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Template:Marxism Prices of production is a concept in Karl Marx's critique of political economy. It refers to the price levels at which newly produced goods would have to sell in order to reach the normal, average profit rate on the capital invested in producing them. A production price for outputs in Marx's sense always has two main components: the cost-price of producing the outputs (including the costs of materials, equipment, operating expenses, and labour) and a gross profit margin (the additional value realized in excess of the cost-price, when goods are sold, which Marx calls surplus value). Marx's argument is that price-levels for products are determined by input cost-prices, turnovers and average profit rates on output, which are in turn determined principally by labour-costs, the rate of surplus value and the growth rate of final demand.

The concept of production prices is introduced in the third volume of Das Kapital, although it is referred to in the earlier volumes. In the third volume, Marx considers the operation of capitalist production as the unity of a production process and a circulation process involving commodities, money, and capital. The argument is that the sales of newly produced commodities in the capitalist mode of production are regulated by their production prices.

The regulating price of a given type of product is a sort of modal average price level, above or below which people would be much less likely to trade the product. This price level is determined by cost-prices, profit margins, and sales turnover.

The production price refers basically to a "normal or dominant price level" that prevails during a longer interval of time. It presupposes that both the inputs and the outputs of production are priced goods and services—that is, that production is fully integrated in fairly sophisticated market relations enabling a sum of capital invested into it to be transformed into a larger sum of capital. In pre-capitalist economies, this was not the case; many inputs and outputs of production were not priced.

Marx's claim is that the production prices of products themselves are fundamentally determined by the comparative labour values of those products, and therefore are constrained by the law of value. Since, however, not all goods are produced or reproducible goods, not all goods have production prices. A production price in Marx's sense can exist only in markets developed sufficiently for a "normal" rate of profit on production capital invested to become the ruling average for a group of producers.

Substantively, Marx argues that the prices of new products sold will, assuming free competition for an open market, tend to settle at an average level that enables at least a "normal" rate of profit on the capital invested to produce them, and, as a corollary, that if such a socially average rate of profit cannot be reached, it is much less likely that the products will be produced at all (because of comparatively unfavourable profitability conditions).

Thus, investment capital is likely to shift out of production activities where the rate of profit is low and toward activities where profitability is higher; the "leading" sectors of industry are those where profitability is highest (today, these are in the production of computer facilities, healthcare, oil products, and finance). The precondition is the free mobility of capital, and thus there is a systemic tendency to remove all obstacles preventing investors from investing in sectors where profits are higher. If, for any reason, the free movement of capital is blocked or restricted, large differences in the profit rates of enterprises are likely to occur.

According to Marx, the movements of different production prices relative to one another importantly affect how the total "cake" of new surplus value produced is distributed as profit among competing capitalist enterprises. They are the basis of the competitive position of the producers, since they fundamentally determine profit yields relative to costs.

Simple definition

For most political economists, the concept of production prices corresponds roughly to Adam Smith's concept of "natural prices" and the modern neoclassical concept of long-term competitive equilibrium prices under constant returns to scale. However, the function of prices of production within Marxian theory is different from that of these other concepts within their own theories.

Simply put, Marx's "price of production" (P) is a price that applies to sales of new outputs produced, and it equals cost price (cp) + average profit of capital invested in production (ap). The cost price could also be computed as the unit cost of a product, the profit component being the normal markup. The production price is the price at which goods would have to sell in order to realize the average profit rate on the capital invested in producing them. The amount ap is often assumed to have the same magnitude relative to the amount of capital invested in all sectors, seemingly representing an equilibrium of flows of capital between different parts of a capitalist economy that results in a "uniform rate of profit".

Thus, $P=cp+ap$

The cost-price equals labour costs incurred (or variable capital measured in price terms) in producing output, plus the monetary cost of constant capital inputs used up.

In the sphere of capitalist production, Marx argues, commodity values are expressed in the form of prices of production, established jointly by average input costs and by the ruling profit margins applying to outputs sold. It is a result of the establishment of regular, developed market trade; the production price averages reflect the fact that production has become totally integrated into the circuits of commodity trade, in which capital accumulation has become the dominant motive. But what prices of production simultaneously hide, he argues, is the social nature of the valorization process—that is, how exactly an increase in capital value has occurred through production. The direct connection between labour time and value, still visible in simple commodity production, is largely effaced; only cost prices and sale prices remain, and it seems that any of the factors of production (which Marx calls the "Holy Trinity" of capitalism) can contribute new value to output, paving the way for the concept of the production function.

In his manuscript, Marx frequently defines a newly produced output of commodities as being equal to a newly formed "commodity capital K" where

K = c + v + s

where c = constant capital (the element of conserved value), v = variable capital, and s = surplus value (the two elements of newly created value). (Marx's standard assumption in his models is that the rate of surplus-value (s/v) is the same in all sectors. But this is just an ideal average; in reality, s/v will differ across sectors and regions. Marx seems to have thought though that assuming a uniform rate was justified, because an open market in labour and capital would tend to make working conditions increasingly similar for a whole population).

One question is then how, exactly, the value of K is distributed as gross revenues among producing enterprises, what determines this distribution, and what factors affect it. In the Marxian view, the answers given to this question have important implications for explaining and predicting the pattern and direction of capitalist economic growth (this is the subject of Marx's theory of economic reproduction and the mobilization of capitals).

Two interpretations of production prices

Unfortunately, Marx never prepared the manuscript of the third volume of Das Kapital for publication. Therefore, his draft text, which sketches complicated issues in a shorthand way, is sometimes ambiguous and incomplete. According to the German Marxian scholar Michael Heinrich, "Marx was nowhere near solving all of the conceptual problems".[10]

Natural prices

Some writers argue that Marx's production price is similar, or performs the same theoretical function, as the "natural prices" of classical political economy found, for example, in the writings of Adam Smith and David Ricardo (though the concept of natural prices is much older). This is the orthodox Marxist view, based on quotations where Marx says that his concept of production prices recalls the classical idea of natural prices. In this case, Marx's production price would be essentially a "centre of gravity" around which prices for outputs in a competitive market will fluctuate in the long run (cf. Fred Moseley's view). This is an interpretation within the framework of equilibrium economics, which suggests that production prices are really a kind of "equilibrium prices". It can be supported with some textual evidence, insofar as Marx sometimes defines the production price as the price that would apply if supply and demand for products were balanced. At other times, he refers to a "longterm average price" or a "regulating price". He does not say precisely how these three different concepts are related.

The main objection against equating production prices with natural prices is that Marx's concept of production prices is a critique of the "natural prices". According to this argument, there is actually nothing "natural" about the allegedly natural prices, and more importantly, the existence of production prices does not logically depend on an equilibrium state. If the classical economists talked about the "naturalness" of price-levels, this was ultimately a theoretical apologism; they could not reconcile their labour theory of value with the theory of the distribution of capital. They assumed a market balance without proving how it could exist.

Production prices as a "pricing regime"

Others argue that the concept of production price plays a different role in Marx's theory: its aim is to show how the distribution, as profit income, of the new surplus value produced (in the form of new outputs of goods and services) is affected by price movements and more specifically by competition between producers, and what variables and dimensions are involved here.

In this case, production prices are not necessarily equilibrium prices but refer much more to a given price level acting as a constraint or limit within which enterprises must operate in a developed, open market: the average or ruling costs and returns applying to their branch of activity, creating in effect a pricing regime or "regulating price". The pricing regime sets upper and lower limits for cost prices and sale prices. Thus, the challenge for entrepreneurs is whether they can produce a product at a normal profit under the condition of a given structure of cost prices and sale prices. This alternative interpretation of production prices rests on four ideas:

• In a developed market, as Marx knew, producers confront a given cost structure applying to their inputs, and a given structure of market prices for their outputs. Within this evolving but predetermined framework, in which the activity of each enterprise affects the overall outcome for all enterprises, each producer aims to manage his or her business in order to realize maximum surplus value, principally by maximizing surplus labour and labor productivity while keeping costs at a minimum. Effectively, producers aim to sell as much product as fast as they can at competitive prices that are below the ruling market valuation while still achieving a normal profit rate on capital invested. If they sell more product more quickly than before, then even if the rate of profit on capital is not spectacular, they still make more money than previously.

• Marx's critics claimed to prove on the one hand that there existed no logical procedure by which to derive prices from values; yet on the other hand they also complained Marx's theory was not empirically verifiable or falsifiable. But the latter proposition does not follow from the former. Marx's theory is indeed verifiable and falsifiable if we investigate whether price movements and businesses' behaviour empirically develop in the direction that Marx predicts that they will on the basis of his value theory. Are market prices for products really proportional to their production costs or not? Are relative quantities of labour time performed proportional to the long-term relative movements of output prices? Do profit rates tend to converge on a "normal" rate of return?

• Most importantly, in a developed market, prices of production will exist regardless of whether supply and demand happen to be in balance; competition would settle an average price level for outputs, but this does not necessarily imply any "equilibrium price" or the absence of price fluctuations. For Marx, the capitalist economy and society owed its "equilibrium" to the maintenance of its relations of production, not to some hypothetical balance between demand and supply that existed only by momentary chance. Equilibrium was less an economic than a socio-political issue (see also law of value). After all, economic fluctuations could occur while the relations of production stayed intact, and capital accumulation continued unabated.

• Marx's purpose was not to prove a static equilibrium system with models of price distributions in which price–value deviations fully cancelled out at the aggregate level; at best, this was only a simplifying assumption to illustrate the effects of the distribution of the total new surplus value created, given that there was a minimum acceptable average profit rate on capital invested, related to the prevailing interest rates, while enterprises were constantly unequally rewarded for the productive labour they performed. This central fact dominated how the production system would develop. Marx aimed to diagnose the main laws that drove capitalist production forward through the dynamics of competition for extra profits. The critical problem for investors was that at any time they could realize more or less money income for the new value produced by enterprises, and this problem led to a systematic pattern of business behaviour to gain competitive advantage, which in turn had definite overall effects for the whole economy. So this was more a theory of the basic parameters of business competition than a theory of how the distribution of new value spontaneously evolved towards an imaginary equilibrium state.

A quote from Marx on production prices

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Problems of interpretation

There are three main conceptual problems in interpreting Marx's production prices.

Different types of production prices

The first interpretative difficulty concerns the existence of various production prices. Most Marxists simply took the concept of production prices for granted, as being more or less the same as Ricardo's idea, and they did not inquire into it in precise detail. They believed that the idea of a production price was simple, obvious and not controversial. So they missed altogether the fact that in Capital Vol. 3 Marx identified (though often not very clearly) at least four main types of production prices:

• the private or enterprise production price which forms the starting-point of the analysis in the first chapter. This price equals the cost-price and profit rate on production capital invested which applies to the new output of a specific enterprise when this output is sold by the enterprise. This production price can be compared to the average production price that obtains for a sector or nationally.

• the sectoral production price. This price equals the average cost-price and average profit rate on production capital invested which applies to the output of a commodity produced by a specific industry, sector or branch of production (at "producer's prices"). This is the average production price which applies for a particular type or class of product, reflecting the average return the producers can normally expect to obtain. In his discussion of ground rent, Marx notes especially the differences between industrial and agricultural production prices.

• the inter-sectoral production price. This price refers to the sale of output at producers' prices which reflect an average profit rate on a quantity of capital invested that applies to various sectors of industry (this is the fully formed production price which Marx most often has in mind in his theoretical discussions of the equalisation process of profit rates; it reflects the product-price at which the average rate of profit on capital applying to a whole economic community is obtained).

• the economic production price. This price equals the average cost price and average profit rate of an output at the point of sale to the final consumer, including labour-value contributed by all the different enterprises participating in its production (factory, storage, transport, packaging etc.). In modern times, "costing" production in order to establish the expected yield on capital invested in it often involves assessing the whole value chain relative to the price level at which products can be sold to the final consumer. The question then is, how can the whole production of a product - from the factory gate to the final consumer - be organized so that it can sell to the final consumer at a price that the market will bear - and still make a good profit? Marx sometimes implies an economic production price when, for the sake of argument, he simply abstracts from everything that happens between the factory gate and the final consumer of a commodity.

These different prices are revealed when we study the composition of the cost structure of a product at different stages of its production. One source of interpretive difficulty is that Marx often assumes in his drafts that these four types of prices are all identical. But that is true only in the special case where one enterprise sells directly to the final consumer.

The reason for this conflation is probably that Marx's real analytical concern was not really with the pricing processes as such, but with the main factors influencing the realisation and distribution of new surplus-value produced, when sales occur. After all, his argument was that competition in capitalism revolves around the quest of obtaining maximum surplus-value from production in the form of generic profit income (profit, interest, rent). The question was: how does a sum of capital invested in production get transformed into a larger sum of capital? What are the dynamics and overall results of that process? What are the implications for the process of economic reproduction?

Oversimplification in the model

A second source of interpretive difficulty is that in his argument Marx often conflates capital advanced (to acquire inputs necessary for production) with capital consumed (that fraction of the value of inputs used up in the production of new output). He just assumes abstractly, for the sake of argument, that:

• the value of output created equals the sum of input costs incurred plus surplus value,
• the sum of input costs is equal to the production capital invested,
• All output is sold.

Most probably the reason was that his real interest was in the overall dynamics of capital accumulation, competition, and the realisation of surplus value produced, assuming output would sell. He was thinking of grand averages and overall results. The simplified picture does not obtain in reality, among other things because, as Marx himself notes, capitalist competition turns on buying commodities below their value and selling them above their value (or, in the ideal competitive situation, to sell them below their value at a good profit).

Marx's theory is frequently confused with input-output economics and the marginalist theory of capital, in which total inputs and total outputs are always exactly equal, an equality accomplished by treating the factor income which is gross profit as an input, so that profit is both a cost and a revenue at the same time. Marx did not talk about inputs and outputs in this double-entry bookkeeping sense; instead, he was concerned with how a sum of capital was transformed into a larger sum of capital through a net addition of new value created by workers in production. He was not really talking about quantitities of input commodities and quantities of output commodities, but about quantities of capital required for commodity production and quantities of capital created by commodity production.

If indeed the value of inputs bought was exactly equal to the value of outputs sold, capitalists would not even invest in production, because they would get no profit out of it. So from Marx's point of view, input-output economics really mystified the "capital-relationship", i.e. the ability of the bourgeoisie to capitalize on the surplus labour of the workforce in virtue of its ownership of the means of production (in chapter 48 of Capital Vol. 3, he refers satirically to the factors of production theory as the "holy trinity" of political economy).

Theoretical status of production prices

A third source of interpretive difficulty concerns the question of what kinds of prices production prices really are. Do these prices really exist, and if so, in what way? Or are they only theoretical or ideal prices? What exactly is the "average" an "average" of? What does the "cost-price" really refer to, and at what point in the process (inputs purchased, output produced before sales, output sold)? Marx talks about production prices variously as

• theoretical prices which are equilibrium prices that would apply, if supply and demand are balanced.
• regulating prices which function as norms for trade, setting upper and lower bounds for price fluctuations.
• empirical price averages across a longer time-interval, obtained by averaging out actual output prices for several accounting intervals.

Consequently, it remains somewhat ambiguous in what way such prices exist in reality. The conceptual challenge in modelling is to show how these three variables are related. It could, in principle, also be argued that some types of production prices are empirical price averages, while other ones only express theoretical price-levels. Obviously, if production prices are regarded only as purely "theoretical" entities, then it is not possible to claim also that they really regulate actual prices. A price level which exists only in theory, and not in reality, cannot be said to determine real price-levels (other than in the sense of publicly available price information influencing market expectations).

In grappling with these issues, it must also be remembered that when Marx lived there was little macro-economic statistical data available that would enable theoretical hypotheses to be tested and relativised. Marx had deduced the motion of capital essentially from an enormous amount of economic literature he read, but when, towards the end of his life, he toyed with the idea of investigating economic fluctuations econometrically, Samuel Moore convinced him this was not possible, because relevant economic data did not exist yet. Comprehensive macro-economic data became available only half a century later.

Marx had pointed the way to solving the problems raised by the classical political economists, without however providing a complete answer. He really believed though that a "general rate of industrial profit", applying economy-wide to all industries, would be formed (in the sense of the minimally acceptable profit rate) but in truth he lacked the data to prove it. He did not discuss in any detail the difference between distributed and undistributed profit, or tax requirements, and how this might affect profit statements. His discussion was limited to physical capital and labour employed, abstracting from ancillary costs and incomes unrelated to production which enterprises usually have (including tax imposts and subsidies).

Production prices and the transformation problem

The concept of production prices is one "building block" in Marx's theory of "the tendency of the rates of profit on production capital to level out through competition" (see Capital Vol. 3, chapter 10 [11]) which aimed to tackle a theoretical problem left unsolved by David Ricardo. This problem concerned the question of explaining how an average or "normal" return on production capital invested (e.g. 8-16%) could become established, so that capitals of equal size reaped equal profits, even although the enterprises differed in capital compositions and amounts of labour performed (see labor theory of value) and consequently generated different amounts of new value.

According to Marx, this was not simply a logical problem, a social accounting problem or theoretical problem, but a structural contradiction intrinsic to the capitalist mode of production, which had to be continually mediated. The fact that more or less value could be appropriated by investors from the labour-efforts of the workers employed, and thus that different labour efforts were unequally rewarded, was in his eyes central to the competitive process - in which the norms of labour effort continually clashed with the norms of profitability. On the surface, it looked to the individual observer as if profit yields on capital determine expenditures on labour, but in aggregate, it is - according to Marx - just the other way around, since the volume of labour-time worked determined how much profit could be distributed among capitalists, via the sales of products. The mass of surplus labour performed in the sphere of production set a limit for the mass of surplus value that could be distributed as profit in the sphere of circulation.

Accounting interpretation

In some interpretations of the Marxian transformation problem, total "(production) prices" for output must equal total "values" by definition, and total profits must by definition equal total surplus value. However, Marx himself explicitly denied in chapter 49 of the third volume of Das Kapital that such an exact mathematical identity actually applies; subsequently, Frederick Engels also denied it explicitly, in a letter to Conrad Schmidt dated March 12, 1895. At best, it is an assumption used in modelling, which is justified if - as Marx believed - the divergence between total values and total production prices is quantitatively not very great, because actual labour expenditures constrain their divergence. But all this has never bothered neo-classical scholars such as Paul Samuelson in their interpretation of what Marx tried to do.

Logically, the only way Marx has to express an identity of aggregated output prices and aggregated output values, is to say that both of the totals are equal to exactly the same quantity of abstract labour time. But this equivalence is only asserted "by definition." In the real world, there exist no causal forces that could guarantee such an exact match. Moreover, the identity cannot be empirically proved in any direct way, since to find the quantitative relationship between labour-time and value, a relationship between labour-time and money must already be assumed.

The "accounting" interpretation of production prices (value/price identity at the macro-level) by economists, according to which price distributions and value distributions can be inferred from each other, would suggest that the production price is empirically obtained from a straightforward statistical averaging of aggregated cost prices and profits. In that case, the production price is a theoretical midpoint which fluctuating actual prices would match exactly only by exception.

Production prices as dominant price-levels

In another interpretation, however, the production price reflects only an empirical output price-level which dominates in the market for that output (a "norm" applying to a branch of production or economic sector, which producers cannot escape from). That is, the prevailing value proportions set a range or band within which prices will move. In practice, that means simply that there exists a minimum sale price at which a commodity can be viably and profitably produced; if it is not possible to sell a product at that price, it is unlikely that it will be produced at all.

• Anwar Shaikh has modelled the formation and change of production prices mathematically using iterative methods. In subsequent writings, he concretizes the concept of the production price as the "regulating price" dominating the market for a type of product.

• Emmanuel Farjoun and Moshe Machover (1984) reject the whole idea that a "uniform rate of profit" would ever exist in reality, contrary to Marx's suggestion that competition would tend to establish at least a minimally "acceptable" average rate of profit on production capital invested to produce outputs, and returns proportional to capital size. Machover consequently rejects the concept of production prices as a useless concept. He argues:

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• Supporters of the Temporal Single System Interpretation, such as Andrew Kliman, believe that Machover's inequality does not really arise, since, if Marx is read correctly, there is no necessity for the value of inputs to be equal to the value of outputs.

These readings of Marx imply that traditional interpretations of the transformation problem are really rather meaningless; the apparent mathematical wizardry is based on false interpretations of the concepts involved, and the reciprocal effects of individual actions and aggregate social outcomes is overlooked. Mathematical equations cannot substitute for conceptual precision in the definition of measuring units; they can only reveal the logical and quantitative implications of concepts and measurement units.

Statics and dynamics

At the beginning of Capital Vol. 3, Marx provides a clue to how he thinks the "transformation problem" is solved in reality. He implies that it can be solved only by examining capital and profit distributions as a dynamic process, rather than statically. His argument is, that what industrial competition really revolves around, is principally the difference between the value of the new commodities produced, and their cost-prices, in other words the potential surplus-value which can be realized from them. There are, in other words, constant disparities in space and time between labour-expenditures and capital returns, but also just as constant attempts to overcome or take advantage of those disparities. Thus, unrestricted economic competition has the result that the law of value regulates the trade in newly produced commodities: the ultimate limits of what products will trade for, i.e. their supply price, are set by comparative costs in labour-time.

In the real world,

• a uniform rate of profit and a uniform rate of surplus value for all industries do not exist.
• the agents of capital do not aim simply to reach the average rate of profit, but an above-average rate of profit (the maximum profit, or a "surplus profit").
• competition is not a "level playing field", but a process in which unequally positioned capitalists try to obtain or maintain extra profits, by blocking competitors in various ways to improve their own market position.
• the relationship between product-values and product-prices is expressible only in probabilistic terms, not as a simultaneous equation.
• total capital consumed diverges from total capital advanced, and total capital advanced is larger than total physical production capital, just as the gross income is greater than the profit component of the new value added.
• since the production price refers only to the cost prices and profit yields for newly produced outputs, the production price can be definitely calculated only after (or on the assumption that) all the newly-produced output is sold, and when the total turnover is known.

When Marx created a simplified, abstract model of profit distributions, he was not primarily trying to prove that the two famous identities (total profit=total surplus value, and total product value=total production price) are compatible with price-value divergences and with profit distributions according to capital employed (to the contrary: Marx assumes that they are compatible). Instead, he was trying to model the basic parameters of business competition for a share of the new surplus-value produced by the working class. By identifying what the business competition is ultimately about, Marx was able to explain both what really motivates the business owners, and why the surface appearance of the business process perceived by an individual is almost the exact inverse of the real economic process in society as a whole.

Value and price

A lot of criticism of Marx's concept originates from the ambiguities referred to earlier. Consequently, many of the criticisms can, according to some Marxists, be dispelled simply by a more exact definition of the cost, product and revenue aggregates used, and of the timing of transactions (see e.g. Temporal Single System Interpretation).

In doing so, it must be admitted though that Marx's draft manuscript often shows sloppy use of terminology and concepts, and that Marx's purpose was often not fully explicit. At a high level of abstraction, he moves very easily and cavalierly from values to prices and back again, and restricts his discussion of "capital invested" to intermediate goods, fixed capital and labour power only.

In Marx's view, a capitalist production process was a valorisation process in which new value was formed. The theoretical problem was, that this value-forming process - the process vital for capital accumulation - took place mainly external to the market, being bracketed by the transactions M-C (purchase of inputs, C, using money, M) and C'-M' (sales of new output, C', for more money, M'). Between the successive exchanges, however, economic value was conserved, transferred and added to. Management then tried to estimate the cost and profit implications of different tasks and activities in production for the growth of capital.

But in that case, the domains of product-values and product-prices, and consequently the domains of value relations and price relations, were separate but co-existing and overlapping domains (unless one is willing to argue that goods have an economic value only at the point where they are being sold for a price). "Price management" was not really possible insofar as prices were determined by markets which individual producers could not control, but value-based management was possible.

• Goods could sell below or above their real or socially average value, and that was precisely the critical problem for capitalists, because it affected their gross income and profit margins. The wealth of capitalist society might present itself as "a mass of commodities" (as Marx himself put it), but before and after the commodities were sold, they existed outside the market as use values. At that point, they had only a value and a use-value, but not an actual market price (though obviously one could estimate an hypothetical selling price - see also real prices and ideal prices).

• Thus, at the point of production, the "factors of production" themselves had no actual market price either, only a value, because they were being used to create new products, rather than being offered for sale (indeed, what a particular business enterprise was currently "worth" in total, as a going concern, might be very difficult to say; it would depend on how much profit income it was expected to yield in the future compared to the capital assets invested in it, but even if a total price could be estimated, its individual assets might change in value continuously).

• A quantity of value was produced by enterprises, but how much of that value would actually be realised by an enterprise as income from sales, or how gross revenues would be distributed among producers, could not be established with certainty in advance. Yet, the value of the total masses of output-values actually produced by all enterprises affected the market prices that could be obtained by each in distribution; it affected how the market would reward each of the producers, and there was a real, systematic relationship between total value produced and total sales revenue (even although these might not be equal).

• More importantly, producers were constantly adjusting their commercial behaviour to the emerging economic reality (the "state of the market"), as far as they could. And that adjustment followed a specific pattern; Marx argued it created a specific trajectory for capitalist development, guided by the quest for realizing extra surplus value. There is, he argues, a permanent imperative to increase productivity, and producers aim to utilize every possibility for gaining competitive advantage (which includes blocking competition from others in some way).

How could this business reality best be modelled? In contemporary "value-based management" by corporations, we can witness a continual cross-reference between past prices, current prices and future prices occurring, because there is practically no other way to do it for business purposes. In the words of group controller Gerard Ruizendaal of Royal Philips Electronics, 36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia. A partner of McKinsey & Company comments: 36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia..

In that case, it is impossible for the sum of input values to be exactly equal to the sum of output values. Indeed, that is exactly what, according to Marx, capitalists are in business for: to invest a sum of capital in production in order to get a larger sum of capital out of it. In bourgeois theories, value appears spontaneously out of trading activity in the sphere of circulation. For Marx, it is in reality exactly the other way around: the more value workers create for their company, the faster companies can increase their revenues and deploy more capital at attractive rates of return. Marx regarded the prices of production as the "outward expression" of the results of a valorisation process in production, and in order to be able to talk about price aggregates at all, he thought reference to value relations was completely unavoidable.

Not only was a value-theoretic principle required simply to group prices, relate them and aggregate them (meaning principles of value equivalence, comparable value, value transfer, value conservation, value creation and value used up or destroyed), but most of the stock of labour-products in an economy at any time had no actual price, simply because they weren't being traded. To what extent their value could be realised through exchange in the future could be known definitely only "after the fact", i.e. after they were actually sold and paid for. In the meantime, one could only hypothesize about their price, working from previous data. But in the final analysis, the attribution of value to products implied a social relation, without which value relations could not be understood. A community of independent private producers expressed their co-existence and mutual adjustment through the trading prices of their products; how they were socially related was expressed through the forms of value.

Facts and logic

The concept of "average profit" (a general profit rate) suggested that a process of competition and market-balancing had already established a uniform (or ruling average, or normal) profit rate previously; yet, paradoxically, what profit volumes would be (and consequently profit rates) could be established only after sales, by deducting costs from gross revenues. An output was produced before it was definitively valued in markets, yet the quantity of value produced affected the total price for which it was sold, and there was a sort of "working knowledge" of normal returns on capital. This was a dynamic business reality Marx sought to model in a simple way.

Lack of a formal proof

Marx's critics interpreting his models often argue he keeps assuming what he needs to explain, because rather than really "transforming values into prices" by some quantitative mapping procedure, such that prices are truly deduced from labour-values, he either (1) equates values and prices, or else (2) he combines both values and prices in one equation.

Thus, for example, either Marx infers a rate of profit from a given capital composition and a given quantity of surplus-value, or else he assumes a rate of profit in order to find the amount of surplus-value applying to a given quantity of capital invested. That might be fine if the aim is to just investigate what profit an enterprise or sector would receive on average, having produced a certain output value with a certain capital composition. But this manoeuvre of itself cannot contain any formal proof of a necessary quantitative relationship between values and prices, nor a formal proof that capitals of the same size but different compositions (and consequently different expenditures of labour-time) must obtain the same rate of profit. It remains only a theory.

Marx insists both that output prices obtained will necessarily deviate from values produced, but also that the sum of prices would equal to the sum of values in the pure case, yet, critics claim, he fails to show quantitatively how a distribution process could then occur such that price magnitudes map onto value magnitudes, and such that a uniform profit rate returns equal profits to capitals of equal sizes (a mapping relation is used here in the mathematical sense of a bijective morphism, involving one-to-one correspondence between value quantities and price quantities via mathematical equations). In that case, there is again no formal proof of any necessary relationship between values and prices, and Marx's manuscript really seems an endless, pointless theoretical detour leading nowhere. In modelling, simple logical paradoxes appear of the type that:

• in a static model, it is impossible to uphold the postulate of a uniform rate of profit and the postulate of total values=total prices at the same time;
• to find production-prices, a uniform rate of profit must be assumed, while at the same time to find a uniform rate of profit, production-prices must already be assumed;
• a price level must be assumed, rather than be deduced from labour-values.

All these conceptual and logical issues mentioned become crucial when attempts are made to model value and price aggregates mathematically to study capitalist competition. Different kinds of theoretical assumptions or interpretations will obviously lead to very different results.

What is the transformation?

In general, many modern Marxists nowadays think that Marx's idea of "transformation" was badly misinterpreted. It does not refer to a "mathematical conversion of values into prices". Rather the transformation means that the direct regulation of the exchange of commodities according to their value is, in a capitalist mode of production, transformed into the regulation of the exchange of commodities by their production prices - reflecting the fact, that the supply of commodities in capitalist society has become conditional on the accumulation of capital, and therefore on profit margins.

If market trade consisted only of simple exchange (the exchange of things of equal value by the direct producers themselves), then balancing production effort, output and demand would be a fairly simple, straightforward matter. But in reality it is not so straightforward precisely because capitalist market trade is not simple exchange. Production effort, output and demand can be balanced in capitalism, only if sufficient profits are made and the accumulation of capital grows. In reality, products are constantly being sold above or below their value, according to what makes the best possible profit on the turnover, given market fluctuations.

Whatever view one takes on the theoretical issues, no one can evade the (either simultaneous or sequential) reciprocal effects of individual business behaviour and aggregate economic outcomes. Additionally, it must also be recognised that "prices" are not all of one kind; actual market prices realised are not the same as ideal prices of various kinds, which may be extrapolated from real prices.

Level of abstraction

A more serious criticism of Marx is that the theory of prices of production is still pitched at a far too abstract theoretical level to be able to explain anything like specific real price movements. That is, Marx only illustrated with examples the general results towards which the competitive process would tend to move in capitalism as a social system. He tried to establish what regulates product prices in the "purest case". He believed that if one could not do that, then one could also not explain all the variations from the pure case. He had not however provided a model for accurately predicting specific price movements. In this regard, it is interesting to study the writings of Michael Porter, in order to see how Marx's original intent relates to modern competitive business practice, and how it might be elaborated on (see further the important studies by Willi Semmler and Christian Bidard).

Some critics conclude that because Marx fails to "transform" value magnitudes into price magnitudes in a way consistent with formal logic, he has not proved value exists, or that it influences prices; in turn, his theory of labour-exploitation must be false. But the validity of Marx's value theory or his exploitation theory may not depend on the validity of his specific transformation procedures, and Marxian scholars indeed often argue that critics mistake what he intended by them. In particular, since value relations - according to Marx - describe the proportionalities between average quantities of labour-time currently required to produce products, value proportions between products exist quite independently of prices.

Essentially, the advantage of distinguishing sharply between values and prices in this context is that it enables us to depict the interaction between shifts in product-values and shifts in product-prices as a dynamic process of real-world business and market behaviour, given the reality of different growth rates of supply and demand, i.e. not a study of the conditions for market balance, but a study of the actual process of market balancing occurring with a specific social framework, through successive adjustments which occur in a specific pattern.

Arguably ideal prices could substitute for values in this analysis, but Marx's argument is that product-values will, ontologically speaking, really exist irrespective of corresponding product-prices, i.e. irrespective of whether product-values are actually being traded, whereas ideal prices do not really exist other than in computations; they are only an hypothetical description. The reason is that product-values refer to empirical quantities of labour-time performed, which are not hypothetical, but an inescapable reality. This type of analysis paves the way for an important new Marxian criticism of Piero Sraffa's otherwise brilliant critique of capital theory. In Sraffa's theory, the value of a commodity "contains" both the average labour directly involved in making it ("direct labour") and past labour contained in the materials from which it is made ("indirect labour"). In Marx's theory, the value of the commodity represents the average labour currently required to make it, given the current state of the whole production complex - it is the current social valuation (the replacement cost) of that commodity. This is a synchronic valuation, not a diachronic one.

Empirical evidence

Some economists and computer scientists, such as Prof. Anwar Shaikh and Dr. Paul Cockshott, argue with statistical evidence that even just a "93% Ricardian labour theory of value" is a better empirical predictor of prices than other theories. That is, the only real proofs of Marx theory and its applicability, beyond showing its internal logical consistency, are to be found in the evidence of experience. But whether more scholars will take up this challenge for research more comprehensively remains to be seen. Mostly, economists have preferred to build mathematical models on the basis of a bunch of assumptions, rather than comprehensively investigate available data for the purpose of creating a grounded theory of economic life.

A very interesting confirmation of the basic idea that Marx had is provided from a most unexpected source: post-Keynesian economics. After mustering a lot of empirical evidence about pricing practices, the leading heterodox "real-world" economist Fred Lee concluded that: 36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia.

However, a sharp distinction must be drawn between Marx's own theory and subsequent Marxist or Sraffian theories. As Lee emphasizes, "the typical statement made by Sraffians and Marxists that prices equal their costs of production (which includes a uniform rate of profit) in long-period positions has no conceptual correspondence to the concepts of costs and prices used by business enterprises." Consequently, the Marxist and Sraffian theories are not grounded in the real world of business operations, because Marxists and Sraffians confuse a purely abstract model with empirical reality. Fred Lee admits that the magnitude and the relative stability of the profit mark-up for products in modern capitalism "remains theoretically underexplained in Post Keynesian theory"

The total circuit of capital

One possible solution to the "transformation problem", ignored in the literature, is that Marx tried to sketch a redistribution of value in too simplistic terms, considering the profitability of different production capitals in abstraction from the total circuit of capital.

The problem that Ricardo failed to solve, was one of how capitals of equal sizes could empirically attract very similar profits, despite empirically manifest unequal expenditures of labour-time. But that problem may be solved more credibly, if we properly consider competition in the sphere of capital finance, i.e. the sphere of credit. In this sense, David Harvey for example mentions that "the growing power of the credit system in relation to industry also tends to force an equalization of the rate of profit (the connection between profit of enterprise and the interest rate is now very strong)" (cited from The Limits of Capital, Verso 2006, p. 303).

See also

• Labour theory of value
• capital controversy
• Cost-of-production theory of value
• Temporal single-system interpretation

References

• Karl Marx, Das Kapital, Volume 3.
• Karl Marx, Grundrisse.
• Christian Bidard and Hans G. Ehrbar, "Relative prices in the classical theory: facts and figures". [12]
• Ulrich Krause and Christian Bidard, "A monotonicity law for relative prices". Economic Theory, vol. 7, issue 1, 1995, pp. 51–61
• Robert Vienneau's FAQ page [13]
• W. Paul Cockshott and Allin F. Cottrell, "Value's Law, Value's Metric", September, 1994 [14]
• Reiner Franke, "Production Prices and Dynamical Processes of the Gravitation of Market Prices". Peter Lang, 1987.
• Makoto Itoh, The Basic Theory of Capitalism.
• G. Stamatis, On the Quantitative Relation between Labour Values and Production Prices. Panteios University, Athens, 1997. [15]
• Ian Wright, "Convergence to natural prices part 1: multisector price and quantity dynamics in simple commodity production", Open University December 2009. [16]
• S. Hollander, Economics of Karl Marx: Analysis and Application. New York: Cambridge University Press, 2008.