. Prices of production However, Marx saw that the importance of the Tableau was not restricted to the problem of quantities and growth: it also provided a much needed general frame- work to determine the general rate of profit consistently. There was a single important difference between the physiocratic and the classical scheme: the rule according to which the social surplus is distributed — as rent in the case of the physiocrats, and as rent and profits in the case of the classical economists from Smith to Ricardo.
It was indeed the determination of the general rate of profit which became a major focus of classi- cal analysis. This reformulation had to leave the basic structure of the approach defined in terms of the exogenous vari- ables untouched.
There, the problem of the rent of land is set aside altogether. The entire surplus is assumed to accrue in the form of profits at a uniform rate.
In a second step this value rate of profit was then used to calculate prices. Marx started from a description of the economic system divided into several sectors or spheres of production, each of which is represented by an equation giving the value of the sectoral output zi as the sum of the sectoral constant capital ci , its variable capital vi and the surplus value si generated in the sector cf.
This description involved given methods of production and a given real wage rate. Otherwise it would be impossible to derive the labour-value magnitudes. With a given and uniform real wage rate and a given and uniform length of the working day reflecting free competition in the labour market , the rate of surplus value is uniform across sectors.
The larger the real wage rate, the larger is the variable capital and the smaller is the sectoral surplus value. A first and obvious error concerns the fact that in the above price equations 3. Marx was aware of this slip in his argument cf. Marx, , pp. He was wrong. Since the rate of profit cannot be determined before knowing the prices of commodities, and since the prices cannot be determined before knowing the rate of profit, the rate of profit and prices have to be determined simultaneously rather than successively.
An answer to this question was provided by Vladimir K. Dmitriev and Ladislaus von Bortkiewicz. Dmitriev investigated first what is meant by the total amount of labour expended in the production of a commodity and how this amount can be ascertained. Dmitriev disposed of this misconception by showing that it is from a knowledge of the current conditions of production of the different commodities alone that one can determine the quantities of labour embodied see Dmitriev, , p.
T is the sign for transpose. In the single-products case contemplated by Dmitriev there are as many series of dated quantities of labour as there are products, and thus there are as many equations as unknowns. With p as the n-vector of prices, w as the nominal wage rate and r as the competitive rate of profit, and taking wages as paid ante factum, we get from equation 3.
The system is complete and not underdetermined, as Walras , Lesson 40 had objected. Kurz and Neri Salvadori The concept of production as a circular flow and that of the surplus prod- uct was further developed by Ladislaus von Bortkiewicz — , who was born in St Petersburg into a family of Polish descent. From he taught eco- nomics and statistics at the University of Berlin, the same university which, in the late s, also had Leontief, von Neumann and Robert Remak among its members.
Second, he was concerned with showing that value analysis is not an indispensable step on the way to a consistent theory of the rate of profit and prices of produc- tion. Third, and notwithstanding what has just been said, he wanted to show that prices and the profit rate can be related to value and surplus value magnitudes in a logically consistent way. His treatise is indeed as much about Ricardo as it is about Marx.
He accused Marx of retrogressing in various ways to opinions that had already been shown to be defective by Ricardo. Von Bortkiewicz pointed out that the data from which the classical approach to the theory of value and distribution starts are sufficient to determine the rate of profit and relative prices; no additional data are needed to determine these variables.
Following Dmitriev, von Bortkiewicz cast his argument in algebraic form. With the real wage rate given from outside the system and fixing a standard of value or numeraire, one gets two additional equations and no extra unknown and the system can be solved for the rate of profit and prices in terms of the numeraire.
Von Bortkiewicz, among other things, generalized the approach to cover fixed capital. It was Georg von Charasoff —? Georg von Charasoff Von Charasoff was born in Tiflis. He wrote his PhD thesis in mathematics at the University of Heidelberg. He published two books in and , respectively, both in German, the second of which, Das System des Marxismus.
Darstellung und Kritik, is of particular interest to us see von Charasoff, In it, von Charasoff anticipated several results of modern reformulations of the classical approach and of input—output analysis.
Because of his highly condensed and abstract argument, which is mathematical without making use of formal language, his contribution was largely ignored at the time of its publication and has only recently been rediscovered see Egidi and Gilibert, Von Charasoff developed his argument within the framework of an interdepen- dent model of single production, which exhibits all the properties of the later input—output model.
The series under consideration is closely related to the expanded Leontief inverse. With circular production this series is infinite. Kurz and Neri Salvadori means of production disappear, etc. A further property of the series of production deserves to be stressed: the capital of the second degree A2 y is obtained by multiplying the capital of the first degree Ay by A. This finding is of the utmost importance for determining the rate of profit and the maximum rate of growth of the system.
As regards these dimensions the requirement is decisive that gross profits of the basic production. Implicit in this reasoning is the abandonment of the labour theory of value as a basis for the theory of relative prices and the rate of profit. With von Neumann von Charasoff shared a concern with the possibility of equi-proportionate growth. In the hypothetical case in which all profits are accumulated, the proportions of the different sectors equal the proportions of the original capital.
In this case the actual rate of growth equals the rate of profit: the system expands along a von Neumann ray. Wassily Leontief Leontief —99 was born in St Petersburg. After his studies at the university of his home town, then Leningrad, he went to Berlin to work on his doctorate under the supervision of von Bortkiewicz.
In he joined the faculty at Harvard University and began the construction of the first input—output tables of the American economy. These tables, together with the corresponding mathematical model, were published in and see Leontief, ; see also Leontief, In what follows, the English version will be used whenever this is possible.
Page numbers in square brackets refer to the latter. Kurz and Neri Salvadori 9. The starting point of the marginalist approach, the homo oeconomicus, is considered inap- propriate because it gives too much room to imagination and too little to facts Leontief, , pp. Throughout his investigation he assumed single production and constant returns to scale; scarce natural resources are men- tioned only in passing. The argument is developed within the confines of what was to become known as the Non-substitution Theorem see Koopmans, ; Samuelson, In much of the analysis it is also assumed that the system of production and consumption is indecomposable.
Leontief suggested , p. Here we shall set aside the second problem. Starting from a physically specified system of production-cum-distribution, Leontief is to be credited with having provided a clear idea of the concept of vertical integration Leontief, , p.
As regards the reduction to dated quantities of labour Leontief, , pp. This reduction has nothing to do with an historical regress Leontief, , p. Next, Leontief addressed exchange relationships. It should be stressed that the system, albeit stationary, generates a surplus. His argument resulted in setting up price equations which reflect the going rule that fixes the distribution of income. Count- ing unknowns and equations, Leontief found that the number of variables exceeds the number of equations by one.
In other words, the same quantity system is assumed to be compatible with different price systems reflecting different distributions of income. Given the rate of profit together with the system of production, relative prices can be determined. One of the main issues tackled by this group was the displacement of workers by technical progress and their absorption, or lack thereof, through capital accumulation.
To enable them to take into account both the direct and indirect effects of technical progress, they developed multisectoral analyses. Kurz and Neri Salvadori temporal view of production Burchardt, — He also tried to calculate the change in the price system made necessary by technical change, assuming that any improvement is eventually passed on to workers in the form of a higher wage rate.
Scrutiny shows, however, that in his input—output analysis he preserved the concept of circular flow and did not, as is maintained by some interpreters, adopt the Walras—Cassel view of production. Unlike the theories of Walras and Cassel, in Leontief there are no given initial endowments of these factors. The values of the coefficients are ascertained empirically; they are commonly derived from statistical input—output tables, which describe the flow of goods and services between the different sectors of a national economy over a given period of time, usually a year.
In static input—output analysis the input coefficients are generally assumed to be constant, that is, independent of the overall level and composition of final demand. The problem of the choice of technique, which plays an important role in classical and neoclassical analysis, is often given only slight attention.
In order for the system of equations to have non-negative solutions, the largest real eigenvalue of matrix A must be unity. Now A represents exclusively the matrix of interindustry coefficients and y the vector of final demand, which is given from outside the system. The matrix of input coeffi- cients is then used to determine the sectoral gross outputs as well as the necessary intersectoral transactions that enable the system to meet final demand and repro- duce all used up means of production.
The equation describing the relationship 15 This does not mean that the economy is unable to produce a surplus. Hawkins and Simon, The price each productive sector is assumed to receive per unit of output equals the total outlays incurred in the course of its production. Assuming a closed economy without a government, the latter represents payments to the owners of productive factors: wages, rents, interest and profits.
Another way of putting it is that in this formulation two things are lost from sight: the constraint binding changes in the distributive variables, and the dependence of relative prices on income distribution — facts rightly stressed by Leontief in his paper. Leontief at times has himself expressed the opinion that his analysis and that of Walras are compatible with one another.
Second, there is the content of the theory. Some observers may be inclined to base the hypothesis of close similarity between the analyses of Leontief and Walras on the observation that the systems of price equations elaborated by Leontief in his paper, starting from schema 3.
Essentially the same formal similarity appears to have prompted some interpreters to consider that the analyses of Walras and Isnard belong to the same tradition in the theory of value and distribution. There is a real and close similarity between the contributions of Leontief and Isnard, whereas there is only a questionable one between those of Leontief and Walras.
In Leontief, the rate of interest is not conceived of as a scarcity index of a given endowment of capital. We may conclude that, setting aside purely formal similarities, the analyses of Leontief and Walras have little in common.
Robert Remak We now turn to the contribution of Robert Remak — He studied math- ematics and, in , acquired the venia legendi at the University of Berlin and was a Privatdozent there until Wittmann, , p. Its calculation requires a detailed knowledge of the socio-technical relations of production, that is, the methods of production in use and the needs and wants of producers Remak, , pp. Discussing system 3. The system refers to a kind of ideal economy with independent producers, no wage labour and hence no profits.
Concluding remarks This chapter contains a short account of some of the most important contributions to the long prehistory of input—output analysis. It has been shown that the latter is an offspring of classical economics with its emphasis on production as a circular flow and the capacity of the economy to create a surplus over and above the physical real costs of production, including the necessary means of subsistence in the support of workers.
The physical scheme of production was considered as crucial for an understanding both of the problem of growth and that of the distribution of income and relative prices.
The theoretical efforts just surveyed bore two major fruits. On the other hand they stimulated further developments in the theory of value, distribution and growth. A discussion of these contributions is, however, beyond the scope of this chapter. References Bortkiewicz, L. Bortkiewicz, L. Burchardt, F. Cantillon, R. Higgs London, Macmillan, Charasoff, G. Dmitriev, V. Nuti Cambridge, Cambridge University Press.
In his paper, von Neumann put forward a general linear analysis of production, distribution and economic expansion, allowing for joint production, fixed capital and a choice of technique. Kurz and Neri Salvadori Egidi, M. Studies in the Surplus Approach, 5 , pp. Eltis, W. Gale, D.
Gehrke, C. Gehrke, Ch. Gilibert, G. Evoluzione di un modello, Annali della Fondazione Luigi Einaudi, 15, pp. Beccatini ed. Hawkins, D. Isnard, A. Isnard, progenitor of the Walrasian general equilibrium model, History of Political Economy, 1, pp. Koopmans, T. Kurz, H. Leontief, W.
Newman eds , The New Palgrave. A Dictionary of Economics, vol. English translation of parts of Leontief with an introduction by P. I Moscow, Progress Publishers. I Hamburg, Meissner, Marx, K. II Moscow, Progress Publishers. II, edited by F. Engels Hamburg, Meissner, III, edited by F. MEW et seq. Marx-Engels-Werke Berlin, Dietz. Morishima, M. English translation of von Neumann , Review of Economic Studies, 13, pp. Petty, W. Hull, two vols originally published in , Cambridge, Cambridge University Press.
Reprinted in one volume New York, Kelley, Remak, R. Ricardo, D. Dobb Cambridge, Cambridge University Press , 11 vols. Rose, A. Samuelson, P. Schumpeter, J. I Oxford, Oxford University Press. Sraffa, P. Stone, R. A short account of input—output studies and their present trends.
Torrens, R. Reprint edited by J. Dorfman New York, Augustus M. Kelley, Walras, L. Definitive edition 5th edn Paris, F. Richon, Wittmann, W. Kurz 1. James W. According to Joseph A. Unless otherwise stated, all emphases in quotations are in the original. Ironically, the author on whom so much praise has been showered has almost totally fallen into oblivion. His name is not only absent from general contribu- tions to economics but also from many studies devoted to the history of economic thought.
He is neither mentioned in the first three editions of Blaug 2 nor in Spiegel , Routh , Brems , Niehans and Rima The situation is somewhat more favourable in books devoted to the history of eco- nomic thought written in his mother tongue, German: see especially Stavenhagen , Schneider and more recently Brandt and Baloglou However, the impression remains that for the community of historians of economic thought taken as a whole the economist under consideration barely existed.
To be praised may be the first step to being lost sight of. The author under consideration is Johann Benedikt Wilhelm Hermann. In and he published a textbook on algebra and arithmetic and two volumes on polytechnical institutes. In King Ludwig I appointed Hermann to the position of the Director of the newly founded Bavarian Statistical Bureau which Hermann held during the rest of his life; the establishment of the Bureau was mainly his work.
In addition, one year later he assumed a position in the Ministry of the Interior and in was promoted to the rank of a Councillor to the Ministry. In the late s he had already become the main advisor on economic and social questions to Maximilian II of Bavaria. This did not pass unno- ticed in Munich and after his return from the Frankfurt Paulskirche he had to leave the Ministry for a lack of adequate missions. From to he was a member of the Bavarian parliament. Blaug, Kurz civil service: the king thought that Bavaria was badly advised to dispense with the services of a man possessed of as many talents and qualities as Hermann.
He served in the Ministry of Finance; chaired, in , the newly founded Commis- sion on Science and Technology of the Bavarian Academy of Sciences; and was appointed, in , to the positions of a Councillor to the Bavarian Government and the Director of the Administration of Bavarian Mines and Saltworks. Hermann died in from pneumonia.
One might be inclined to think that this reflects the impact of his teachers in Erlangen, in particular Karl Heinrich Rau. None of these lectures seems to have been very fertile in the sense of exposing the student to different traditions of economic thought. Apparently, Hermann was essentially self-taught: he read the English and continental authors in their mother languages English, French, Italian and thus did not see them through the lenses of received German interpretations.
Belonging to a minority of Protestants in an environment dominated by Roman Catholics, Hermann appears to have followed the Protestant Bildungsideal as best he could. In he got his doctoral degree without presenting an inaugural dissertation. When in he applied for a Habilitation, a fight broke out in the Philosophical Faculty about the procedure.
Eventually, Hermann presented two dissertations, one in mathematics, the other in cameralism. Only the latter had to be printed and, curiously, Hermann was forced to defend it twice. The work is written in Latin and deals with economic concepts and analyses in early Roman authors cf.
Hermann, Interestingly, the dissertation foreshadows several of the concerns and ideas of the Untersuchungen. This chapter attempts to recall some of the achievements of this remarkable German economist, paying special attention to his contribution to the theory of capital and profits. It comes as no surprise that in Karl Diehl edited a reprint of the first and not the second edition. Recently Horst Claus Recktenwald published a facsimile edition of the first edi- tion, accompanied by a commentary Recktenwald, In what follows I shall occasionally refer to the latter.
Section 2 deals with the aim and composition of the Staatswirthschaftliche Untersuchungen. Section 6 addresses his theory of price which was meant to rectify and generalize the classical doctrine. Section 7 enters into a discussion of what he and many of his interpreters consid- ered his main contribution: his theory of profits.
It will be argued that Hermann was one of the first authors who attempted to generalize the classical principle of diminishing returns and the related concept of the scarcity of a factor of produc- tion from the explanation of the rent of land to the explanation of all distributive variables, including wages and profits.
Section 10 contains some concluding remarks. The aim and structure of Staatswirthschaftliche Untersuchungen Hermann makes it clear right at the beginning of the Untersuchungen that the book is not a compendium. It rather seeks to address only those issues with regard to which its author finds the state of the art unsatisfactory. However, according to him political econ- omy is far from complete. Yet there is one area in which the state of the art is said to be especially disappointing: the theory of capital, which has negative implications for the theory of profits.
Kurz by Ricardo; however, since he does not proceed in a sufficiently general way, his results are often only valid under restrictions, which deprive them of almost any truth value. Hermann, , p. The Untersuchungen is thus first and foremost a contribution to the theory of capital and distribution. First treatise. Second treatise. These four chapters account for more than two thirds of the pages of the book, the chapter on profits being the longest pages. Hermann generally proceeds in three steps.
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Atmospheric 60s B-horror film with a cult following. Mary Henry is enjoying the day by riding around with two friends but everything goes wrong when challenged to a drag race and their car gets forced off of a bridge.
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