Simply put, Marx's "price of production" (P) is a price which applies to sales of new outputs produced, and it equals cost price (cp) + average profit (ap). The cost price could be computed as the unit-cost of a product, the profit component being the mark-up. 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 "general rate of profit".
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 valorisation process, i.e. 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 (what 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
where c = constant capital (the element of conserved value), v = variable capital, and s = surplus value (the two elements of newly created value). Again, each of these is measured per unit of output. (Marx's standard assumption 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 in different 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 revenues among producing enterprises, what determines this distribution, and what factors affect it. In the Marxian view, 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 mobilisation of capitals).
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.
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 e.g. in the writings of Adam Smith and David Ricardo. In that 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 the dominant interpretation, which suggests that production prices are really a kind of "equilibrium prices". There is textual evidence for that, insofar as Marx sometimes defines the production price as the price which applies if supply and demand are balanced. At other times, he refers to a ""longterm average price" or a ""regulating price".
Others argue that the concept of production price plays a different role in Marx's theory: the aim of the concept 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, and what variables and dimensions are involved here.
In that 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".
This alternative interpretation of production prices rests on three ideas:
(1) 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 business in order to realise maximum surplus value, principally by maximising surplus labour and labor productivity while keeping costs to the minimum.
(2) Marx's critics claimed to prove on the one hand that there existed no logical procedure to derive prices from values, yet on the other hand they also complained Marx's theory is not empirically verifiable or falsifiable. But the latter proposition obviously does not follow from the former. Obviously Marx's theory is verifiable and falsifiable, if we investigate whether price movements and business behaviour observably do 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?
(3) 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 did 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. Equilibrium was less an economic, than a socio-political issue (see also law of value). After all, sorts of economic fluctuations could occur while the relations of production stayed intact, and capital accumulation continued unabated.
Most Marxists missed the fact that Marx identified (though often not very clearly) four main types of production prices:
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?
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 that the output created will equal the sum of input costs incurred plus surplus value, and that the sum of input costs is equal to the production capital invested, given that 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.
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)? Sometimes Marx talks about production prices as theoretical prices (equilibrium prices), at other times as regulating prices or empirical price averages and consequently it remains somewhat ambiguous to what extent such prices exist in reality.
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 profit", applying economy-wide to all industries, would be formed, but in truth he lacked the data to prove it. He did not discuss in any detail the difference between distributed and undistributed profit, and how this might affect profit statements.
The concept of production prices is one "building block" in Marx's theory of the "equalising tendency of the rate of profit through competition" (see Capital Vol. 3, chapter 10 ) 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 capital invested (e.g. 8-12%) 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.
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. But all this has never bothered neo-classical scholars such as Paul Samuelson in their interpretation of what Marx tried to do).
This "accounting" interpretation of production prices (value/price identity at the macro-level) by economists 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 mid-point which fluctuating actual prices would match exactly only by exception.
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 relations set a range or band within which prices will move.
Anwar Shaikh (1977) has modelled the formation and change of production prices mathematically using iterative methods. 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 an average rate of profit for outputs, and returns proportional to capital size.
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.
A lot of criticism of Marx's concept originates from the ambiguities referred to earlier. Consequently, many of the criticisms can be dispelled simply by a more exact definition of the cost, product and revenue aggregates used, and of the timing of transactions.
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, 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. 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.
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; 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 market prices 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 extra surplus value. How could this 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, "The main idea is to improve our economic value-added (EVA) every year so our return of capital is more than our cost of capital." (cited in "The value creation equation", Corporate Finance Magazine, March 2004)
Marx however regarded the prices of production as the "outward expression" of the results of a valorisation process, 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, 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.
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.
But 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 maneouvre 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 deviate from values produced, but also that the sum of prices will 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. 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 (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 modelling, simple logical paradoxes appear of the type that
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.
But whatever view one takes, 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.
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 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 (1984) and Christian Bidard (2004)).
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 relations 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. This type of analysis paves the way for an important new Marxian criticism of Piero Sraffa's otherwise brilliant critique of capital theory.
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 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.
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 transactions between 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 attract very similar profits, despite unequal expenditures of labour-time. But that problem may be solved, if we properly consider competition in the sphere of capital finance, i.e. the sphere of credit.