In a word, no. While we have assumed the validity of "marginal productivity" theory in relation to capital in the previous two sections, the fact is that the theory is deeply flawed. This is on two levels. Firstly, it does not reflect reality in any way. Secondly, it is logically flawed and, even worse, this has been known to economists for decades. While the first objection will hardly bother most neo-classical economists (what part of that dogma does reflect reality?), the second should as intellectual coherence is what replaces reality in economics. However, in spite of "marginal productivity" theory being proven to be nonsense and admitted as such by leading neo-classical economists, it is still taught in economic classes and discussed in text books as if it were valid.

We will discuss each issue in turn.

The theory is based on a high level of abstraction and the assumptions used to allow the mathematics to work are so extreme that no real world example could possibly meet them. The first problem is determining the level at which the theory should be applied. Does it apply to individuals, groups, industries or the whole economy? For depending on the level at which it is applied, there are different problems associated with it and different conclusions to be drawn from it. Similarly, the time period over which it is to be applied has an impact. As such, the theory is so vague that it would be impossible to test as its supporters would simply deny the results as being inapplicable to their particular version of the model.

Then there are problems with the model itself. While it has to assume that factors are identical in order to invoke the necessary mathematical theory, none of the factors used are homogenous in the real world. Similarly, for Euler's theory to be applied, there must be constant returns to scale and this does not apply either (it would be fair to say that the assumption of constant returns to scale was postulated to allow the theorem to be invoked in the first place rather than as a result of a scientific analysis of real industrial conditions). Also, the model assumes an ideal market which cannot be realised and any real world imperfections make it redundant. In the model, such features of the real world as oligopolistic markets (i.e. markets dominated by a few firms), disequilibrium states, market power, informational imperfections of markets, and so forth do not exist. Including any of these real features invalidates the model and no "factor" gets its just rewards.

Moreover, like neo-classical economics in general, this theory just assumes the original distribution of ownership. As such, it is a boon for those who have benefited from previous acts of coercion — their ill-gotten gains can now be used to generate income for them!

Finally, "marginal productivity" theory ignores the fact that most production is collective in nature and, as a consequence, the idea of subtracting a single worker makes little or no sense. As soon as there is "a division of labour and an interdependence of different jobs, as is the case generally in modern industry," its "absurdity can immediately be shown." For example, "[i]f, in a coal-fired locomotive, the train's engineer is eliminated, one does not 'reduce a little' of the product (transportation), one eliminates it completely; and the same is true if one eliminates the fireman. The 'product' of this indivisible team of engineer and fireman obeys a law of all or nothing, and there is no 'marginal product' of the one that can be separated from the other. The same thing goes on the shop floor, and ultimately for the modern factory as a whole, where jobs are closely interdependent." [Cornelius Castoriadis, Political and Social Writings, vol. 3, p. 213] Kropotkin made the same point, arguing it "is utterly impossible to draw a distinction between the work" of the individuals collectively producing a product as all "contribute . . . in proportion to their strength, their energy, their knowledge, their intelligence, and their skill." [The Conquest of Bread, p. 170 and p. 169]

This suggests another explanation for the existence of profits than the "marginal productivity" of capital. Let us assume, as argued in marginal productivity theory, that a worker receives exactly what she has produced because if she ceases to work, the total product will decline by precisely the value of her wage. However, this argument has a flaw in it. This is because the total product will decline by more than that value if two or more workers leave. This is because the wage each worker receives under conditions of perfect competition is assumed to be the product of the last labourer in neo-classical theory. The neo-classical argument presumes a "declining marginal productivity," i.e. the marginal product of the last worker is assumed to be less than the second last and so on. In other words, in neo-classical economics, all workers bar the mythical "last worker" do not receive the full product of their labour. They only receive what the last worker is claimed to produce and so everyone bar the last worker does not receive exactly what he or she produces. In other words, all the workers are exploited bar the last one.

However, this argument forgets that co-operation leads to increased productivity which the capitalists appropriate for themselves. This is because, as Proudhon argued, "the capitalist has paid as many times one day's wages"rather than the workers collectively and, as such, "he has paid nothing for that immense power which results from the union and harmony of labourers, and the convergence and simultaneousness of their efforts. Two hundred grenadiers stood the obelisk of Luxor upon its base in a few hours; do you suppose that one man could have accomplished the same task in two hundred days? Nevertheless, on the books of the capitalist, the amount of wages would have been the same." Therefore, the capitalist has "paid all the individual forces" but "the collective force still remains to be paid. Consequently, there remains a right of collective property" which the capitalist "enjoy[s] unjustly." [What is Property?, p. 127 and p. 130]

As usual, therefore, we must distinguish between the ideology and reality of capitalism. As we indicated in section C.1, the model of perfect competition has no relationship with the real world. Unsurprisingly, marginal productivity theory is likewise unrelated to reality. This means that the assumptions required to make "marginal productivity" theory work are so unreal that these, in themselves, should have made any genuine scientist reject the idea out of hand. Note, we are not opposing abstract theory, every theory abstracts from reality is some way. We are arguing that, to be valid, a theory has to reflect the real situation it is seeking to explain in some meaningful way. Any abstractions or assumptions used must be relatively trivial and, when relaxed, not result in the theory collapsing. This is not the case with marginal productivity theory. It is important to recognise that there are degrees of abstraction. There are "negligibility assumptions" which state that some aspect of reality has little or no effect on what is being analysed. Sadly for marginal productivity theory, its assumptions are not of this kind. Rather, they are "domain assumptions" which specify "the conditions under which a particular theory will apply. If those conditions do not apply, then neither does the theory." [Steve Keen, Debunking Economics, p. 151] This is the case here.

However, most economists will happily ignore this critique for, as noted repeatedly, basing economic theory on reality or realistic models is not considered a major concern by neoclassical economists. However, "marginal productivity" theory applied to capital is riddled with logical inconsistencies which show that it is simply wrong. In the words of the noted left-wing economist Joan Robinson:

"The neo-classicals evidently had not been told that the neo-classical theory did not contain a solution of the problems of profits or of the value of capital. They have erected a towering structure of mathematical theorems on a foundation that does not exist. Recently [in the 1960s, leading neo-classical economist] Paul Samuelson was sufficiently candid to admit that the basis of his system does not hold, but the theorems go on pouring out just the same." [Contributions to Modern Economics, p. 186]

If profits are the result of private property and the inequality it produces, then it is unsurprising that neoclassical theory would be as foundationless as Robinson argues. After all, this is a political question and neo-classical economics was developed to ignore such questions. Marginal productivity theory has been subject to intense controversy, precisely because it claims to show that labour is not exploited under capitalism (i.e. that each factor gets what it contributes to production). We will now summarise this successful criticism.

The first major theoretical problem is obvious, how do you measure capital? In neoclassical economics, capital is referred to as machinery of all sorts as well as the workplaces that house them. Each of these items are, in turn, made up of a multitude of other commodities and many of these are assemblies of other commodities. So what does it mean to say, as in marginal productivity theory, that "capital" is varied by one unit? The only thing these products have in common is a price and that is precisely what economists do use to aggregate capital. Sadly, though, shows "that there is no meaning to be given to a 'quantity of capital' apart from the rate of profit, so that the contention that the 'marginal product of capital' determines the rate of profit is meaningless." [Robinson, Op. Cit., p. 103] This is because argument is based on circular reasoning:

"For long-period problems we have to consider the meaning of the rate of profit on capital . . . the value of capital equipment, reckoned as its future earnings discounted at a rate of interest equal to the rate of profit, is equal to its initial cost, which involves prices including profit at the same rate on the value of the capital involved in producing it, allowing for depreciation at the appropriate rate over its life up to date.

"The value of a stock of capital equipment, therefore, involves the rate of profit. There is no meaning in a 'quantity of capital' apart from the rate of profit." [Collected Economic Papers, vol. 4, p. 125]

In other words, according to neoclassical theory, the rate of profit and interest depends on the amount of capital, and the amount of capital depends on the rate of profit and interest. One has to assume a rate of profit in order to demonstrate the equilibrium rate of return is determined. This issue is avoided in neo-classical economics simply by ignoring it (it must be noted that the same can be said of the "Austrian" concept of "roundaboutness" as "it is impossible to define one way of producing a commodity as 'more roundabout' than another independently of the rate of profit . . . Therefore the Austrian notion of roundaboutness is as internally inconsistent as the neoclassical concept of the marginal productivity of capital." [Steve Keen, Debunking Economics, p. 302]).

The next problem with the theory is that "capital" is treated as something utterly unreal. Take, for example, leading neoclassical Dennis Robertson's 1931 attempt to explain the marginal productivity of labour when holding "capital" constant:

"If ten men are to be set out to dig a hole instead of nine, they will be furnished with ten cheaper spades instead of nine more expensive ones; or perhaps if there is no room for him to dig comfortably, the tenth man will be furnished with a bucket and sent to fetch beer for the other nine." ["Wage-grumbles", Economic Fragments, p. 226]

So to work out the marginal productivity of the factors involved, "ten cheaper spades" somehow equal nine more expensive spades? How is this keeping capital constant? And how does this reflect reality? Surely, any real world example would involve sending the tenth digger to get another spade? And how do nine expensive spades become nine cheaper ones? In the real world, this is impossible but in neoclassical economics this is not only possible but required for the theory to work. As Robinson argued, in neo-classical theory the "concept of capital all the man-made factors are boiled into one, which we may call leets . . . [which], though all made up of one physical substance, is endowed with the capacity to embody various techniques of production . . . and a change of technique can be made simply by squeezing up or spreading out leets, instantaneously and without cost." [Contributions to Modern Economics, p. 106]

This allows economics to avoid the obvious aggregation problems with "capital", make sense of the concept of adding an extra unit of capital to discover its "marginal productivity" and allows capital to be held "constant" so that the "marginal productivity" of labour can be found. For when "the stock of means of production in existence can be represented as a quantity of ectoplasm, we can say, appealing to Euler's theorem, that the rent per unit of ectoplasm is equal to the marginal product of the given quantity of ectoplasm when it is fully utilised. This does seem to add anything of interest to the argument." [Op. Cit., p. 99] This ensures reality has to be ignored and so economic theory need not discuss any practical questions:

"When equipment is made of leets, there is no distinction between long and short-period problems . . . Nine spades are lumps of leets; when the tenth man turns up it is squeezed out to provide him with a share of equipment nine-tenths of what each man had before . . . There is no room for imperfect competition. There is no possibility of disappointed expectations . . . There is no problem of unemployment . . . Unemployed workers would bid down wages and the pre-existing quantity of leets would be spread out to accommodate them." [Op. Cit., p. 107]

The concept that capital goods are made of ectoplasm and can be remoulded into the profit maximising form from day to day was invented in order to prove that labour and capital both receive their contribution to society, to show that labour is not exploited. It is not meant to be taken literally, it is only a parable, but without it the whole argument (and defence of capitalism) collapses. Once capital equipment is admitted to being actual, specific objects that cannot be squeezed, without cost, into new objects to accommodate more or less workers, such comforting notions that profits equal the (marginal) contribution of "capital" or that unemployment is caused by wages being too high have to be discarded for the wishful thinking they most surely are.

The last problem arises when ignore these issues and assume that marginal productivity theory is correct. Consider the notion of the short run, where at least one factor of production cannot be varied. To determine its marginal productivity then capital has to be the factor which is varied. However, common sense suggests that capital is the least flexible factor and if that can be varied then every other one can be as well? As dissident economist Piero Sraffa argued, when a market is defined broadly enough, then the key neoclassical assumption that the demand and supply of a commodity are independent breaks down. This was applied by another economist, Amit Bhaduri, to the "capital market" (which is, by nature, a broadly defined industry). Steve Keen usually summarises these arguments, noting that "at the aggregate level [of the economy as a whole], the desired relationship — the rate of profit equals the marginal productivity of capital — will not hold true" as it only applies "when the capital to labour ratio is the same in all industries — which is effectively the same as saying there is only one industry." This "proves Sraffa's assertion that, when a broadly defined industry is considered, changes in its conditions of supply and demand will affect the distribution of income." This means that a "change in the capital input will change output, but it also changes the wage, and the rate of profit . . . As a result, the distribution of income is neither meritocratic nor determined by the market. The distribution of income is to some significant degree determined independently of marginal productivity and the impartial blades of supply and demand . . . To be able to work out prices, it is first necessary to know the distribution of income . . . There is therefore nothing sacrosanct about the prices that apply in the economy, and equally nothing sacrosanct about the distribution of income. It reflects the relative power of different groups in society." [Op. Cit., p. 135]

It should be noted that this critique bases itself on the neoclassical assumption that it is possible to define a factor of production called capital. In other words, even if we assume that neo-classical economics theory of capital is not circular reasoning, it's theory of distribution is still logically wrong.

So mainstream economics is based on a theory of distribution which is utterly irrelevant to the real world and is incoherent when applied to capital. This would not be important except that it is used to justify the distribution of income in the real world. For example, the widening gap between rich and poor (it is argued) simply reflects a market efficiently rewarding more productive people. Thus the compensation for corporate chief executives climbs so sharply because it reflects their marginal productivity. Except, of course, the theory supports no such thing — except in a make believe world which cannot exist (lassiez fairy land, anyone?).

It must be noted that this successful critique of neoclassical economics by dissident economists was first raised by Joan Robinson in the 1950s (it usually called the Cambridge Capital Controversy). It is rarely mentioned these days. While most economic textbooks simply repeat the standard theory, the fact is that this theory has been successfully debunked by dissident economists over four decades go. As Steve Keen notes, while leading neoclassical economists admitted that the critique was correct in the 1960s, today "economic theory continues to use exactly the same concepts which Sraffa's critique showed to be completely invalid" in spite the "definitive capitulation by as significant an economist as Paul Samuelson." As he concludes: "There is no better sign of the intellectual bankruptcy of economics than this." [Op. Cit., p. 146, p. 129 and p. 147]

Why? Simply because the Cambridge Capital Controversy would expose the student of economics to some serious problems with neo-classical economics and they may start questioning the internal consistency of its claims. They would also be exposed to alternative economic theories and start to question whether profits are the result of exploitation. As this would put into jeopardy the role of economists as, to quote Marx, the "hired prize-fighters" for capital who replace "genuine scientific research" with "the bad conscience and evil intent of apologetics." Unsurprisingly, he characterised this as "vulgar economics." [Capital, vol. 1, p. 97]