From the two last members of this equation, we can check that the rate of surplus-value $k_c$ has exactly its expected value. Indeed since $L_I = kL_{II}$, we can rewrite equation (16) as follows:

$$L_{II} + kL_{II} + cL_{II} + ck_cL_{II} = L_{II} + k_cL_{II} \Rightarrow (k+c)L_{II} = k_cL_{II} - ck_cL_{II} \Rightarrow k_c = \frac{k+c}{1-c}$$

As for the overall price of fixed capital goods $Y_I$, we know that it is:

$$P_I = Y_I = \frac{L_I}{(1-a)(1-c^*)} = L_I(1+\alpha+\gamma^*+\alpha\gamma^*) \quad (17)$$

It is immediate that the price of the product of section I is the sum of:

Wages in section I, i.e. $L_I$, and profits in section I, i.e. $L_I(\alpha+\gamma^*+\alpha\gamma^*)$

Here too we can see that the realization of the product of section I is possible, and therefore accordingly the reproduction of the whole economic system. The fact that reproduction is extended does not create any other additional problem, as opposed to simple reproduction, than the necessary adjustment of prices to reflect the new and supposedly higher amounts of surplus-value, investments or capital accumulation, and wages. But contrarily to Marx's schemes, these schemes above show that a number of parameters, like $k$, $c$, $a$ and $c^*$ (and thus $\alpha$, $\gamma$ and $\gamma^*$), have to adjust simultaneously to the new amounts of surplus-value, investments or capital accumulation and wages, which in the real world is not self-evident.

### 5.3. Reproduction cannot go smoothly in the real world

In the context of this analysis, using a model which itself relies on only the most basic principles of the functioning of the capitalist system, it seemed preferable not to embark on a necessarily complex theoretical analysis of all the parameters concerned by the evolution of this system. But no more than the introduction of the consumption of capitalists, there is no reason a priori that extending this analysis to extended reproduction should call into question the theoretical possibility of the realization of the product.

As long as wages paid to workers are advanced as monetary wages and money is a credit money and an endogenous variable, the system embeds mechanisms that theoretically allow for the product to be realized and for reproduction to take place in each of the two sections of production, provided that prices are set at appropriate levels. To increase the product and create additional value, it is easy for capitalists to borrow additional money in order to finance additional investments and pay additional workers. But for this to happen it would be indispensable for capitalists to have the right expectations, and that these expectations be exactly compatible with each other's.

That prices may be established precisely at the appropriate levels in the reality of the functioning of markets, allowing reproduction to take place smoothly at any time, is indeed quite a serious problem, because it has already been shown that prices reflect distribution, among other things. And what is at stake is not only distribution between workers and
capitalists, where the shares of the product going to each category are achieved through the
level of wages and the pricing of consumer goods, but also distribution between capitalists
themselves, because the distribution of surplus-value among them is achieved through fixing
the prices of the various means of production constituting fixed capital. This fixation depends
for each particular market on the power relations which specifically characterize their
functioning, something that the theory of contracts tries to explain to a certain extent. In such
a context, that neither simple reproduction nor extended reproduction can be considered as
taken for granted can be understood with two simple examples.

As a first example, although simple reproduction implies an unchanged level of parameter $k$, it is not incompatible with an increase in the rate of surplus-value $k_c$, which means that capitalists of section II increase the price of consumption goods $P_{II}$. This should normally raise their profits and parameter $c$, i.e. their share of consumption goods. It is possible however that capitalists do not increase their consumption, but instead decide to use the additional expected profits - deriving from the rise in prices in section II, to buy some already existing assets. These assets may be art works, or real estate, or shares, but in any case buying them instead of consumption goods will cause the realized sale of consumption goods to be lower than their production, which would prevent the expected rise in profits from materializing.

As a second example with extended reproduction, let us imagine that capitalists in section I decide to invest more, which means that they must produce and accumulate more fixed capital and hire additional workers ($\Delta L_I$) to meet this objective. Then $L_I$ and $k$ are going to increase, and therefore the rate of surplus-value $k_c$ should also increase to $k'_c$, as a result of this increase in $k$. If however capitalists in section II do not increase the price of consumption goods, i.e. $P_{II} = L_{II}(1+k_c)$, the rise in $k_c$ will not happen, and there will be a shortage of consumption goods which in an open economy would be offset either by additional imports or by inflation.

In a capitalist system where investment and pricing decisions are decentralized there is indeed no reason to think that at any time a coordination is established between capitalists of section I and those of section II. Such a price-setting logic therefore has no particular reason to lead to equilibrium.

All the more so that the main problem which can hamper extended reproduction remains the inherent tendency of the capitalist system to reduce the amount of wages. As we already pointed out it is indeed a normal behavior of capitalists at the level of the firm to consider wages as a cost of production which should always be minimized in order to increase profits. This is based on the standard accounting practice which considers wages as an accounting charge. Business managers seek to achieve this objective by reducing their workforce, i.e. $L_I$ and $L_{II}$ and/or the amount of wages per unit of labor time.
With unchanged prices of consumption goods this microeconomic actions create a permanent trend towards an increase in $k_c$, the rate of surplus-value, but at the same time towards a reduction in the demand for these goods from workers. This reduction could hypothetically be offset by an increase in $c$, the share of capitalist consumption, if the consumption patterns of workers and capitalist were the same, which however is unlikely to be the case. The end result of such a process has every chance to be a chronic shortage of demand for consumption goods, which cannot but affect the level of investment in both sections.

This difficulty of the productive system to reach an equilibrium can also be highlighted on other grounds. First at the level of production relations and the realization of the product, which has been analyzed so far, because the necessary differentiation of profit rates, which it has been possible to demonstrate, can only become more complex in a situation of extended reproduction. Indeed extended reproduction implies a priori a growth of the different branches of the productive system at a specific and distinct rhythm for each of them. This corresponds to investments needs which are quite different from one branch to another: higher in the new and fast developing branches and lower in the old and declining ones. In turn this leads to a need for higher profits and profit rates in the fast growing branches, which is a powerful factor for the differentiation of these rates.

The fact that competition is supposed to lead to the equalization of profit rates, to the extent that it could be demonstrated, would in any case only play against this differentiation, thus making the reproduction of the system more difficult. Indeed it has been shown that the rates of profit must be different, both between section I and section II, as well as within section I, so that the realization of the product and thus the reproduction of the system can take place without any disturbance.

Consequently, if competition really pushed for the equalization of profit rates, then this would simultaneously create the conditions for some misalignments, i.e. the non-realization of the product in at least some branches. All this can only oppose the harmonious reproduction of the system! More generally, there can be no guarantee that profits accrued in various sectors will be reinvested so as to allow for this harmonious reproduction of the system, and in particular its extended reproduction. All this implies that at each production cycle the architecture of the productive system is modified, with a variation of the relative weight of the different branches which compose it, reflecting the variation of the growth rate of each one of them. It is this kind of phenomenon that we designated as constituting a factor of structural instability within the system. In other words, the realization of the entire product is theoretically always possible, but in practice quite unlikely.

It must also be pointed out that this source of instability can only underlie another one, which lies at a second level and comes out of another problem and another type of analysis, because it concerns the specific monetary nature of the capitalist economy. This other source of instability comes from the nature of money and the conditions of its creation, circulation, and destruction. It involves monetary and financial variables, including debt and interest rates. This is however not the object of this work, being understood that the author, as indicated previously, adheres to the analyzes which in the extension of Keynes' theory of money were
developed inter alia by Minsky, Schmitt, Keen, Godley, Lavoie and others, and are constitutive of what is often labelled as modern monetary theory (MMT) or circuit theory.

To conclude this chapter by coming back to the evolution of the rate of profit, the numerical examples given in this chapter have shown that taking into account extended accumulation and reproduction does not call into question, in the generality of cases (for the most probable values of the parameters) the fact that an increase in the organic composition of capital is in itself associated to a decline in this rate, which validates Marx's analyzes on this point, however with the important nuance that this trend can be countered by an increase in capitalist consumption, as a share of global consumption. This allows us to formulate a last principle.

**Principle 45:** In a situation of extended reproduction and accumulation of capital, the Marxist law of the tendency of the rate of profit to fall when the organic composition of capital increases remains valid, again as a mere tendency. Such a fall can also be caused by an increase in the rate of surplus-value, as well as by an increase in the average lifespan of fixed capital. However, this evolution 1) is not monotonous over time, because the rate of profit initially tends to rise in response to an increase in accumulation and 2) is always countered by an increase in capitalist consumption.

## References

Marx, Karl (1885). *Capital: A Critique of Political Economy. Volume II - Book One: The Process of Circulation of Capital*. Edited by Friedrich Engels. Source: First English Edition of 1907. Marx/Engels Archive [online]. Available at: https://www.marxists.org/archive/marx/works/download/pdf/Capital-Volume-II.pdf
Accessed 18 Aug 2018.
Chapter 23 - Conclusion

In this concluding chapter all the lessons learned during the course of this book will allow us to come back first to the object of economic theory (section 1). We will then expose the final view that we can have on the concepts of production, value and money (section 2), and those of distribution, exchange and prices (section 3). All this will allows us to elaborate on the incompleteness of economic theory (section 4), before a few final words (section 5).

However, having reached the end of this work, it may be useful to start its conclusion by pointing out its limitations. Indeed our objective was not to produce a full-fledged economic theory. More simply, since a satisfying, encompassing and broadly accepted economic theory still does not exist at the beginning of the 21st century, our aim was to ask again, two and a half centuries later, the basic questions that were at the heart of the approach of Adam Smith, the founding father of what we would like to be a truly scientific economic theory: “what are the nature and causes of the wealth of nations?” And if this wealth is made of commodities, where do they come from? This immediately brings us to the question of the nature of commodities, and of their production and distribution.

The object of this book was thus to try and logically define these most basic concepts of commodities, production and distribution. Since production and distribution occur in the context of a social and political system, which establishes the rights of its members on commodities, in particular through the social institution of property, we had to take as a basic assumption that the analysis was set in the broader context of the capitalist mode of production, as it is by far the most dominant system on earth. And since in the real world distribution is carried out through exchanges between commodities and money, which take place on the basis of prices, we had also to be very clear about what money is and what it is not, and what is a monetary price. Finally, since prices are usually defined through the concept of value, it was similarly indispensable to go back to this concept.

Without any false modesty, we think that we have succeeded, since all of the main concepts and the basic principles that underlie them have been defined on the way, in a coherent and logical manner, which should give the possibility for other fellow economists to go further with a view to rebuilding little by little the entire economic theory. But from the outset we need to underline that these principles were not put together from scratch. On the contrary they were defined by going back to the old classical economists, who had already asked the right questions, even though they had not been able to answer all of them. We are thus greatly indebted to Smith and Ricardo, as well as to Marx and Keynes.

However we did not answer all questions which are raised by the economic functioning of the real world. Indeed the theoretical bricks that we have laid under the form of basic principles do not constitute a theory of money, which is understandable, because in our view - and in the wake of Keynes, modern monetary theory (MMT) already exists and is precisely a scientific theory of money, which only lacks to be theoretically linked to a theory of value and prices. As such MMT plays the role of a kind of background for our own theory. The views
developed here and summarized in our principles do not constitute either a theory of the firm,
of investment, growth and development, or a theory of crises, etc. But they open some tracks
which should help to move forward in all of these other fields of economic theory, and we are
hopeful that this will happen, if indeed we have properly defined the right concepts as regards
production and values, distribution and prices, reproduction and profits.

For instance, since our principles show that prices are closely connected to distribution, it
should be possible to combine monetary theory and our theory of value and prices to devise a
coherent theory of inflation. Finally, using some of our concepts should allow to devise some
modified national accounts, with the aim of - among others, providing a better empirical
understanding of the functioning of modern economies, as well as of the building up of
inequalities which has plagued them over the last 40 years.

Such a task would highlight two additional limitations: first the fact that even though there is
money in our analysis, there are no banks as the institutions that create money. Indeed we
have voluntarily restricted this approach to two categories of economic agents: workers and
capitalists. This allowed us not to unduly complicate the circulation schemes, and to focus on
the two main actors who drive a capitalist economic system: workers and capitalists. Second,
the State is also missing, for similar reasons, despite the fact that it is the regulating authority
of the system and an important actor, which connects to the circuit of incomes to both collect
and inject resources into it.

These limitations being acknowledged, this conclusion will aim at synthesizing and
summarizing our main findings, under the headings of production, value and money,
distribution, exchange and prices. We will do that while briefly recalling how they relate to
the economic literature. Moreover, claiming as we do that our principles have a scientific
status implies that we start first with a quick reminder on epistemology, as regards the object
of a scientific theory.

# 1. The object of economic theory

Since science aims at producing “true” descriptions of the world, its object is supposed to be
the real world or rather - since scientific knowledge covers a number of different areas of the
world, one of these areas, on which science is supposed to product such a description, taking
the form of a theory.

Such areas, in the case of economic theory as for all other theories, have to be built by the
theories themselves. This means that a theory must begin by delimiting its perimeter, i.e. the
part or aspect of the real world that it intends to represent, and which distinguishes it from
other theories. This presupposes that this corresponding part of the real world exists within it,
regardless of the theory, and therefore has a material existence, made of material objects,
accessible by the sensible, empirical experience that we can have of this real world, i.e. by a
first level of knowledge acquired through the senses, especially through observation and
experimentation. Building the concepts which define its object, i.e. the basic elements of a
theory and the essential interrelations between them, constitutes what we have called the basic principles of a theory, which are nothing else than an appropriate set of propositions.

It seems obvious that such an object of a theory must exist in the real world, and we think that it is clearly the case as regards the theoretical approach which we have followed in this research, because what we wanted to describe is what in the real world has to do with commodities and the way in which they are produced and distributed among the members of a human society, and more precisely a capitalist economy. Indeed the material existence of commodities, in the broad sense of the word, encompassing goods and also services, like transport, teaching etc., can be ascertained and observed by all of us in the real world. We know also by empirical knowledge that these commodities do not fall from the sky and are produced within the economic system. In contrast, the most famous neo-classical definition of Economics, given by Lionel Robbins in his well-known book "An Essay on the Nature and Significance of Economic Science", is that "Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses." (Robbins, 1932, p. 16).

From the start, we can suspect that this definition is made to be quite problematic. First because its main object is not made of material elements but of a particular human behavior, which is an activity corresponding in fact to a methodology. To be sure, this activity can have a material component, to the extent that it concerns indeed "scarce means". However, a serious problem arises here, because one would normally expect that the theory itself should normally tell us what are these means and where they come from, in other words how they have been created, and if they do not appear simply by teleportation, where and how they were produced.

At this stage, however, we are simply told that at the beginning of the neo-classical theoretical story, all individuals have previously received (from whom and from where?) an endowment of various quantities of all these (scarce) means, or goods. Then these people go to a market where they exchange their goods among themselves in order to allow for the program exposed in the above definition to be carried out. This will materialize, once an equilibrium of supplies and demands is reached on the market for each good, in the form of exchange ratios between all of these goods, which will define their value or price (both words being viewed as equivalent), and allow finally for exchanges to take place, at prices or values which are necessarily relative prices or values.

This neoclassical view suffers from several problems. First, there is no production as such in this description. Nobody knows where the goods endowed to each individual come from. Second, exchanges take the form of barter trade, although it does not exist in the real world, or only in small and residual markets. Third, there must be an auctioneer, to register all proposals of supply and demand, and make the market evolve towards equilibrium, through the announcement of successive systems of exchange ratios, or prices, but there is no auctioneer on most markets in the real world. Fourth, to avoid having a myriad of exchange ratios announced at each stage of the process (n! for n commodities), there must be a general equivalent, taking the form of money, which cannot be other than a particular commodity
chosen as such, allowing to have only n - 1 exchange ratios if there are n goods. Again in the
real world there is no such thing as a commodity-money.

Finally and to go one step further in the working of the mechanism supposed to lead to
equilibrium, the demands and supplies must be formulated on the basis of each participant's
own utility function, taking into account the particular utility which each of them attaches to
each quantity of each commodity. Although it is not mentioned in Robbins's definition, utility
is indeed an indispensable ingredient to define the functions of supply and demand.

The problem is that the utility attached to a particular commodity is a subjective feeling which varies from one individual to the other and from one commodity to the other. Therefore, and despite huge quantities of economic literature on the question, nobody has been able to prove that utility is a dimension of commodities in the scientific sense of the word, i.e. a measurable characteristic of commodities. Therefore utility functions cannot be written without postulating that they are made homogeneous by an ad hoc and arbitrary common unit of measurement. This has been called the postulate of homogeneity, or postulate of the existence of a numeraire. Needless to say that such a numeraire as a measurement unit for utilities does not exist in the real world, and it should in any case be conceptually built.

Indeed, even without going so far as to say that there is science only if there is measurement, it is clear that all sciences which deal with quantities, and consequently with numbers, always need to have a measurement of these quantities, and it is obviously the case in Economics. The problem is that this question is almost never addressed, or is left implicit, by the vast majority of economists, which gives the impression that they are always dealing with pure numbers, or scalars (for instance units of money). This leaves obviously unanswered the question of the dimension of the objects that are measured, as a property which needs to be measurable, all the more so that the question is most often not even asked. Such a dimension is characterized by the nature of the unit of measurement, or the way it is defined. Physical science has defined all the fundamental dimensions that material objects can take in the real world, and there are only seven of them. All the other dimensions are necessarily derived dimensions, i.e. a combination of these seven fundamental ones.

Going back to neo-classical theory, when neo-classical economists are confronted to the
question of the measurability of their objects, i.e. commodities whose common property is
their utility, since they cannot link this property to any known dimension of the real world,
they simply avoid the problem by postulating a unit of measurement that is not defined: it
should normally be a unit of utility, if only utility was a measurable property! The end result
of all this is that neo-classical theory is unable to build its object in a coherent way, and
therefore has no object, in the scientific sense of the term. To say it otherwise, Robbins's
definition, although it seems prima facie to be based on common sense, is ultimately devoid
of any scientific significance, it is a nonsense on which no scientific theory can be built.

This failure of a theory which tries to build its object starting directly from exchanges
between commodities, without explaining in the first place how these commodities were
produced, validates the approaches of economic theories which want to start building their
object from the production of commodities, or what brings them into existence. This is the case with classical economists, Smith and Ricardo, as well as Marx, their most famous heir, and with the approach that we have followed. However, if one wants to build the object of economic theory on the concept of production, one has to be extremely careful in defining this concept, which these economists unfortunately failed to do in a totally coherent way.

## 2. Production, value and money

Unlike the Physiocrats, for whom land was the essential source of any production, Smith, Ricardo and Marx rightly point out that production depends on the productive power of labor, but from this observation Ricardo and Marx conclude that during the activity of production labor can be considered as some kind of a common substance which is passed on to the commodities that it produces. This substance is thus embodied or incorporated into all commodities. Besides they consider that exchange is the exchange of commodities against commodities, if only because money itself - against which commodities are primarily exchanged, is considered by them as a commodity. For them exchange is consequently an equivalence relation between commodities, which defines their value. Values are thus relative values. It results from these premises that the equivalence of commodities on the occasion of their exchange results from the equivalence of the quantities of labor incorporated in them, directly or indirectly, on the occasion of their production. We are here at the heart of the labor theory of value.

The definition of value is quite different for Adam Smith, since in the Wealth of Nations (op. cit.) he writes in chapter 5 “Of the Real and Nominal Part of the Price of Commodities, or of their Price in Labor, and their Price in Money”: “The value of any commodity, therefore, to the person who possesses it, ... is equal to the quantity of labor which it enables him to purchase or command” (Smith, 1776, p. 49). Since wages are paid in money, Smith from the start situates himself at the level of monetary prices, and thus confuses price and value. In other words there is an equivalence in exchange between a quantity of money and the monetary price of a commodity, but not between commodities at the level of production.

Going back to Ricardo and Marx's approach, a first problem that this approach encounters is that it is wrong to consider labor as a substance, because even in the real world labor has no material content, or does not exist as a material or tangible physical object. Labor is an activity, and what we have shown is that as such the only link that can be established between labor and the dimensions of the real world is that this activity, whatever the form it takes, is carried out during time, time being precisely one of the seven existing dimensions defined by physical science. It follows that if labor can allow for the establishment of an equivalence relation between commodities, which gives them their value, it is because this activity has this common dimension of time, which itself has several measurement units, like an hour, a week, a month or a year, all these units being related. Thus values, based on labor time, have the dimension of time.

This explains that seeing values as made of a substance which would be labor is wrong, and has a bearing on the definition of the value of a commodity as incorporating part of the value
of fixed capital, a theoretical position which is developed by both Ricardo and Marx. Indeed fixed capital is supposed to transfer to the product, in each production cycle, a part of its value supposed to be lost through its use. This view comes down to seeing fixed capital as quite similar to circulating capital, i.e. intermediate goods or raw materials which are used and in fact transformed in the production process.

Such a view suffers from logical flaws. First, because production is indeed a transformation process, which implies that quantities produced as an output by any productive system - be it an economical or chemical one, through the transformation of other quantities, cannot be more (or less) than these last quantities used as inputs in this process. If they were more, this would mean that spontaneous generation exists, and if they were less, this would mean that spontaneous disappearance or annihilation exists, and none of these proposals can be scientifically supported. It is moreover a fact that fixed capital, unlike intermediate goods or raw materials, does not transfer any substance, i.e. any material component or physical part to the product during a production process: it does not enter into the production process to be transformed by it. Second, because transferring a part of its value would imply that this value, as a dimension attached to fixed capital, could be detached from it and independently transferred to the product. But such an assumption has no logical foundation, because the dimension of an object is an intrinsic characteristic which cannot be detached from it.

In passing we have shown that defining production as a transformation process implies for the same reason that there can be no physical surplus. Indeed, leaving aside the existence of precautionary stocks of some goods, which by definition, if stocked, are not transformed, the quantities of intermediate goods which are produced during a production cycle are necessarily exactly the same as the quantities which are needed to be then transformed into final goods.

In order to balance inputs and outputs in equations supposed to represent the production process, a precise and complete description of this process (usually not performed by economists), should make explicit the existence on the input side of free goods, like water from rain, carbon dioxide from the air, photons from the sun, or nitrogen from the soil. Since they are free goods their price would obviously be zero. This treatment should apply similarly to minerals like iron ore or crude oil stocked underground: the corresponding quantities pre-exist to their transformation, which takes the form of mining or extraction, being understood 1) that minerals in underground deposits and mineral brought to surface should be considered as two distinct commodities and 2) that all quantities produced as intermediate goods are transformed in the production process. This leaves no place to any surplus, since final goods, made from the transformation of all intermediate goods, have no reason to be considered as such: they are not a surplus, but the end-result of this process. This would avoid the nonsense of Sraffa equations where any intermediate good can be produced in higher quantities than those in which it is used in the production process.

In any case we have shown that the conception of production as transformation allows for the definition of values and for their calculation in a coherent way, and that the dimension of these values is time, understood as the time of physics, which is the reason why we proposed to call them physical values. Moreover we have demonstrated that this calculation is possible
even in the case of joint production. Thus values are logically defined as a measurable dimension of commodities which makes possible to think of them as equivalent at the stage of production. This explains that on the contrary any approaches defining values at the stage of exchange are doomed to failure.

What we showed also is that values cannot exist without money. Indeed in the real world labor time as such is made of very different and heterogeneous types of labor, what Marx called concrete labor, which can hardly be compared. But 1) wages are paid in money, which as a general measurement for values and according to the mathematical theory of measurement is a pure system of numbers, or scalars, and 2) wages are always defined, even implicitly (in the case of task payment) in terms of a quantity of money paid for a quantity of physical time (be it one hour, one week, one month, or even one year). This means that to any quantity of concrete labor, as long as it is paid for a given time, can always be associated a pure quantity of money, which as a scalar or a pure number without any dimension is totally homogeneous. It follows that once all types of concrete labor are paid, they all become homogeneous since to any kind of labor corresponds a quantity of money, itself defining a quantity of abstract labor corresponding to a quantity of average social labor time. This average social labor time is the ratio of total wages by total labor time.

This draws our attention on the paramount importance of wages. First, because they are the only income created in the sphere of production, and as such a primary income. Second, because their payment in money brings money into the productive system, which will allow for circulation to take place. And third, because of their dual dimension, as a scalar or real number without dimension per unit of time. As such wages are not only a derived unit of measurement of the global standard, the *International System of Units*, but an operator in the mathematical sense of the term. Indeed using the average wage per unit of time allows to go from the values of commodities defined in physical time (or physical values) to their monetary values, and reciprocally. In turn this allows to calculate social values, a defined as quantities of average social time. This means that to the system of physical values of commodities defined as a number of time units (with the dimension of time) corresponds a system of social values and a system of money values defined in money units, with a tangible existence in the real world. It follows also from this observation that the money value of the global product is equivalent the overall wage-bill of the productive system.

### 3. Distribution, exchange and prices

The problem with the labor theory of value as exposed by Ricardo and Marx is that it defines value at the level of exchange, conceived as a relation of equivalence between commodities, but simultaneously founds this equivalence at the level of production. In so doing it misses the fact that in the real world exchanges do not take place between commodities, but between commodities and money, which itself is not a commodity: in other words money exchanges against commodities and commodities exchanges against money, but commodities do not exchange against commodities. This implies that the equivalence at the level of exchange is an equivalence between money and the monetary price of a commodity, a price which must logically pre-exist to its exchange against money. To say it otherwise exchanges do not define
relative prices, but monetary prices. Thus prices are not defined by an equivalence relation between commodities in the sphere of circulation, whereas it is in the sphere of production only that values can be defined as such, i.e. on the basis of such an equivalence relation.

This conceptual divergence between prices and values would not be a problem if commodities were exchanged at prices reflecting solely their content in labor, which once converted in money takes the form of wages. The value of a commodity could thus be initially assimilated to its price, itself being measured by its content in terms of wages. To some extent, it is the conceptual path followed by Adam Smith.

However the big conceptual problem that arises at this stage is that exchanges also allow for completing the distribution of incomes with the distribution of profits, i.e. the income of capitalists. Indeed the only income which is distributed at the level of production is wages, because the determination and payment of wages is a condition for production to take place. As for profits, they cannot appear before previously produced commodities are sold on the market. Moreover these profits are a monetary income, and they are not allocated proportionately to the quantity of labor or wages, but to the quantity of fixed capital.

Ricardo and Marx thus realized that exchanges in the real world did not take place according to the value of commodities, measured as they had defined it in terms of quantities of labor embodied into them in the production process. However they continued to stick to the idea that exchange is defined as an equivalence relation between commodities.

As for Smith he had understood that the quantity of labor that can be purchased by the monetary price of a commodity is higher than the amount of all wages paid directly or indirectly to produce this commodity, precisely because this price also contents profits on top of these wages. That these profits were for him additional to wages is clear from this quotation, taken from Chapter 6 “On the Component Part of the Price of Commodities” of “the Wealth of Nations”: “an additional quantity, it is evident, must be due for the profits of the stock which advanced the wages and furnished the materials of that labor” (Smith, 1776, p. 83).

Smith was even conscious that: “In the price of commodities, therefore, the profits of stock constitute a component part altogether different from the wages of labor, and regulated by quite different principles. In this state of things, the whole produce of labor does not always belong to the laborer. He must in most cases share it with the owner of the stock which employs him. Neither is the quantity of labor commonly employed in acquiring or producing any commodity, the only circumstance which can regulate the quantity which it ought commonly to purchase, command or exchange for” (Smith, 1776, pp. 82-83). As for the provenance of these profits, it seems obvious from the above citation that for Smith they were a share of the product of labor.

Indeed he believed that labor was the only factor of production and that fixed capital in itself was not productive, but increased the productivity of labor, as it appears clearly from this citation from Chapter 2 of Book II of the “Wealth of Nations”: “The intention of the fixed
capital is to increase the productive powers of labor, or to enable the same number of laborers to perform a much greater quantity of work" (Smith, 1776, p. 471). Nevertheless he just fell short to qualify profits as a levy on the workers' product, which as such could have been interpreted as constitutive of an exploitation of these workers. Such a recognition would have been opposite to what appeared as the common view of his time.

Owing to a quite different definition of values, it is not surprising that the views of Ricardo were rather different from Smith's theoretical position. Indeed the title of Section IV of the first Chapter of Ricardo's Principles precisely states: "the principle that the quantity of labor bestowed on the production of commodities regulates their relative value (is) considerably modified by the employment of machinery and other fixed and durable capital" (Ricardo, 1817, p. 22). In other words he realized that prices at which commodities were exchanged were not proportional to wages and thus to their labor content, and were as such different from their values. But he nevertheless stuck to the idea that these prices were revolving around their value, and that consequently, unlike Adam Smith's view, a rise in wages implied a fall in profits, and reciprocally. Therefore, for given conditions of production, these prices would change with the rise and fall of wages and the corresponding fall and rise of profits. This is what led him to the search for an invariable measure of value, to which he devoted Section VI of Chapter 1 "On Value" of his Principles. This Section remained nevertheless inconclusive.

However it is this same kind of reasoning which was followed by Sraffa, with the introduction of profits, not at the level of circulation, but at the level of production, as a share of a surplus in the quantities of commodities produced compared to the quantities used in the production process. This is the reason why Sraffa's theory is known as a theory of production prices, or as a neo-Ricardian theory of prices. We demonstrated in Chapter 4 that this theory is wrong, because it suffers from a number of logical flaws, as regards in particular the nature of commodities and the existence of a surplus of commodities. This should not be surprising, because from a conceptual point of view, prices belong to the sphere of circulation, and not to the sphere of production.

As for Marx, he realized like Ricardo and for the same reasons that prices were necessarily different from values, which explains why he considered that it was necessary to transform values into prices. He devoted considerable efforts to this end in book III of Capital, but the result did not satisfy him. It was the reason why he did not published this third book, which was edited by Frederick Engels and completed by him in 1894, i.e. eleven years after Marx's death. Had he continued in the way in which he had started, with the proper mathematical apparatus, Marx might possibly have arrived to the same point as Sraffa.

In fact Marx's great contribution to economic theory was to combine the Ricardian definition of values, implying that fixed capital is not a factor of production, with Smith's implicit view of profits as a share of the product of labor, and therefore as a share of the value of this product. Starting from this basis, he just had to go to the end of its logic by introducing the concept of surplus-value, which is precisely the share of the value of the product which is levied by capitalists, as the owners of both fixed capital and the product of labor. This
logically led him to define the remaining share going to workers, not as the value of their labor, but as the value of their labor-power, a new concept which he needed to introduce for the coherence of his demonstration. This indeed allowed him to introduce the concept of surplus-value, which he defined quite simply as the difference between the value produced in the production process and the value of labor-power, itself being considered as the value of the commodities that workers can obtain in exchange of their wages.

Marx himself considered - and we share this view - that the discovery of surplus-value was one of his main findings. In chapter 2 “Marx and his discoveries” of his book “Reading Capital” (written with E. Balibar) Althusser indeed recalls that in a letter to Engels on 24 August 1867, Marx writes: “The best points in my book are: (1) the two-fold character of labor, according to whether it is expressed in use-value or exchange value. (All understanding of the facts depends on this). It is emphasized immediately, in the first chapter; (2) the treatment of surplus-value independently of its particular forms as profit, interest, ground rent, etc.” (Althusser, 1970, p. 79). A logical consequence of the introduction of this concept is that profits do not reward the productivity of capital but its property.

This citation also shows clearly that for Marx profits were a monetary form of surplus-value, and as such a component of monetary prices, but as we just indicated his theory of transformation of values into prices was wrong. As we also showed this mistake came from his theory of money as a commodity, and from his reproduction schemes, which did not give a correct view of circulation and of the formation of profits in a monetary economy, where money is not a commodity and prices are not relative prices, but monetary prices.

In fact, what we elucidated in chapters 11 and 12 of this book is precisely the mode of formation of profits at the level of the realization of the product, i.e. in the sphere of circulation. We succeeded in this endeavor by taking as a point of departure a remark made by Keynes in his “Treatise on Money”, where he explains that profits spent on consumption goods are a source of new profits for the entrepreneurs whom theses goods are bought from, which means in other words that the spending of profits generate new profits. Keynes went as far as considering that this source could never dry up, writing indeed: “If entrepreneurs choose to spend a portion of their profits on consumption (and there is, of course, nothing to prevent them from doing this), the effect is to *increase* the profit on the sale of liquid consumption goods by an amount exactly equal to the amount of profits which have been thus expended.”...“Thus profits, as a source of capital increment for entrepreneurs, are a widow’s cruse which remains undepleted however much of them may be devoted to riotous living” (Keynes, 1930, p. 139).

Reflecting on this remark, our contribution has consisted firstly in generalizing this mechanism to all types of goods, including fixed capital goods, and secondly to show that at each stage of profit spending, and contrary to what Keynes indicates, there is a partial loss in the purchasing power of these profits. This depletion comes from the fact that wages have to be deducted from the amount of the proceeds, because they represent the money value of the product. Thus the purchasing power of these profits is exhausted in this purchase, and for the amount of this monetary value: first because it represents the realization of a money value
which has already been produced and cannot be realized twice; and second because initially,
at the start of a new production cycle, a corresponding amount of money has to be borrowed
from the banks, which create new money on this occasion to pay for wages. The repayment of
this borrowed money destroys the money previously created and closes its circuit. As a result,
and because of this "leakage", the widow's cruse cannot continue forever undepleted as
Keynes wrongly thought.

Having in mind this mechanism, we had also to get rid of the misconception that workers (or households) should be considered as capitalists to the extent that they own their homes, an idea which comes from the treatment of housing as fixed capital in national accounting. Since such an ownership does not involve the hiring of any workers, there is indeed no reason to consider real estate owned by individuals as fixed capital, even if it is rented. Housing must be considered instead as a consumption good, to be sure with a particularly long life. Indeed renting a dwelling does not appear as different from selling a temporal share of its use, an act which transfers income from the buyer to the seller, without adding any value to the existing global product.

On this basis, we have used two models, the first one without, and the second one with
capitalist consumption, to show that the realization of the whole product is always possible,
provided that the price system and the values of some underlying variables fit well to each
other.

In the simplified system without capitalist consumption, since the whole surplus-value is
restricted to fixed capital, which has to be recovered by capitalists, prices in section II
producing consumption goods must be such as they allow 1) for the workers to buy all of the
consumption goods available, and 2) for capitalists to recover the full value of fixed capital.
This is the case when the global price of consumption goods is equal to the amount of wages
in both sections of the productive system, whereas their money value corresponds to wages in
the section producing these goods. Then the amount of profits in the section producing
consumption goods corresponds exactly to the money value of fixed capital, i.e. wages in the
section producing it. It also corresponds to surplus-value measured in money, with the
consequence that the ratio of profits to wages in section II is exactly equal to the rate of
surplus-value. These profits are then redistributed among capitalists through successive
purchases of fixed capital, a process inspired by the widow's cruse, but more reminiscent of
the nesting of Russian dolls. What emerges from this process is that all profits have to be
spent for them to be realized.

To be sure, the introduction of consumption in our second model complicates somewhat the description of the realization of the product, as well as the calculation of the values of the main variables, but does not question its main conclusions. Indeed profits in section II still correspond to surplus-value in its money form, a surplus-value whose rate is increased because it now depends not only on the relative weight of fixed capital in the overall product, but also on the value of consumption goods obtained by capitalists.
In fact the main lesson from this last model is maybe the paramount importance of this
capitalist consumption as a key variable of the economic system. Indeed, once the appropriate
amount of surplus-value has been levied to match the need for investment in fixed capital, all
the remaining surplus-value has by construction to be devoted to acquiring consumption
goods. This last part can well represent a majority share of surplus-value, higher than the
share of investment, and it is certainly its permanent increase that lies behind the rise in
inequalities observed over the last decades in most capitalist economies all around the world.

It is not surprising therefore to find again this variable as an important determinant of the
evolution of the rate of profit. Our models have indeed allowed us to shed some light on the
old controversies among economists about the rise or fall of this rate in parallel with capital
accumulation supposed to cause a rise in the organic composition of capital. What we have
demonstrated is that Marx’s law of the tendency of the rate of profit to fall is wrong when
there is no capitalist consumption. However, with his own definition of the profit rate (with
variable capital at the denominator of the expression giving this rate), the law is true as soon
as the share in value of capitalist consumption over total consumption exceeds a threshold
which is in fact rather low ($c > \frac{1}{1+t}$, where $t$ is the average lifespan of fixed capital).

Furthermore, with the current definition of the profit rate, an increase in the organic
composition of capital always causes a decrease in the profit rate, *ceteris paribus*. These last
two words are important, because we also showed that this decrease can be counterbalanced
by an increase in the share of capitalist consumption, causing the rate of profit to rise, despite
the increase in the organic composition of capital.

Going back to the divergence between Smith and Ricardo as regards the effect on wages of a
rise in profits, we can say now that both were right, but each one in his own reference system.
Indeed Smith’s reasoning concerns monetary prices, and thus a rise in profits of course
increases these prices, but has no reason to decrease money wages, once they have been
established and paid to workers. As for Ricardo, who reasons not in terms of prices, but of
labor values, an increase in monetary prices and thus in profits corresponds to a rise in the
share of capitalists in the value of the product, and thus to a fall in the share of workers. It is
because Ricardo did not have the concept of surplus-value that he was unable to conclude, as
Marx would have, that this situation is equivalent to an increase in the rate of surplus-value, if
the increase in prices concerns consumption goods. However if the increase in prices were
restricted to fixed capital alone, without influencing the price of consumption goods, we have
shown that it would only affect the redistribution of surplus-value between capitalists, without
materializing in a reduction in the workers’ share of the product.

In any case an important by-product of our demonstration is to make us understand the nature
of monetary incomes. Indeed the only primary incomes are wages, because they are the only
income whose distribution is needed before production takes place. And this for a quite
straightforward reason, which is that nothing would come out of the production process
without the labor done by workers, and that workers would not work if they were not paid
their wages. Although workers are generally paid after having worked for some time (one
week, or at most generally one month), most of the time the commodities that they have produced have not yet reached the market and been sold at the time when they receive their salary. This explains that for classical economists wages were usually considered as advanced. On the contrary the payment of profits is not a condition for the production process to start, and anyway profits could not be paid if commodities were not sold beforehand. Thus it is the realization of the product in the sphere of circulation which allows for the formation of profits.

This elementary finding explains why all incomes other than wages are necessarily transfer revenues derived from wages. Unlike wages, they cannot be linked directly to production, and even more contribute to it, quite simply because they are realized and formed after production has already taken place, i.e. in the sphere of circulation, where previously produced commodities are exchanged against money, which flows in an opposite direction.

The only reason which can be found for the existence of these incomes derived from wages is that they are the counterpart of property, as a social institution giving a right to the use and/or to what is perceived as the fruit of some assets. Profits thus come from the property of fixed capital and rents form the property of non-produced resources like land. All of these transfer incomes are generated through exchanges which can take place only after the production process has been completed and commodities are therefore available to be exchanged.

Profits made in the banking sector also obey to the same logics, and represent a share of the overall surplus-value, whatever the specificities of this sector, where debtor interests correspond to the price of the service of money creation and/or financial intermediation, and creditor interests to the price of parting with liquidity. The evolution of interest rates since the great financial crisis of 2008 has showed definitively that both these rates were heavily influenced by the policy decisions of central banks. Like a number of other prices, they are thus mainly institutionally determined. This finding is important, since it shows that contrarily to neo-classical theory and even to what Sraffa hinted to, the rate of profit and the rate of interest (be it creditor or debtor), are two different variables, which are quite independent because their determination obeys to very different mechanisms.

In passing, as regards Piketty's views on this question, let us recall first that he prefers to talk, not of the rate of profit, but of the rate of return on wealth (a term for him synonymous with capital), which is clearly a rate of return on the ownership of property, knowing that in an interview given on 7 January 2015 he admitted that the marginal productivity explanations of income are wrong, even indicating: "I do not believe in the basic neoclassical model" (Piketty, 2015, Potemkin Review interview). In Piketty's theory the long-term interest rate is part of this global rate of return, it is the rate of return on financial bonds, whereas the rate of profit is the rate of return on more risky investments in real fixed capital. This means that implicitly for him the rate of interest is determined by the rate of profit minus a risk premium. Obviously this is theoretically wrong, and the extremely low level of long term interest rates in developed economies since the world financial crisis has demonstrated that it is also empirically wrong.
In any case all of these incomes other than wages thus appear through the establishment of prices, and none of them can correspond to a primary income corresponding to a creation of value, which by definition can occur only in the sphere of production. Exchanges by themselves cannot generate values ex-nihilo, but only transfer the property of previously produced commodities, by changing their previous distribution. Indeed in the sphere of circulation, any income obtained from a sale corresponds to an income simultaneously spent in a purchase, and which thereby loses part of its purchasing power, corresponding to the money value realized through this purchase, and transfers the remaining part in the form of the seller's profit. One function of these prices is therefore to allow for the creation of these transfer incomes and simultaneously for the distribution of the product. Whereas values can be considered as "production values", this is the reason why these prices, although they derive from values, should not be considered primarily as production prices, but should rather be named "distribution prices".

Acknowledging this particular dimension and role of prices as a determinant of the distribution of commodities has important theoretical implications, which deserve some more elaboration.

**4. Distribution and the incompleteness of economic theory**

Distribution of the available goods is one of the most important activities of any society, from a tribe of hunter-gatherers in the Neolithic period to the highly developed capitalist economies of today. It must have become a powerful factor of inequalities within societies as soon as agriculture started to develop, around 10 000 years ago, which gave birth to the social institution of hereditary private property, at the basis of inequalities of wealth, translating to inequalities of income, as recently recalled in a fascinating book by Walter Scheidel, published in 2017 under the title "The great Leveler. Violence and the History of Inequality from the Stone Age to the Twenty-First Century".

In capitalist economies with fiat money, what we have showed is that the main instrument for the primary distribution of the social product appears to be the price system. It is a fact that distribution of incomes among the members of a given society starts at the stage of production with a first distribution among workers themselves, through wage setting and the pricing of various types of labor.

We have demonstrated that, although this pricing is certainly influenced by what might be called "pure" economic factors, like the situation of supply and demand for each category of labor, the salary scale cannot be reduced to these factors alone. Indeed, once they have been taken into account, it remains an irreducible element, or residue, which can be explained only by non-economic factors. These other factors can be ideological, cultural, political, institutional, and they may have an historical component. In some cases, like the gender bias which works against women, it is easy to understand that labor price can also reflect the balance of power between men and women within human societies. In any case it has nothing to do with the so-called productivity of various types of labor.
It is easy to see the importance of these non-economic factors by comparing two countries with similar levels of development and standard of living. There can be a discrepancy between the relative level of wages for manual and intellectual work, as for instance between France and Germany: in this last country, manual work is comparatively better paid than in France. Or taking self-employed into account, there is a big difference between the incomes of doctors in the USA and France, especially as regards general practitioners.

This is one of the reasons why the theory which has been developed all along this book did not deal with individual prices of particular goods, but only with the overall price of some main categories of goods: final goods, including consumption goods and fixed capital, and intermediate goods. It is thus truly a macroeconomic theory. The global quantities corresponding to each of these categories must be considered as statistical averages, which result from an aggregation approach, and mask the dispersion of individual variables. But it is precisely what made it possible to highlight some general relations between these different variables and to establish basic principles governing the functioning of a capitalist economic system. This gives us the framework within which individual prices are set.

It is our conviction that a microeconomic theory of prices is possible only by taking this framework as a background allowing for setting limits on the magnitude of individual prices, and working then on each price, on a case by case basis, to disentangle the multiple factors which can explain it. In other words microeconomics can only be applied economics<fnref n="14" />, with some of the explanatory factors being purely economic ones, like obviously, to begin with, the underlying money value of a particular commodity, which links it to its conditions of production (wages being given), or the situation of supply and demand for it. But many of these factors will be outside the usual economic scope, since they will have to do with cultural traditions, fashion, the institutional setting or even political interference. An important factor is the market power of the producers of a particular good, which depends in particular on the market structure and on the degree of competition among these producers.

This is reflected when we examine among others the price of intermediate goods, which so far we have tended somewhat to put aside, because we have been reasoning on integrated sectors for consumption goods and fixed capital. If we take for instance the price of crude oil, a good example of an intermediate commodity, it is undeniable that it is not determined primarily by its production cost or even by the balance between supply and demand, to the extent that oil supply itself is decided by complex negotiations between sovereign States, some of them being members of the Organization of the Petroleum Exporting Countries (OPEC). As for the price of oil at consumption level, once it has been transformed into refined products, it varies from one country to another with among others the level of taxes.

The case of supply chains is also worth emphasizing, because at each step of these chains there is some kind of negotiations or arm twisting among stakeholders along the chain. It is in particular the case in the agricultural sector, where a myriad of farmers have to face a few big

<footnote n="14">¹⁴ An interesting approach in this regard has been coined as « Experimental Economics », but its interest remains limited by its narrow scope. As an example see Duflo, E., (2006) "Field Experiments in Development Economics". Massachusetts Institute of Technology. Cambridge. USA.</footnote>
industrial transformers, which themselves must confront with just a few giant supermarket chains. At the end of these chains millions of individual consumers cannot be anything else than disarmed price-takers. Understanding the final price of food products implies therefore a detailed analysis of each case, or each particular supply chain, which cannot be reduced to the neo-classical equations of supply and demand.

This leads us to emphasize the fact that the whole existing economic theory is based on the fundamental assumption that one good or commodity has only one price. In the case of neo-classical theory, because it is a microeconomic theory, supposed to provide the theoretical foundations of macroeconomic theory, based on the determination of prices in a state of general equilibrium on all markets, and because this task would be totally insurmountable if one same good could have several different prices. In the case of other theories, because they have been contaminated by neo-classical reasoning and the use of supply and demand curves, supposed to be an abstract representation of real markets. They just forget that real markets do not function like that, and it is therefore more than doubtful that supply and demand curves provide a good image of the real world...

On the contrary, the assumption of uniqueness of prices was not formulated in the case of this book, for several epistemological reasons: first that the whole is more than the sum of its parts, secondly that if there are general economic laws, they must be defined at a general level which is the level of an economy as a whole, and thirdly that defining these laws implies to work on statistical averages. Therefore the fact that any particular good can have several different prices simultaneously has absolutely no importance, since values were defined as average social values, and since it is always possible to define an average price and work on this basis.

Recognizing at theoretical level the existence of a multiplicity of prices for the same good helps to understand that there is similarly a multiplicity of profit rates, because it is a necessary corollary. Indeed we never made the assumption of a single profit rate, which would be brought about by competition. On the contrary the models that we used to describe the realization of the product showed already that this realization implied different rates for both sections of the economic system, and also within section I producing fixed capital, even without capitalist consumption.

But the introduction of the consumption of capitalists as codetermined with the level of the prices that they can control is also a powerful motive for each individual firm to increase its profit above the average level of its competitors. Finally, if we reason in terms of dynamics, an economic system is permanently changing due to technical progress, the invention of new products and the spur of competition. Old companies whose products become obsolete die and new firms are created every day to exploit new opportunities. This implies that rates of profits are declining and become negative for the first ones and on the contrary start at negative level for the last ones, then grow and can become sometimes very high for members of the second group, made of successful start-ups. And we should not forget that among start-ups, only a minority is usually successful!
What all this tells us as regards economic theory is that it can be compared to other sciences like for instance human physiology, which is a true science in its own right as long as it deals with an average human being, for whom it has defined first the average value of many parameters, like temperature, blood pressure, heart rate, etc., and various ratios of physiological constants, like cholesterol, uric acid, and so on. Obviously human physiology has also established their interrelationships. It is on the basis of this established and recognized science that doctors intervene to diagnose and possibly cure the disease(s) of their patients. But although they can and indeed do rely on an enormous amount of scientific knowledge, validated by numerous experiments and clinical observations, they know that each patient is different from the others and that there are multiple factors that must be taken into account in each case, like genetic factors, the way of living, the influence of environment, patient and family history, and so on and so forth. This is precisely the reason why physicians themselves consider that clinical medicine is not a science, but an art!

This comparison is illuminating, since we can infer from it that microeconomics, for the same obvious reasons, to be sure can and must rely on macroeconomics and on economic laws, in order to perform its own analyses concerning one particular product, price, or profit rate. But there are many factors which then must be taken into account to understand the individual variables which constitute its object, and these factors come under other disciplines than economic theory, like history, anthropology, sociology, psychology, political science, etc. The contributions of these sciences are indispensable to complete its own analyzes which in themselves cannot be comprehensive. This situation, based on scientific methodology, reflects the complexity of the real world and explains that economic laws cannot be fully defined at microeconomic level. Therefore microeconomics in itself is condemned to always remain incomplete and as such to be more an art than a science!

This incompleteness of microeconomic theory does not mean that it cannot produce scientific knowledge, but that do so it must resort to these other social sciences mentioned above, because in the real world pure economic phenomena do not exist. Economic phenomena are closely related to multiple other fields of reality. Since microeconomics is an integral part of economic theory, and since macroeconomics itself - as we have seen with the case of the salary scale as a determinant of money values, is embedded within other aspects of reality, the inescapable conclusion is the incompleteness of economic theory as a whole. As such economic theory is not in any way different from all the other social sciences.

## 5. A few final words

"Pure logical thinking cannot yield us any knowledge of the empirical world; all knowledge of reality starts from experience and ends in it. Propositions arrived at by purely logical means are completely empty as regards reality" (Albert Einstein, in Ideas and Opinions. 1933).

We have now reached the end of this intellectual journey. Along the way, we have gone from production to values, from values to prices, from prices to distribution and profits. In short we tried to redefine the bases of an economic theory which has been in dire straits for decades, and in fact since neoclassical theory has become hegemonic in universities as well as in
publications, and even more in the mind of most rulers all over the world. To get back at this
stage to Wittgenstein and some epistemology, but not being myself a philosopher or a
specialist of Wittgenstein's epistemology beyond the Tractatus, I relied greatly for the four
following paragraphs on an excellent article published in 2005 by Christiane Chauviré:
"Wittgenstein, Sciences and Epistemology Today". Quotes are from this article.

She emphasizes the fact that “the direct cognitive or representational content of a scientific
theory is necessarily limited”, which after all is quite normal since language can only provide
a limited image of the real world. As such, a scientific theory gives but an image of reality
with a certain number of stipulated elements, or assumptions, connected by logical
constraints. Although a theory has a descriptive claim, “it is not intended to capture the inner
and hidden essence of phenomena”. In other words, proposals made by scientific theories
cannot be tightly coupled with the real world, since “the referential and representational link
is only indirect” (Chauviré, 2005, pp. 157-179).

Thus, proposals of a theory do not simply reproduce the real world, much less the immediate
experience, even supposing that language can do it. These proposals “reproduce only the form
of the facts, and cannot account for their full content”, because a whole scientific system is an
"image" less close to the real world than the basic principles that represent “the state of
affairs”. But “science is not limited to recording or photographing a reality that verifies it. A
scientific theory cannot be a copy of the phenomena that would verify it, because it is quite a
complicated and tiered construction” (ibidem).

Indeed economic theory must be viewed as staged on several levels: on the level immediately
descriptive of the elementary logical images or basic principles which already retain only the
form or the structure of the facts, it must superimpose less basic principles and laws which
“move scientific modeling away from a simple factual depiction” (ibidem). The present work
must thus be viewed as an attempt to provide essentially the first stage, i.e. basic principles
and some immediately derived and less basic principles, which could also be viewed as first
laws. They constitute what we chose to call the main principles of political economy.

The theoretical foundations laid here could also be seen as providing the beginning of a
grammar of economic theory. Within this grammar basic principles constitute what might be
called its semantics, giving a precise meaning to basic concepts like value, price, production,
capital, profit etc. As for less basic principles, they provide the first elements of its syntax,
providing the relationships between these concepts which structure them.

Basic principles reproduce only formally or schematically the real world, even though their
objective is nevertheless to lay the foundations of a scientific system which itself can only be
indirectly connected to this real world. This does not mean that basic principles cannot be
submitted to verification. On the contrary, as "complete logical images" formally reproducing
“states of affairs” they can be directly verified by comparison with the real world, in
particular by using all kinds of experiments or statistical data.

Indeed everybody knows from direct experience, for instance from examining his/her bank
account, paying with a credit card or making a wire transfer, that money is not a commodity
with material existence, but a set of figures which are pure numbers without any dimension,
i.e. scalars in the mathematical sense of the word. Everybody also knows empirically that
nothing can be produced whatsoever without spending some quantity of labor, or that wages
received in payment for labor under an employment contract are defined and paid in money
units per unit of physical time, and thereby that all possible types of labor share a common
dimension, which is precisely time.

Similarly all of us know that the vast majority of exchanges take the form, not of a barter
trade between buyers and sellers of commodities, but of simultaneous purchases and sales
where some amounts of money from buyers are given in exchange for commodities provided
by sellers. In another vein, watching any machine working as fixed capital in a production
process provides a convincing evidence that no material component of this machine is
transferred to its final products, in which it would be incorporated. We could continue such a
list, but it would be useless.

Although this would certainly be more complicated, by taking advantage of progress made in
national accounts statistics it should also be possible to verify the evolution of the average rate
of profit as a function of various parameters like capitalist consumption, the stock of
productive fixed capital and its average lifespan, etc., and to check our laws of evolution
concerning the behavior of profit rates over time. The theoretical principles and proposals
established in this book are therefore entirely refutable, and thus certainly meet the criteria to
be falsifiable in the sense of Popper.

Hoping nevertheless that they are not going to be refuted in a near future, we are looking
forward to the work that could be done by our fellow economists to extend and improve these
theoretical foundations. This should be instrumental in finally completely wiping out the
imposture and the false pretenses of neoclassical theory.

Because it succeeded in persuading the political elite in Western countries that it had a true
scientific status, this bunch of theoretical nonsense without any connection to the real world
has indeed been the main support of neo-liberal economic policies that have little by little
after 1980 completely reversed the mode of regulation of capitalist economies which had
prevailed for more than thirty years after the Second World War. State intervention and
Keynesian policies were abandoned in favor of these neo-liberal policies based on
deregulation, globalization and financialisation.

These neo-liberal policies have led to a regression in the rates of growth, de-industrialization,
a fall in labor productivity, a rise in unemployment rates and a significant increase in
inequalities for nearly forty years in almost all the major capitalist countries of the Western
world. I provided some elements for an explanation of this evolution, showing how a reversal
would be possible, in section 3 of my article previously cited about Piketty's book "Capital in
the 21st Century" (Flamant, 2015a, pp. 32-38).

My sincere hope would therefore be that this book could constitute a contribution, in a not so
distant future and in its field, i.e. the area of scientific practice and intellectual confrontation,
to providing an alternative theoretical background to the neo-classical narrative. This might be
of some help for policymakers eager to start a reversal of these harmful neo-liberal policies.

Paris, September 2018

References

Althusser, Louis & Balibar, Etienne (1965). *Lire le Capital*. Paris: François Maspero. English edition: Althusser, L. & Balibar, E. (1970) *Reading Capital* (translation: Brewster, B.). New York: Pantheon Books, Random House.

Chauviré, Christiane (2005). *Wittgenstein, Les sciences et l'épistémologie aujourd'hui (Wittgenstein, Sciences and Epistemology today)*. *Revue de métaphysique et de morale*, vol. 46, N°2, pp. 157-179.

Flamant, Christian (2015a). Again on Piketty's Capital in the Twenty-First Century or Why National Accounts and Three Simple Laws Should not be a Substitute for Economic Theory. *World Economic Review*, issue N° 5 (July 2015), pp. 22-39.

Keynes, John Maynard (1930). *A Treatise on Money*. Last edition: 1971. London: Macmillan.

Ricardo, David (1817). *On the Principles of Political Economy and Taxation*. London: John Murray. Last edition: 2001. Kitchener (Canada): Batoche Books.

Robbins, Lionel (1932). *An Essay on the Nature and Significance of Economic Science*. 2nd edition, revised and extended: 1935. Reprinted, 1945. London: Macmillan.

Scheidel, Walter (2017). *The Great Leveler. Violence and the History of Inequality from the Stone Age to the Twenty-First Century*. Princeton: Princeton University Press.

Smith, Adam (1776). *An Inquiry into the Nature and Causes of the Wealth of Nations*. Published by Political Economy [online]. Available at: http://political-economy.com/wealth-of-nations-adam-smith/ Accessed 5 Sep 2018.
# APPENDIX 1 – FUNDAMENTAL PRINCIPLES OF POLITICAL ECONOMY

**Principle 1:** An elementary commodity is a multidimensional object.

**Corollary to Principle 1:** Commodities are heterogeneous.

**Principle 2:** Commodities must have been produced before being exchanged.

**Principle 3:** Money is not a commodity.

**Principle 4:** Commodities exchange against money and money exchanges against commodities: commodities do not exchange against commodities.

**Principle 5:** Commodities have a monetary price before exchanges take place.

**Principle 6:** As the measurement of a dimension of commodities which appears when it is exchanged against them and called their price, money is a pure set of numbers belonging to the set of positive real numbers $R^+$. As such money has itself no dimension, and is composed of scalar numbers.

**Corollary to Principle 6:** Monetary prices are therefore also dimensionless, scalar numbers.

**Principle 7:** Money is created ex nihilo by banks through credits that they provide to the other economic agents, taking the form of a double asset and a double debt: money is cancelled by the repayment of these credits.

**Principle 8:** Wages are paid in money and have the dimension of dimensionless numbers per unit of time.

**Corollary to Principle 8:** Wages are not paid to workers in wage-goods.

**Principle 9:** Workers buy consumption goods out of their wages, previously paid in money.

**Corollary to Principle 9:** There are no specific consumption goods bought by workers that could be isolated as pure wage-goods.

**Principle 10:** Intermediate goods are bought, not by individuals, but by producers, to enter the production process, where they are physically transformed into other intermediate goods or final goods.

**Corollary to Principle 10:** Goods bought by workers as consumption goods, as well as all the other consumption goods, are not intermediate goods, but final goods.

**Principle 11:** Production, or the activity which creates goods, is a transformation process, which creates new goods through the transformation of pre-existing or already produced goods. As such production does not create any physical surplus.
**Principle 12:** Labor is the human activity which produces goods through the transformation of other goods, and as such is the only factor of production.

**Corollary to Principle 12:** Fixed capital, as well as energy, is not an activity, but a produced good, and as such is not a factor of production. As a good its specificity is that it is not transformed in the production process, but intervenes into it through increasing the productivity of labor. Fixed capital goods are therefore final goods.

**Principle 13:** The only way to think of commodities as homogeneous through a common property, which is by definition their value, is to consider that they are produced by abstract labor, i.e. labor reduced to its only dimension of physical time. Therefore values, and commodities through this common property, have the dimension of time.

**Corollary to Principle 13:** Since time in which values are expressed is the time of physics, measured in physical units like hours, days, weeks, months or years, values at the level of production of commodities must be considered as "physical values".

**Principle 14:** Since fixed capital is not itself transformed in the production process, its value as an intrinsic characteristic of commodities cannot be transmitted to the products in the production of which fixed capital participates only as a catalyst.

**Corollary to Principle 14:** The value of intermediate commodities is transferred to a product because these commodities themselves are transferred to this product through their transformation as a part or an element of it, in the course of its production process. In some cases (like energy) this transformation can be a disappearance.

**Principle 15:** Joint production, defined as the production of several distinct commodities by a single method of production, is compatible with the existence and calculation of positive labor values, as long as different methods produce these commodities in different proportions.

**Principle 16:** In the real world, labor is heterogeneous: there are many kinds of labor, which differ from one branch of production to another and according to the degree of qualification of labor. This is the reason why there is a differentiation of wages. But the precise range of this differentiation cannot be determined within the ambit of economic theory, since it depends on many factors external to this theory, and which are also of a political, ideological, cultural and institutional nature.

**Corollary to principle 16:** the differentiation of wages, as it exists in the real world, as well as the average wage level, must be considered as a given set of data for economic theory, which is one reason why this theory should rather be named political economy.

**Principle 17:** Taking as given the existing wage scale (which provides the level of wages for every kind of labor) allows for the conversion of different kinds of labor expressed in physical time into average social labor, or labor which is paid the average money wage, while keeping the same unit of physical time. This in turn makes it possible to calculate the average social values of all commodities, expressed in average social labor time.
**Corollary to principle 17:** Multiplying the social values of commodities by the average wage expressed in money units per unit of average social time, gives their money value at the stage of production.

**Principle 18:** The wage bill is the measurement of the monetary value of the product.

**Principle 19:** In the capitalist mode of production, fixed capital is by definition the property of capitalists but not of workers, who own neither the means of production nor the commodities which they create through their labor. The simple reproduction of this system as it is implies therefore that workers cannot get on the market, from the spending of their wages the property of at least this part of the product consisting of means of production. The difference between the whole product of labor and the share obtained by workers is defined as surplus-value.

**Principle 20:** Surplus-value is created in the sphere of production, but extracted in the sphere of circulation, where commodities are distributed among various stakeholders. This results from the fact that wages, as the money price of labor-power representing the money value of the whole product, can buy only a share of this product consisting in consumption goods, whose price is always higher than their money value. Surplus-value thus materializes under its monetary form as profits in the section producing consumption goods. These profits are then distributed among capitalists.

**Principle 21:** The only primary incomes are the revenues created on the occasion of the production process, and are the monetary counterpart or remuneration of labor, i.e. wages in a pure capitalist mode of production.

**Principle 22:** Profits, as any income other than wages or the remuneration of labor, derive from the property of commodities or assets. They are transfer revenues which arise from exchanges against money of previously produced commodities (or assets) taking place in the circulation process.

**Principle 23:** A levy imposed on the purchasing power of primary incomes through an increase in the price of consumption goods also constitutes a transfer of purchasing power to secondary money incomes. Spending these incomes creates a new levy on secondary incomes when they buy consumption goods as well as fixed capital, and a new transfer of purchasing power. The same process can continue as long as purchasing power is remaining and ensures henceforth the full realization of the whole product from both sections of the productive system.

**Principle 24:** Rent is the income that comes from the property of non-produced means of production, such as land or mines, and is collected by the owners of these means of production. There are two kinds of rent: differential rent and absolute rent. Differential rent comes only from the heterogeneity of each type of non-produced means of production, i.e. from differences in their intrinsic characteristics, and varies according to this heterogeneity. Because of its origin in property rights, absolute rent is the rent perceived even on the least
"productive" (i.e. with no differential rent) of a particular type of non-produced means of production (otherwise it would not be rented). It is also perceived on all the other non-produced means of production of the same type.

**Principles 25:** There is no rent as such coming from the heterogeneity of the techniques which can be employed by various firms using homogeneous non-produced means of production, which already pay a rent for this use. This heterogeneity only results in profit rate differentials. However, owing to the use of non-produced means of production, the corresponding differences in production costs from the average cost can be called "quasi-rents", to distinguish them from other types of profit differentials.

**Principle 26:** Actual rents are always a combination of differential and absolute rents. Whatever their combination, the nature of rent is not different from that of profits: rent is also a transfer income, which is levied as a part of total surplus-value. Changes in differential rents can result from an exogenous change in the price system. They also correspond to changes in the scale of production, implying the use of additional non-produced means of production (in the case of an increase). Such changes therefore always entail a change in the value of the product and the price system.

**Principle 27:** Theoretically, for a given and fixed value of the product, if an increase in rent (hence absolute rent) could leave prices unchanged, the amount of surplus-value would not change, and the amount of rent would be deducted from profits. In practice, such an increase will have repercussions on prices, whose magnitude depends on the balance of power between the three involved groups of agents: rentiers, capitalists and workers. The ultimate effect on the amount of surplus-value and its distribution between rentiers and capitalists will depend on the balance of power between these groups, under the arbitration of the State.

**Principle 28:** Because of their close connection to money values, which themselves reflect the conditions of production, it is not wrong to consider prices as also reflecting these conditions, and thus as production prices. However this is a very partial view of reality. First because money values themselves are depending on the distribution of wages between workers. And second because their fixing is linked to the extraction of surplus-value (for section II prices), and to the distribution of this surplus-value between capitalists (for section I prices). As a result, prices must be further considered as distribution prices, being understood 1) that the understanding of distribution involves many factors, a number of which have nothing to do with economy as such, because they are of a sociological, ideological, institutional and political nature, and 2) that distribution itself must be seen ultimately as a distribution of commodities.

**Principle 29:** Prices, in so far as they are distribution prices, are the object and the resultant of multiple conflicts, which may or may not be arbitrated by the State. They ensure the continuity of the capitalist mode of production by ensuring the distribution of fixed capital among capitalists. But even more they also ensure the collection and distribution of consumption goods among these same capitalists. They make us realize that the ultimate goal
of capitalists is not only the accumulation of fixed capital, but also the accumulation of
consumption goods.

**Principle 30:** The banking sector plays a fundamental role in the capitalist mode of production, by creating the money which among others is indispensable for the payment of wages. The service that the sector renders, by providing this money as well as the service of financial intermediation, has like all services a value measured by the amount of average social labor time spent in the sector, and a money value, measured by the amount of money wages paid to the sector' workers, who contribute like all workers to the creation of surplus-value. The macroeconomic cost of the services of money creation and intermediation is made of wages and of a cost which is the creditor interest rates paid to depositors of money in the banking sector. To this cost must be added the profits of the banking sector, to obtain the price of the service.

**Principle 31:** Like rent is the price paid to or income received by the owners of non-produced goods for obtaining the right to use them during a defined period, creditor interest rates must be considered as the price paid to or income received by the owners of money assets so that banks can use these assets during a defined period. This is why interest rate can be viewed as the price received for parting with liquidity. Interests paid by borrowers are similarly the price paid by them to banks to be able to use defined amounts of money during a specified period, and which constitutes the banks gross income. It follows that interest as an income remunerates the property of money assets, owned either by depositors or by banks. Therefore, like profits or rents, interests are a transfer income.

**Principle 32:** Formally money should be considered as produced by banks, to some extent ex nihilo, because it is not the result of a transformation. But it must be considered nevertheless as non-produced, because – like land for instance, it does not belongs as such to the production process, where it does not results from a transformation and is not itself transformed. It is so because money is not a good that could be sold against itself, which would be a nonsense. Only the right to use it for a definite period is sold (also like for land), against payment of an interest. As such money cannot be considered neither as a final good, which could be consumed or stored, because at global level it always has to be repaid, which ultimately destroys it, nor as an intermediate good or service, which would disappear in the production process.

**Principle 33:** Apart from various fees, the price of the services of money creation and financial intermediation rendered by banks corresponds to the debtor interest rates charged by banks to borrowers. Their overall amount during a given period of time is part of the total price of the product of this period. It includes wages paid in the banking sector, i.e. the money value of bank services, creditor interests paid to depositors and bank profits. Both creditor interests and bank profits are part of global surplus-value. Bank services can be sold both to firms and individuals, be they capitalists or workers. When they are sold to firms, they play the same role as intermediate commodities, and their price becomes a part of the price of the final product, either of consumption goods or fixed capital goods, depending on the section which the firms are part of. When they are sold to individuals, these are part of their
consumption, and thus play the same role as consumption goods, of which they are a
particular type.

**Principle 34:** A macroeconomic theory is a theory where all prices are statistical averages, and consequently where the magnitude of all "real" variables, since they are measured in terms of prices of their constitutive commodities, is itself a statistical average. A microeconomic theory of prices should therefore restrain itself to the disaggregation of these statistical averages, with a view to understanding the formation of the price or multiplicity of prices of each particular commodity included in these same averages.

**Principle 35:** The aim of microeconomic theory should be to understand and explain the divergence between individual prices and statistical averages. This should be done first for the various prices of a same commodity, which come from differences in the conditions of production and in the rates of profit, as well as in the level of rents. This should also apply to the explanation of the difference between the rates of profit affecting the production and distribution of different commodities.

**Principle 36:** The average rate of profit cannot be considered as a meaningful element of economic theory. Indeed, apart from the difficulty to simply measure it in the real world, it is nothing else than a mere statistical average. The real world, as well as a number of theoretical factors deriving from the nature of profit formation and realization, show that there is a multiplicity of profit rates both in theory and practice, and that the nature of economic activity, based on competition among firms, always pushes to a differentiation of these profit rates. The profit/wage ratio plays a more important role for the understanding of economic processes.

**Principle 37:** It might exist a set of variables which make it theoretically possible to guarantee a balanced reproduction of a capitalist economy, in the neo-classical sense of ensuring a simultaneous equilibrium on all markets. However such a reproduction is practically impossible to obtain, for a number of equally theoretical reasons. First, because of the decentralized nature of such an economic system, which implies that decisions by capitalists, who fix prices and make investment decisions, are made independently, moreover in situations of imperfect information, and not coordinated. Second, because these decisions are made within time frames and based on expectations about the future which cannot be rational, because of the natural uncertainty which characterizes what happens in the future. Third, because the dynamics of the system, if they are left unregulated by State authorities, go in the direction of a permanent increase in the rate of surplus-value, which in itself has destabilizing effects.

**Principle 38:** It is the very engine of the capitalist system, i.e. the pursuit of maximum profit at micro-economic level, which at macro-economic level constitutes a powerful factor of structural instability. Starting with a reduction in wages, it leads to cascading maladjustments that do not allow a full realization of the product and therefore hamper the reproduction of the system.
**Principle 39:** An autonomous increase in capitalist consumption financed through money creation can be a remedy to crises deriving from insufficient demand from workers, since it offsets the slump in workers consumption, and results in a higher share of profits. However higher profits may end up being at least partly spent for the purchase of existing assets instead of commodities. This cannot but perpetuate the insufficiency in demand for commodities and trigger speculation, which has been shown to be at the origin of financial crises.

**Principle 40:** As Keynes had well understood, autonomous investment financed by money creation is the most effective tool to help an economic system out of a crisis. However Keynes, like his followers, was wrong in thinking that it would trigger a net multiplier effect such that the outcome in terms of product would be higher than 1. Because of leakages due to the existence of transfer incomes at each stage of spending, the overall amount of the multiplier between autonomous investment or spending and the corresponding product cannot be greater than 1.

**Principle 41:** In a situation of simple reproduction where there is no capitalist consumption and all surplus-value is invested, the rate of profit rises with the increase in organic composition of capital, both being the result of an increase in the rate of surplus-value.

**Principle 42:** In a situation of simple reproduction where capitalist consumption is introduced, then the rate of profit defined as Marx does becomes dependent on the share of this capitalist consumption in total consumption. The validity of the Marxist law of the tendency of the rate of profit to fall when the organic composition of capital increases depends therefore on this share. If this share exceeds a threshold linked to the lifespan of fixed hospital and defined by $c = \frac{1}{1+t}$, the Marxist law is valid. If this share is lower than this threshold the Marxist law is not verified and the rate of profit increases on the contrary as a function of the organic composition of capital.

**Principle 43:** When then the rate of profit defined according to its current definition (i.e. without applying this rate to wages - as if they were advanced), and in a situation of simple reproduction with capitalist consumption, this rate is an increasing function of $k$, the primary rate of surplus-value, $k_c$, the actual rate of surplus-value with capitalist consumption, and $c$, the share of capitalist consumption in total consumption. On the contrary it is decreasing in terms of $q_c$, the organic composition of capital. This confirms the validity of the Marxist law of the tendency of the rate of profit to fall when the organic composition of capital increases. But this law remains a mere tendency, since it can be thwarted by an increase in capitalist consumption, which shows the paramount importance of this variable.

**Principle 44:** The share of profits in the product (named $\pi$) is also an increasing function of the primary rate of surplus-value and of the share of capitalist consumption, and thus necessarily of $k_c$, the actual rate of surplus-value. The rate of profit itself is an increasing function of $\pi$.
**Principle 45:** In a situation of extended reproduction and accumulation of capital, the Marxist law of the tendency of the rate of profit to fall when the organic composition of capital increases remains valid, again as a mere tendency. Such a fall can also be caused by an increase in the rate of surplus-value, as well as by an increase in the average lifespan of fixed capital. However, this evolution 1) is not monotonous over time, because the rate of profit initially tends to rise in response to an increase in accumulation and 2) is always countered by an increase in capitalist consumption.
# APPENDIX 2 - THE ERRONEOUS NATURE OF MARX'S REPRODUCTION SCHEMES IN BOOK II OF CAPITAL

On the basis of the distinction made by MARX, the value produced in each period is $L_I$ for section I and $L_{II}$ for section II. The assumption that fixed capital transfers its value to the product can then be incorporated into the reproduction scheme on the basis of two different interpretations, of which it will be demonstrated that neither of them adequately solves the problem of realizing the product.

## 1. A first interpretation of the transfer of value of fixed capital

This first interpretation consists in considering that in simple reproduction the value lost and transmitted by fixed capital in the two sections of production is identical with the value of the product of Section I, which produces fixed capital.

Let us consider that $a$ is the fraction of the value of fixed capital that is consumed and transferred to the product in Section I, and $b$ the fraction consumed and transferred to the product in Section II.

$$ \text{We thus have } a + b = 1 \text{ and } b = 1 - a \text{ with } 0 < a < 1 \text{ and } 0 < b < 1 \qquad (1) $$

In order for the reproduction scheme to be in accordance with the adopted interpretation, it is first necessary to determine the value of the product of section I, which represents a certain factor of the value newly produced in this section (the difference being the transfer of value from fixed capital). Let us call $x$ this factor, with $x > 1$ and such that:

$$ \frac{\text{value of the section I product}}{\text{Value newly produced in section I : } L_I} = x \qquad (2) $$

The following scheme is thus obtained for the value produced in each section:

$$ \text{Section I: } a(xL_I) + L_I = xL_I \qquad (3) $$

$$ \text{Section II: } b(xL_I) + L_{II} = (1-a)(xL_I) + L_{II} \qquad (4) $$

From the conditions of production of value in Section I we derive:

$$ L_I = (1-a)xL_I \qquad (5) $$

$$ \text{Hence it follows that } x = \frac{1}{1-a} \qquad (6) $$
It is thus possible to write the reproduction schemes of equations (3) and (4) as a function
only of L<sub>I</sub>, L<sub>II</sub> and <sup>a</sup>, which gives the following identities, for each of the two sections:

$$
\text{Section I: } a \frac{1}{1-a} L_I + L_I = \frac{1}{1-a} L_I = K \qquad (7)
$$

$$
\text{Section II: } (1-a) \frac{1}{1-a} L_I + L_{II} = \frac{(1-a)}{1-a} L_I + L_{II} \qquad (8)
$$

$$
\text{Thus for section II: } L_I + L_{II} = L_I + L_{II} \tag{9}
$$

Let us name Y the value of the total output of the two sectors, it is thus:

$$
Y = \frac{1}{1-a} L_I + (L_I + L_{II}) \Rightarrow Y = \left(\frac{2-a}{1-a}\right) L_I + L_{II}: \qquad (10)
$$

Does this scheme allow for a correct analysis of the realization of the product of both
sections? Apparently yes, since equations (7) and (8) show first that the value of the variable
capital advanced in the two sections, L<sub>I</sub> + L<sub>II</sub>, is identical to the value of the product of Section
II, which can thus be sold to and bought by workers. Similarly, the value K of the product of
Section I, the fixed capital produced during the period, i.e. <sup>1</sup>&frasl;<sub>1-a</sub> L<sub>I</sub> (see equation 7), is equal to

$$
\frac{a}{1-a} L_I + L_I \text{, the sum of the value of fixed capital consumed productively and transmitted to} \\
\text{the product in Section I, i.e. } \frac{a}{1-a} L_I \text{, and in Section II, i.e. } (1-a) \frac{1}{1-a} L_I = L_I \text{ respectively.}
$$

But this presentation, although arithmetically correct, is nevertheless possible only at the cost
of an error of logic which will now be explained and will consequently lead to reject the
initial assumption (that the value lost and transmitted by fixed capital in the two sections of
production is identical with the value of the product of Section I).

The reason why the above scheme is not logically coherent can be summarized as follows: the
interpretation on which the above scheme is based is contradictory with an obligatory
corollary of the assumption of the transmission of the value of fixed capital, according to
which the value transmitted by fixed capital must by definition be necessarily identical to the
value lost by this fixed capital because of its consumption, itself necessarily identical, in fine,
to the initial value of this fixed capital. This contradiction results from the fact that the
interpretation adopted implies that fixed capital transfers its value several times to the
product.

To show it, it suffices to note that the value transmitted to the value of the newly produced
fixed capital during one period is then necessarily retransmitted to the following period by the
same fixed capital when in turn it becomes to operate, and so on and so forth. The value
transmitted by the fixed capital in section I is thus carried out in an iterative manner during
the successive production periods.
From the above reproduction scheme, it is in fact immediate, according to equation (7), that at each period a fraction $a$ of the value of the fixed capital produced and realized in section I is constituted of value transmitted by the consumption during that same period of the fixed capital in operation. This fraction $a$ is then in turn transmitted and realized during the periods when this capital is in function, and so on and so forth. The same fixed capital in this way transmits its value over an infinity of periods, in such a way that, if the sum of these successive transmissions is made, one obtains for a fixed capital of an initial value K, equal to

$$ \frac{1}{1-a} L_I : $$

$$ \text{Value transmitted over n periods} = K + aK + a^2 K + \dots + a^n K = \frac{1}{1-a} K = \frac{1}{(1-a)^2} L_I \quad (11) $$

For example, for $a = \frac{1}{2}$, the value transmitted by the fixed capital K during the successive periods is thus from equation (11) equal to $4 L_I$, i.e. twice its initial value $2 L_I$, and for $a = \frac{3}{4}$ the transmitted value is equal to $16 L_I$, i.e. four times the value $4 L_I$ of the fixed capital. In passing, one notes the importance of the value of the $a$ coefficient!

Since the value transmitted varies as a function of $a$, and since its compulsory logical corollary: transmitted value = lost value, is not verified, we must conclude that the Marxist assumption of the transmission of value of fixed capital is not consistent with the interpretation of simple reproduction which implies the identity between the value of the fixed capital which is produced and the value which is transmitted during one period.

This explains in passing another strange phenomenon, which may not have escaped the reader, although it may seem anecdotal: the reasoning which was developed on the basis of the hypothesis of transmission of the value of fixed capital to the product implies that the value of the fixed capital K produced in Section I and that of the total product Y depend on the $a$ coefficient, which reflects the share of the total value of fixed capital used and accumulated in Section I, and consequently the distribution of fixed capital between the two Sections of production. One will admit that this is not logically coherent, which confirms that the assumption which has been tested in this subsection leads to absurd reasoning.

## 2. A second interpretation of the transfer of value of fixed capital

It is possible to show that the phenomenon of transmission by fixed capital of a value greater than its initial value does not take place if one considers that the transmission of the value of fixed capital results solely from the fraction of the value of fixed capital newly produced by living labor. We have indeed in section I, again on the basis of equation (7):

$$ \text{Newly produced value} = L_I = (1-a)K \quad (12) $$

$$ \text{Value transmitted over n periods:} = (1-a) \frac{K}{1-a} = K = \frac{1}{1-a} L_I \quad (13) $$
It can be seen that the value K transmitted by the newly produced part $(1-a)K$ of the value of fixed capital is identical to the total value of this capital. It can be inferred that for fixed capital to transfer to the product a value identical to that which it can lose, and which cannot be different from its initial value, it is necessary and sufficient that this transmission concerns only the fraction of its value resulting from living labor.

One can thus be tempted to adopt a second interpretation allowing the integration to simple reproduction of the assumption of transmission of the value of fixed capital. In this interpretation it is therefore considered that the value transmitted by fixed capital during each period is identical to the value of the fixed capital newly produced by living labor implemented in section I.

In this case the value of the product of each of the two sections becomes:

$$ \text{Section I: } aL_I + L_I = (1+a)L_I \qquad (14) $$

$$ \text{Section II: } bL_I + L_{II} \qquad (15) $$

Is the realization of the product possible in this framework? To answer this question, let us recall first of all that if we follow Marx in his reasoning in Volume II of Capital, there is no surplus value in our model, and consequently no profit, from which it follows that the commodities produced are exchanged at their value. To address the question of realization comes down therefore to ask oneself what are the condition for the commodities produced in both sections to be disposed of at their value. With regard to section II above, the realization of the consumer goods produced there implies that the value of the variable capital advanced in the two sections, i.e. $L_I + L_{II}$ (in the absence of surplus value), is identical to the value of consumer goods. One must therefore have:

$$ L_I + L_{II} = bL_I + L_{II} $$

But this identity is verified only if $b = 1$, which implies ipso facto $a = 0$. This means that the realization of consumer goods requires that the totality of fixed capital be used for the production of consumer goods, And that no fixed capital is used for the production of goods of production!

This very special hypothesis is necessary in order to ensure that simple reproduction takes place in the absence of exploitation of workers, who receive in exchange for the value of their labor power ($L_I + L_{II}$), on the one hand the value newly produced of consumption goods ($L_{II}$) and on the other hand the totality of the value transmitted by the fixed capital, which is by hypothesis (in this second interpretation) only $L_I$.

But such a hypothesis is not logically permissible, since the production of fixed capital without the aid of means of production, besides being totally artificial and therefore unrealistic, means that the capitalists producing the fixed capital, owning in fact no means of production, are not actually capitalists!
APPENDIX 3 - SUMMARY TABLES OF VALUES AND PRICES OF
THE MAIN VARIABLES OF THE MODELS
<table><caption>Table 1 – TABLE OF VALUES AND PRICES IN THE SIMPLE MODEL</caption><thead><tr><th rowspan="2"></th><th colspan="2">Output</th><th colspan="3">Labor power</th><th colspan="3">Surplus-value/Profit</th></tr><tr><th>Output of section I</th><th>Output of section II</th><th>Global output</th><th>Section I</th><th>Section II</th><th>Total of two sections</th><th>Section I</th><th>Section II</th><th>Total</th></tr></thead><tbody><tr><th>Values</th><td>$L_I = kL_{II}$</td><td>$L_{II}$</td><td>$L_I + L_{II}$</td><td>$V_I = \frac{L_I}{1+k}$</td><td>$V_{II} = \frac{L_{II}}{1+k}$</td><td>$L_{II}$</td><td>$\frac{k}{1+k}L_I$</td><td>$\frac{k}{1+k}L_{II}$</td><td>$L_I = kL_{II}$</td></tr><tr><th>Prices</th><td>$\frac{1}{L_I} = \frac{1}{1-a}$</td><td>$\frac{L_I + L_{II}}{(1+k)L_{II}} = \frac{2-a}{(1-a)+\frac{1}{k}}$</td><td>$L_I(\frac{2-a}{(1-a)+\frac{1}{k}})$</td><td>$W_I = L_I$</td><td>$W_{II} = L_{II}$</td><td>$W = L_I + L_{II}$</td><td>$\frac{a}{1-a}L_I$</td><td>$L_I = kL_{II}$</td><td>$\frac{1}{L_I} = \frac{1}{1-a}$</td></tr></tbody></table>

<table><thead><tr><th rowspan="2"></th><th colspan="2">Ratio</th><th colspan="3">Organic composition of capital</th><th colspan="3">Rate of profit</th></tr><tr><th>Section I</th><th>Section II</th><th>Total</th><th>Section I</th><th>Section II</th><th>Total</th><th>Section I</th><th>Section II</th><th>Total</th></tr></thead><tbody><tr><th>Values</th><td>$k = \frac{L_I}{L_{II}}$</td><td>$k = \frac{L_I}{L_{II}}$</td><td>$k$</td><td>$at(1+k)$</td><td>$(1-a)(1+k)kt$</td><td>$q_{=k,t}$</td><td>$\frac{k}{akt+at+1}$</td><td>$\frac{k}{kt(1-a)(1+k)+1}$</td><td>$\frac{k}{kt+1}$</td></tr><tr><th>Prices</th><td>$\frac{a}{1-a}$</td><td>$k = \frac{L_I}{L_{II}}$</td><td>$\frac{k}{(1-a)(1+k)}$</td><td>$q_I = \frac{at}{1-a}$</td><td>$q_{II=kt}$</td><td>$\frac{k.t}{(1-a)(1+k)}$</td><td>$\frac{a}{at+1-a}$</td><td>$\frac{k}{kt+1}$</td><td>$\frac{k}{kt+(1-a)(1+k)}$</td></tr></tbody></table>
<table><caption>Table 2 - TABLE OF VALUES AND PRICES IN THE MODEL WITH CAPITALIST CONSUMPTION</caption><thead><tr><th rowspan="2"></th><th colspan="2">Output</th><th colspan="3">Labor power</th><th colspan="3">Surplus-value and Profit</th></tr><tr><th>Output of section I</th><th>Output of section II</th><th>Section I</th><th>Section II</th><th>Total of 2 sections</th><th>Section I</th><th>Section II</th><th>Total</th></tr></thead><tbody><tr><th>Values</th><td>L<sub>I</sub> = kL<sub>II</sub></td><td>L<sub>II</sub></td><td>V<sub>I</sub> = <sup>L<sub>I</sub></sup>&frasl;<sub>1 + k<sub>c</sub></sub></td><td>V<sub>II</sub> = <sup>L<sub>II</sub></sup>&frasl;<sub>1 + k<sub>c</sub></sub></td><td>V<sub>c</sub> = L<sub>II</sub>(1 - c)</td><td><sup>L<sub>I</sub>k<sub>c</sub></sup>&frasl;<sub>1 + k<sub>c</sub></sub> = L<sub>I</sub><sup>k + c</sup>&frasl;<sub>1 + k</sub></td><td><sup>L<sub>II</sub>k<sub>c</sub></sup>&frasl;<sub>1 + k<sub>c</sub></sub> = L<sub>II</sub><sup>k + c</sup>&frasl;<sub>1 + k</sub></td><td>Pl = L<sub>II</sub> (k + c)</td></tr><tr><th>Prices</th><td><sup>L<sub>I</sub></sup>&frasl;<sub>(1 - a)(1 - c*)</sub></td><td>1 + k/L<sub>II</sub></td><td>W<sub>I</sub> = L<sub>I</sub></td><td>W<sub>II</sub> = L<sub>II</sub></td><td>W = L<sub>I</sub> + L<sub>II</sub></td><td>L<sub>I</sub>(α + γ* + αγ*)</td><td>L<sub>II</sub>·kc = L<sub>II</sub><sup>k + c</sup>&frasl;<sub>1 - c</sub></td><td>L<sub>I</sub>(α + γ* + αγ*) + L<sub>II</sub>k<sub>c</sub></td></tr></tbody></table>

<table><thead><tr><th rowspan="2"></th><th colspan="2">Ratio</th><th rowspan="2">Organic Composition of capital</th><th colspan="3">Rate of profit<br>We put Ψ=1+α+γ*+αγ*</th></tr><tr><th>Section I</th><th>Section II</th><th>Total</th><th>Section I</th><th>Section II</th><th>Total</th></tr></thead><tbody><tr><th>Values</th><td>k<sub>c</sub> = <sup>k + c</sup>&frasl;<sub>1 - c</sub></td><td>k<sub>c</sub> = <sup>k + c</sup>&frasl;<sub>1 - c</sub></td><td>k<sub>c</sub> = <sup>k + c</sup>&frasl;<sub>1 - c</sub></td><td>Section I</td><td>Section II</td><td>Section I</td><td>Section II</td><td>Total</td></tr><tr><th>Prices</th><td>α + γ* + αγ*</td><td>k<sub>c</sub> = <sup>k + c</sup>&frasl;<sub>1 - c</sub></td><td>Cf. equat. 54<br>In chapter 12</td><td>at(1 + k<sub>c</sub>)</td><td>kt(1 - a)<br>(1 + k<sub>c</sub>)</td><td><sup>k<sub>c</sub></sup>&frasl;<sub>at(1 + k<sub>c</sub>) + 1</sub></td><td><sup>k<sub>c</sub></sup>&frasl;<sub>kt(1 - a)(1 + k<sub>c</sub>) + 1</sub></td><td><sup>k + c</sup>&frasl;<sub>kt + 1 - c</sub> = <sup>k<sub>c</sub></sup>&frasl;<sub>(k<sub>c</sub> - γ)t + 1</sub></td></tr></tbody></table>
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DETAILED TABLE OF CONTENTS

<table><tr><td>CONTENTS</td><td>9</td></tr></table>

<table><tr><td>LIST OF ABBREVIATIONS</td><td>13</td></tr></table>

<table><tr><td>LIST OF FIGURES AND TABLES</td><td>17</td></tr></table>

<table><tr><td>Chapter 1. Introduction: the basic concepts and principles. Commodities, Exchange and Money</td><td>19</td></tr></table>

<table><tr><td>1. MAIN STEPS OF THE APPROACH</td><td>19</td></tr></table>

<table><tr><td>2. THE BACKGROUND</td><td>20</td></tr></table>

<table><tr><td>3. ECONOMIC VARIABLES HAVE A DIMENSION</td><td>21</td></tr></table>

<table><tr><td>4. COMMODITIES</td><td>22</td></tr></table>

<table><tr><td>5. EXCHANGE</td><td>24</td></tr></table>

<table><tr><td>5.1. The neo-classical approach</td><td>25</td></tr></table>

<table><tr><td>5.2. The classical approach</td><td>25</td></tr></table>

<table><tr><td>5.3. Exchange and money</td><td>26</td></tr></table>

<table><tr><td>6. MONEY</td><td>28</td></tr></table>

<table><tr><td>6.1. The mathematical theory of measurement</td><td>28</td></tr></table>

<table><tr><td>6.2. The nature of money</td><td>33</td></tr></table>

<table><tr><td>PART I - PRODUCTION WITH A SURPLUS: A THEORETICAL DEAD-END</td><td>37</td></tr></table>

<table><tr><td>Chapter 2. The Ricardian theory of production, distribution and value</td><td>39</td></tr></table>

<table><tr><td>1. THE RICARDIAN PROBLEMATICICS AND ITS BASIC DATA</td><td>39</td></tr></table>

<table><tr><td>1.1. The Ricardian problematics</td><td>39</td></tr></table>

<table><tr><td>1.2. The exogenous data</td><td>39</td></tr></table>

<table><tr><td>2. A FIRST TRY TO SOLVE THE DISTRIBUTION PROBLEM: "THE ESSAY ON PROFITS"</td><td>40</td></tr></table>

<table><tr><td>2.1. A mathematical presentation of the Essay on Profits</td><td>40</td></tr></table>

<table><tr><td>2.2. The underlying conception of production and distribution</td><td>44</td></tr></table>

<table><tr><td>2.3. A highly questionable model</td><td>45</td></tr></table>

<table><tr><td>3. THE PROBLEM OF VALUE AND PRICES FOR RICARDO</td><td>47</td></tr></table>

<table><tr><td>3.1. The problem in terms of labor values</td><td>47</td></tr></table>

<table><tr><td>3.2. The same problem in terms of production prices</td><td>51</td></tr></table>

<table><tr><td>3.3. The contradictions and limitations of the Ricardian analysis</td><td>54</td></tr></table>

<table><tr><td>Chapter 3. Distribution and prices in Piero Sraffa's theory</td><td>61</td></tr></table>

<table><tr><td>1. SRAFFA'S PROBLEMATIC OF REPRODUCTION: QUITE DIFFERENT FROM RICARDO'S</td><td>61</td></tr></table>

<table><tr><td>1.1. Reproduction and accumulation of capital</td><td>61</td></tr></table>

<table><tr><td>1.2. The question of returns</td><td>62</td></tr></table>

<table><tr><td>2. WAGES AND THE CONSTRUCTION OF AN INVARIABLE STANDARD</td><td>63</td></tr></table>

<table><tr><td>2.1. Two Ricardian models with wages as wage-goods</td><td>63</td></tr></table>

<table><tr><td>2.2. A new conception of wages as part of a surplus</td><td>65</td></tr></table>

<table><tr><td>2.3. The consequences of wages not being advanced</td><td>66</td></tr></table>

<table><tr><td>3. THE CONSTRUCTION OF THE INVARIABLE STANDARD</td><td>69</td></tr></table>

<table><tr><td>3.1. A new system with n+2 unknown variables</td><td>69</td></tr></table>

<table><tr><td>3.2. The determination of the second distribution variable</td><td>70</td></tr></table>

<table><tr><td>3.3. Changes in distribution and the measurement unit</td><td>71</td></tr></table>

<table><tr><td>3.4. The existence of an invariable measurement unit</td><td>72</td></tr></table>

<table><tr><td>3.5. The nature of the standard commodity and its consequences</td><td>74</td></tr></table>
<table><tr><td>4.</td><td>NATURE OF THE ASSUMPTIONS AND SIGNIFICANCE OF PRODUCTION PRICES</td><td>78</td></tr><tr><td>4.1.</td><td>The invariable measurement unit and the conception of distribution</td><td>78</td></tr><tr><td>4.2.</td><td>The blurred significance of production prices</td><td>81</td></tr></table>

<table><tr><td>Chapter 4. Commodities do not produce commodities: the biased concept of production in Sraffa's theory</td><td>83</td></tr></table>

<table><tr><td>1.</td><td>SRAFFA'S APPROACH: PRODUCTION AS A CIRCULAR PROCESS</td><td>84</td></tr><tr><td>2.</td><td>PRODUCTION FOR SUBSISTENCE</td><td>84</td></tr><tr><td>3.</td><td>PRODUCTION WITH A SURPLUS</td><td>87</td></tr><tr><td>4.</td><td>THE INTRODUCTION OF FIXED CAPITAL</td><td>88</td></tr><tr><td>5.</td><td>THE CONTRADICTIONS OF SRAFFA'S SYSTEM WITH FIXED CAPITAL</td><td>92</td></tr><tr><td>6.</td><td>THE CONSEQUENCES FOR THE STANDARD SYSTEM</td><td>93</td></tr><tr><td>6.1.</td><td>The notion of basic goods</td><td>93</td></tr><tr><td>6.2.</td><td>The notion of surplus</td><td>95</td></tr><tr><td>6.3.</td><td>The notion of Standard commodity</td><td>96</td></tr><tr><td>7.</td><td>THE INTRACTABLE PROBLEM OF LAND AND NATURAL RESOURCES</td><td>98</td></tr><tr><td>8.</td><td>CONCLUSIONS ON SRAFFA'S SYSTEM AND THE STANDARD COMMODITY</td><td>99</td></tr></table>

<table><tr><td>PART II - PRODUCTION AND VALUES</td><td>103</td></tr></table>

<table><tr><td>Chapter 5. Production and values</td><td>105</td></tr></table>

<table><tr><td>1.</td><td>THE ANALYTICAL DISTINCTION BETWEEN PRODUCTION AND DISTRIBUTION</td><td>105</td></tr><tr><td>2.</td><td>PRODUCTION AS A TRANSFORMATION PROCESS</td><td>106</td></tr><tr><td>2.1.</td><td>The background</td><td>106</td></tr><tr><td>2.2.</td><td>Production as a physical process</td><td>109</td></tr><tr><td>2.3.</td><td>Homogeneity and the nature of abstract labor</td><td>111</td></tr><tr><td>2.4.</td><td>Values have the dimension of time</td><td>113</td></tr><tr><td>2.5.</td><td>Fixed capital cannot transfer its value to the product</td><td>114</td></tr></table>

<table><tr><td>Chapter 6. A first determination of values as physical values</td><td>117</td></tr></table>

<table><tr><td>1.</td><td>THE ASSUMPTIONS</td><td>117</td></tr><tr><td>2.</td><td>A FIRST METHOD FOR THE DETERMINATION OF VALUES</td><td>118</td></tr><tr><td>2.1.</td><td>A first definition of values</td><td>118</td></tr><tr><td>2.2.</td><td>The calculation of values with the first method</td><td>119</td></tr><tr><td>3.</td><td>A SECOND METHOD FOR THE DETERMINATION OF VALUES</td><td>123</td></tr><tr><td>3.1.</td><td>A second definition of values</td><td>123</td></tr><tr><td>3.2.</td><td>The calculation of values with the second method</td><td>123</td></tr><tr><td>3.</td><td>THE EQUIVALENCE OF THE TWO METHODS OF VALUE DETERMINATION</td><td>130</td></tr><tr><td>4.</td><td>THE EQUIVALENCE OF TOTAL DIRECT LABOR TIME AND TOTAL PRODUCT VALUE</td><td>131</td></tr></table>

<table><tr><td>Chapter 7. A few teachings about the concept of value</td><td>133</td></tr></table>

<table><tr><td>1.</td><td>THE FIELD OF VALIDITY OF VALUES</td><td>133</td></tr><tr><td>2.</td><td>THE DETERMINATION OF VALUES IS POSSIBLE AND FEASIBLE</td><td>134</td></tr><tr><td>3.</td><td>THE DISTINCTION BETWEEN ABSOLUTE VALUES AND RELATIVE VALUES AND THE INVARIABLE STANDARD OF VALUE</td><td>135</td></tr><tr><td>4.</td><td>THE LABOR THEORY OF VALUE AND MARX'S MISTAKES</td><td>138</td></tr><tr><td>4.1.</td><td>A first and main error: an inaccurate vision of exchange</td><td>138</td></tr><tr><td>4.2.</td><td>A second error: money as a commodity</td><td>138</td></tr><tr><td>4.3.</td><td>A third error: the common dimension of values and prices</td><td>139</td></tr><tr><td>4.4.</td><td>A fourth error: the transmission of value by fixed capital</td><td>139</td></tr><tr><td>5.</td><td>SOME MISCONCEPTIONS ABOUT THE LABOR THEORY OF VALUE</td><td>140</td></tr><tr><td>5.1.</td><td>Elementary misconceptions</td><td>140</td></tr></table>
Chapter 12. A more realistic model integrating capitalist consumption 243

1. THE MAIN CHANGES TO THE INITIAL SIMPLE MODEL 243

2. REALIZATION OF THE PRODUCT AND PROFITS IN A MODEL WITH CAPITALISTS CONSUMPTION 244

2.1. Realization of consumption goods and profits in section II 244

2.2. Realization of fixed capital goods and profits in section I 247

3. THE VALUES OF A FEW VARIABLES REFLECTING THE DISTRIBUTION OF THE PRODUCT 255

3.1. The price of total product 255

3.2. The share of wages and profits in the product 256

3.3. A quick consistency test 261

4. AGAIN ON THE REALIZATION OF THE PRODUCT AND PROFITS 262

4.1. A little problem of logics 262

4.2. Some remarks on money and exchanges 263

4.3. The realization of profits and product 264

Chapter 13. A numerical example of a model with capitalist consumption 273

1. EXOGENOUS VARIABLES 273

2. ENDOGENOUS VARIABLES 274

3. THE DISTRIBUTION OF INCOME AND PRODUCT 276

3.1. In section II 276

3.2. In section I 277

4. THE VALUES OF A FEW VARIABLES REFLECTING THE DISTRIBUTION OF THE PRODUCT 280

4.1. The price of total product 280

4.2. The share of wages and profits in the product 280

4.3. The profits/wages ratio 282

Chapter 14. Distribution and prices: a close connection 285

1. A GENERALIZATION OF THE MODEL WITH CAPITALIST CONSUMPTION 285

2. FROM MACROECONOMIC TO MICROECONOMIC PRICES 287

2.1. Prices of fixed capital 287

2.2. Prices of consumption goods 290

2.3. Prices of intermediate goods 290

3. FROM VALUES TO PRICES 291

3.1. A few calculations of values and prices 291

3.2. Some preliminary findings 295

Chapter 15. A coherent theory of rent 299

1. THE NATURE OF RENT, DIFFERENTIAL RENT AND ABSOLUTE RENT 299

1.1. The price of wheat with a zero total rent 300

1.2. The price of wheat with a zero total rent and equalization by the State 303

1.3. The price of wheat with a zero differential rent on marginal land 304

1.4. The price of wheat with a zero differential rent and a positive absolute rent on marginal land 305

2. TYPE II DIFFERENTIAL RENT FOR SRAFFA AND MARX 306

3. THE EFFECT OF RENT ON THE PRICE SYSTEM AND DISTRIBUTION 309

Chapter 16. Some theoretical lessons from the models 315

1. THE NATURE OF FIXED CAPITAL 315

1.1. Fixed capital and circulating capital 315

1.2. Intermediate goods, final goods and fixed capital 316

1.3. The ambiguous treatment of fixed capital in national accounts 318

1.4. Fixed capital and some contradictions in economic theory 320

2. AGAIN ON THE ARTICULATION BETWEEN VALUES AND PRICES 321
<table><tr><td>2.1.</td><td>The mode of determination and the significance of prices in both models</td><td>321</td></tr><tr><td>2.2.</td><td>System of values and price system</td><td>322</td></tr><tr><td>3.</td><td>THE CONDITIONS OF PROFIT FORMATION</td><td>325</td></tr><tr><td>3.1.</td><td>The dual regime of setting shares of profit</td><td>325</td></tr><tr><td>3.2.</td><td>The conflict between capitalists for the distribution of surplus value</td><td>327</td></tr><tr><td>3.3.</td><td>Sharing surplus-value with the banking system</td><td>329</td></tr><tr><td>4.</td><td>A TRULY MICRO-ECONOMIC PRICE THEORY</td><td>333</td></tr><tr><td>4.1.</td><td>The circularity of neo-classical price theory</td><td>333</td></tr><tr><td>4.2.</td><td>Exchange as the expression of a balance of power</td><td>334</td></tr></table>

# PART IV - REPRODUCTION AND THE RATE OF PROFIT .................................................. 341

## Chapter 17. Profits, rate of profit and reproduction ................................................................. 343

<table><tr><td>1.</td><td>THE COMPLEX NATURE OF PROFIT RATES</td><td>343</td></tr><tr><td>1.1.</td><td>The practical difficulties to measure profit rates in the real world</td><td>343</td></tr><tr><td>1.2.</td><td>The multiplicity of profit rates</td><td>344</td></tr><tr><td>1.3.</td><td>Alternative indicators: the amount of profits and the profit/wage ratio</td><td>349</td></tr><tr><td>2.</td><td>REPRODUCTION OF THE SYSTEM IS PROBLEMATIC</td><td>350</td></tr><tr><td>2.1.</td><td>Reproduction is possible, but not probable</td><td>350</td></tr><tr><td>2.2.</td><td>Crisis as coming from inherent difficulties of reproduction</td><td>353</td></tr><tr><td>3.</td><td>SOME REMEDIES AGAINST CRISES</td><td>356</td></tr><tr><td>3.1.</td><td>Capitalist consumption as a remedy for crises</td><td>356</td></tr><tr><td>3.2.</td><td>Another remedy for crises: autonomous investment and the Keynesian multiplier</td><td>360</td></tr><tr><td>4.</td><td>CRISES AND EVOLUTION OF THE RATE OF PROFIT</td><td>363</td></tr></table>

## Chapter 18. The Marxist definition of the rate of profit in the simple model ........................ 367

<table><tr><td>1.</td><td>SOME REMINDERS ON THE TENDENCY OF THE RATE OF PROFIT TO FALL</td><td>367</td></tr><tr><td>2.</td><td>MEASURING THE STOCK OF FIXED CAPITAL</td><td>369</td></tr><tr><td>3.</td><td>THE AVERAGE RATE OF PROFIT IN THE SIMPLE MODEL</td><td>373</td></tr><tr><td>3.1.</td><td>The organic composition of capital</td><td>374</td></tr><tr><td>3.2.</td><td>The average rate of profit</td><td>376</td></tr></table>

## Chapter 19. The evolution of the rate of profit as defined by Marx in the simple model ...... 381

<table><tr><td>1.</td><td>THE EVOLUTION OF THE RATE OF PROFIT AND THE PROPORTION OF MARX</td><td>381</td></tr><tr><td>2.</td><td>A GRAPHICAL REPRESENTATION OF FUNCTION R = F (Q) IN TERMS OF VALUES</td><td>384</td></tr><tr><td>3.</td><td>A NUMERICAL EXAMPLE CORRESPONDING TO THE SIMPLIFIED MODEL</td><td>385</td></tr><tr><td>4.</td><td>THE EVOLUTION OF THE RATE OF PROFIT IN TERMS OF PRICES</td><td>386</td></tr><tr><td>5.</td><td>RATE OF PROFIT, RATE OF ACCUMULATION AND INTENSITY OF CAPITAL</td><td>389</td></tr></table>

## Chapter 20. The rate of profit as defined by Marx and its evolution in the model with capitalist consumption................................................................................................................ 393

<table><tr><td>1.</td><td>CAPITAL STOCK AND THE ORGANIC COMPOSITION OF CAPITAL</td><td>393</td></tr><tr><td>1.1.</td><td>Capital stock</td><td>393</td></tr><tr><td>1.2.</td><td>The organic composition of capital</td><td>394</td></tr><tr><td>2.</td><td>THE AVERAGE RATE OF PROFIT AS DEFINED BY MARX IN THE MODEL WITH CAPITALIST CONSUMPTION</td><td>396</td></tr><tr><td>2.1.</td><td>The average rate of profit expressed as a function of the rate of surplus-value k<sub>c</sub></td><td>396</td></tr><tr><td>2.2.</td><td>The average rate of profit expressed as a function of the organic composition of capital q<sub>c</sub> ...</td><td>397</td></tr><tr><td>2.3.</td><td>The average rate of profit expressed as a function of the variables of the simple model</td><td>399</td></tr><tr><td>3.</td><td>THE EVOLUTION OF THE RATE OF PROFIT WITH THE MARXIST DEFINITION</td><td>400</td></tr><tr><td>3.1.</td><td>The evolution of the rate of profits at global level in terms of q<sub>c</sub></td><td>400</td></tr></table>
3.2. *The evolution of the rate of profit at global level in terms of q*.................................................. 401

3.3. *The graphical representation of the evolution of the profit rate in terms of values* ........................ 401

3.4. *A numerical example for the Marxist model with capitalist consumption*........................................ 403

4. Some preliminary findings about the evolution of the rate of profit defined in terms of values as a function of the organic composition of capital .................................................................................. 405

5. THE EVOLUTION OF THE RATE OF PROFIT IN TERMS OF PRICES.................................................................................. 408

5.1. *The expression of the rate of profit in terms of prices*................................................................................ 408

5.2. *The evolution of the average rate of profit in terms of prices* ................................................................................ 411

Chapter 21. The evolution of the rate of profit - based on its current definition - and the share of profits .................................................................................................................................................. 415

1. THE INTEREST OF THE CURRENT DEFINITION OF THE RATE OF PROFIT ................................................................................ 415

2. THE CURRENT DEFINITION OF THE RATE OF PROFIT ................................................................................................................ 416

2.1. *Within the framework of the simplified model*................................................................................................................ 416

2.2. *Within the framework of the model with capitalist consumption*................................................................................ 417

3. A GRAPHICAL REPRESENTATION OF THE EVOLUTION OF THE RATE OF PROFIT................................................................................ 424

3.1. *The setting of parameters*................................................................................................................................................................................ 424

3.2. *A graphical representation of function r<sub>c</sub> (values)*................................................................................................................ 425

3.3. *A graphical representation for function r<sub>c</sub> (prices)*................................................................................................................ 427

3.4. *The relation between the actual rate of surplus value k<sub>c</sub> and the consumption of capitalists* ..... 429

3.5. *A comparison between two expressions of the profit rate: in terms of values and in terms of prices* 432

4. THE EVOLUTION OF THE SHARE OF PROFITS IN THE PRODUCT .................................................................................. 433

4.1. *The share of profits in the product of section I*................................................................................................................ 434

4.2. *The share of profits in the product of Section II*................................................................................................................ 436

4.3. *The share of profits in the overall product*................................................................................................................ 439

4.4. *The share of profits and the rate of profit*................................................................................................................ 442

Chapter 22. Some reflections and first elements of discussion to introduce extended reproduction .................................................................................................................................................. 445

1. EXTENDED REPRODUCTION IN MARX'S CAPITAL ................................................................................................................ 445

2. SOME QUESTIONS OF DEFINITIONS................................................................................................................................................ 446

3. A FIRST NUMERICAL EXAMPLE, WITHOUT CAPITALIST CONSUMPTION ................................................................................ 447

4. A SECOND EXAMPLE, WITH CAPITALIST CONSUMPTION ................................................................................................................ 450

4. THE INFLUENCE OF THE LIFESPAN OF FIXED CAPITAL AND K<sub>c</sub>................................................................................................................ 454

5. THE REALIZATION OF THE PRODUCT IN THE CONTEXT OF EXTENDED REPRODUCTION WITH CAPITALIST CONSUMPTION................................................................................ 456

5.1. *Marx's extended reproduction schemes in volume II of Capital*................................................................................ 456

5.2. *Another way to deal with reproduction schemes*................................................................................................................ 458

5.3. *Reproduction cannot go smoothly in the real world*................................................................................................................ 461

Chapter 23 - Conclusion.................................................................................................................................................. 465

1. THE OBJECT OF ECONOMIC THEORY ................................................................................................................................................ 466

2. PRODUCTION, VALUE AND MONEY................................................................................................................................................ 469

3. DISTRIBUTION, EXCHANGE AND PRICES................................................................................................................................................ 471

4. DISTRIBUTION AND THE INCOMPLETENESS OF ECONOMIC THEORY................................................................................ 478

5. A FEW FINAL WORDS ................................................................................................................................................................................ 481

APPENDIX 1 – FUNDAMENTAL PRINCIPLES OF POLITICAL ECONOMY ................. 485
<table><tr><td>APPENDIX 2 - THE ERRONEOUS NATURE OF MARX'S REPRODUCTION SCHEMES IN BOOK II OF CAPITAL</td><td>493</td></tr></table>

<table><tr><td>APPENDIX 3 - SUMMARY TABLES OF VALUES AND PRICES OF THE MAIN VARIABLES OF THE MODELS</td><td>497</td></tr></table>

<table><tr><td>BIBLIOGRAPHY</td><td>503</td></tr></table>

<table><tr><td>DETAILED TABLE OF CONTENTS</td><td>511</td></tr></table>