THE pillars of the system of Marx are his conception of value and his law of value. Without them, as Marx repeatedly asserts, all scientific knowledge of economic facts would be impossible. The mode in which he arrives at his views with reference to both has been described and discussed times without number. For the sake of connection I must recapitulate briefly the most essential points of his argument.
The field of research which Marx undertakes to explore in order " to come upon the track of value" (i. 23) he limits from the beginning to commodities, by which, according to him, we are not to understand all economic goods, but only those products of labour which are made for the market.  He begins with the "Analysis of a Commodity" (i.9). A commodity is, on one side, a useful thing, which by its properties satisfies human wants of some kind; and on the other, it forms the material medium of exchange value. He then passes to an analysis of this latter. "Exchange value presents itself in the first instance as the quantitative relation, the proportion, in which values in use of one kind are exchanged for values in use of another kind, a relation which constantly changes with time and place." Exchange value, therefore, appears to be something accidental. And yet there must be in this changing relation something that is stable and unchanging, and this Marx undertakes to bring to light. He does it in his well-known dialectical manner. "Let us take two commodities, wheat and iron, for example. Whatever may be their relative rate of exchange it may always be represented by an equation in which a given quantity of wheat is equal to a given quantity of iron: for example, 1 quarter wheat = 1 cwt. iron. What does this equation tell us? It tells us that there exists a common factor of the same magnitude in two different things, in a quarter of wheat and in a cwt. of iron. The two things are therefore equal to a third which is in itself neither the one nor the other. Each of the two, so far as it is an exchange value, must therefore be reducible to that third."
"This common factor," Marx goes on, "cannot be a geometrical, physical, chemical or other natural property of the commodities. Their physical properties come into consideration for the most part only in so far as they make the commodities useful, and so make them values in use. But, on the other hand, the exchange relation of commodities is obviously determined without reference to their value in use. Within this relation one value in use is worth just as much as any other, if only it is present in proper proportion. Or, as old Barbon says, "One sort of wares are as good as another, if the value be equal. There is no difference or distinction in things of equal value." As values in use commodities are above everything of different qualities; as exchange values they can only be of different quantities, and they can, therefore, contain no atom of value in use.
"If then we abstract from the value in use of commodities, there remains to them only one common property, that of being products of labour. But even as products of labour they have already, by the very process of abstraction, undergone a change under our hands. For if we abstract from the value in use of a commodity, we, at the same time, abstract from the material constituents and forms which give it a value in use. It is no longer a table, or a house, or yarn, or any other useful thing. All its physical qualities have disappeared. Nor is it any longer the product of the labour of the carpenter, or the mason, or the spinner, or of any other particular productive industry. With the useful character of the labour products there disappears the useful character of the labours embodied in them, and there vanish also the different concrete forms of these labours. They are no longer distinguished from each other, but are all reduced to identical human labour–abstract human labour.
"Let us examine now the residuum. There is nothing but this ghostly objectivity, the mere cellular tissue of undistinguishable human labour, that is, of the output of human labour without regard to the form of the output. All that these things have now to show for themselves is that human labour has been expended in their production–that human labour has been stored up in them; and as crystals of this common social substance they are–values."
With this, then, we have the conception of value discovered and determined. It is in dialectical form not identical with exchange value, but it stands, as I would now make plain, in the most intimate and inseparable relation to it. It is a kind of logical distillation from it. It is, to speak in Marx's own words, "the common element that manifests itself in the exchange relation, or exchange value, of commodities;" or again conversely, "the exchange value is the only form in which the value of commodities can manifest itself or be expressed " (i. 13).
After establishing the conception of value Marx proceeds to describe its measure and its amount. As labour is the substance of value so the amount of the value of all goods is measured by the quantity of labour contained in them, which is, in its turn, measured by its duration,–but not by that particular duration, or working time, which the individual who made the commodity has happened to need, but by the working time that is socially necessary. Marx defines this last as the "working time required to produce a value in use under the normal conditions of production, and with the degree of skill and intensity of labour prevalent in a given society" (i. 14). "It is only the quantity of socially necessary labour, or the working time socially necessary for the production of a value in use, which determines the amount of the value. The single commodity is here to be regarded as an average specimen of its class. Commodities, therefore, in which equal quantities of labour are embodied, or which can be produced in the same working time, have the same value. The value of one commodity is related to the value of any other commodity as the working time necessary for the production of the one is to that necessary for the production of the other. As values, all commodities are only specific quantities of crystallised working time." From all this is derived the subject-matter of the great "law of value," which is "immanent in the exchange of commodities" (i. 141, 150), and governs exchange relations. It states, and must state, after what has gone before, that commodities are exchanged in proportion to the socially necessary working time incorporated in them(i. 52). Other modes of expressing the same law are that "commodities exchange according to their values" (see i. 142, 183; iii. 167), or that "equivalent exchanges with equivalent" (see i. 150, 183). It is true that in isolated cases according to momentary fluctuations of supply and demand prices occur which are over or under the values. But these "constant oscillations of market prices ... compensate and cancel each other, and reduce themselves to the average price as their inner law" (i. 151, note 37). In the long run "the socially necessary working time always asserts itself by main force, like an overruling natural law, in the accidental and ever fluctuating exchange relations" (i. 52). Marx declares this law to be the "eternal law of the exchange of commodities" (i. 182), and "the rational element" and "the natural law of equilibrium" (iii. 167). The inevitably occurring cases already mentioned in which commodities are exchanged for prices which deviate from their values are to be looked upon, in regard to this rule, as "accidental" (i. 150, note 37), and he even calls the deviation "a breach of the law of the exchange of commodities" (i. 142).
On these principles of the theory of value Marx founds the second part of the structure of his teaching, his renowned doctrine of surplus value. In this part he traces the source of the gain which capitalists obtain from their capital. Capitalists lay down a certain sum of money, convert it into commodities, and then–with or without an intermediate process of production–convert these back again into more money. Whence comes this increment, this increase in the sum drawn out as compared with the sum originally advanced? or whence comes "the surplus value" as Marx calls it?
Marx proceeds to mark off the conditions of the problem in his own peculiar way of dialectical exclusion. He first declares that the surplus value cannot originate either in the fact that the capitalist, as buyer, buys commodities regularly under their value, nor in the fact that the capitalist, as seller, sells them regularly over their value. So the problem presents itself in the following way: "The owner of money must buy the commodities at their value, then sell them at their value, and yet at the end of the process must draw out more money than he put in. Such are the conditions of the problem. Hic Rhodus, hic salta!" (i. 150 seq.)
The solution Marx finds in this, that there is one commodity whose value in use possesses the peculiar property of being a source of exchange value. This commodity is the capacity of labour, the working powers. It is offered for sale in the market under the twofold condition that the labourer is personally free, for otherwise it would not be his working powers only that would be for sale, but his whole person as a slave; and that the labourer is destitute of "all the means necessary for the realising of his working powers," for otherwise he would prefer to produce on his own account and to offer for sale his products rather than his working powers. It is by trading in this commodity that the capitalist obtains the surplus value; and he does so in the following way: The value of the commodity, "working powers," is regulated like any other commodity by the working time necessary for its reproduction; that is, in this case, by the working time which is needed to create so much means of subsistence as is required for the maintenance of the worker. If, for example, a working time of six hours is required in a given society for the production of the necessary means of subsistence for one day, and, at the same time, as we will suppose, this working time is embodied in three shillings of money, then the working powers of one day can be bought for three shillings. If the capitalist has concluded this purchase, the value in use of the working powers belongs to him and he realises it by causing the labourer to work for him. But if he made him work only so many hours a day as are embodied in the working powers themselves, and as must have been paid for in the buying of the same, no surplus value would arise. For, according to the assumption, six hours of labour could not put into the products in which they are embodied a greater value than three shillings, and so much the capitalist has paid as wages. But this is not the way in which capitalists act. Even if they have bought the working powers for a price which only corresponds to six hours' working time, they yet make the labourer work the whole day for them. And now in the product made during this day there are incorporated more hours of labour than the capitalist was obliged to pay for. He has, therefore, a greater value than the wages he has paid, and the difference is "surplus value," which falls to the capitalist.
Let us take an example: Suppose that a worker can spin ten pounds of cotton into yam in six hours; and suppose this cotton has required twenty hours of labour for its own production and possesses accordingly a value of ten shillings; and suppose, further, that during the six hours of spinning the spinner uses up so much of his tools as corresponds to the labour of four hours and represents consequently a value of two shillings; then the total value of the means of production consumed in the spinning will amount to twelve shillings, corresponding to twenty-four hours' labour. In the spinning process the cotton "absorbs" another six hours of labour. Therefore the yarn that has been spun is, as a whole, the product of thirty hours of labour, and will have accordingly a value of fifteen shillings. On the supposition that the capitalist has made the hired labourer work only six hours in the day, the production of the yam has cost him at least fifteen shillings: ten shillings for cotton, two shillings for wear and tear of tools, three shillings for wages of labour. Here there is no surplus value.
It is quite a different thing, however, if the capitalist makes the labourer work twelve hours a day. In twelve hours the labourer works up twenty pounds of cotton in which forty hours of labour have been previously embodied, and which are, therefore, worth twenty shillings. He further uses up in tools the product of eight hours' labour, of the value of four shillings. But during a day he adds to the raw material twelve hours' labour, that is, a new value of six shillings. And now the balance-sheet stands as follows: The yarn produced during a day has cost in all sixty hours' labour, and has, therefore, a value of thirty shillings. The outlay of the capitalist amounted to twenty shillings for cotton, four shillings for wear and tear of tools, and three shillings for wages; in all, therefore, only twenty-seven shillings. There remains now a "surplus value" of three shillings.
Surplus value, therefore, according to Marx, is due to the fact that the capitalist makes the labourer work for him a part of the day without paying him for it. In the labourer's working-day two portions may be distinguished. In the first part–the "necessary working time"–the worker produces the means necessary for his own support, or the value of those means; and for this part of his labour he receives an equivalent in wages. During the second part-the "surplus working time"–he is worked for another's benefit (exploité), he produces "surplus value" without receiving any equivalent for it (i. 205 seq.). "All surplus value is in substance the embodiment of unpaid working time " (i. 554).
The following definitions of the amount of surplus value are very important and very characteristic of the Marxian system. The amount of surplus value may be brought into relation with various other amounts. The different proportions and proportionate numbers which arise out of this must be clearly distinguished.
First of all there are two elements to be distinguished in the capital which enables the capitalist to appropriate surplus values, each of which elements in relation to the origin of surplus value plays an entirely different part from the other. Really new surplus value can only be created by the living work which the capitalist gets the worker to perform. The value of the means of production which are used is maintained, and it reappears in a different form in the value of the product, but adds no surplus value. "That part of the capital, therefore, which is converted into the means of production, i.e., into raw material, auxiliary material, and implements of labour, does not alter the amount of its value in the process of production," for which reason Marx calls it "constant capital." "On the other hand, that part of capital which is converted into working powers does alter its value in the process of production. It reproduces its own equivalent and a surplus in addition," the surplus value. Therefore Marx calls it the "variable part of capital" or "variable capital" (i. 199) Now the proportion in which the surplus value stands to the advanced variable part of capital (in which alone the surplus value "makes good its value"), Marx calls the rate of surplus value. It is identical with the proportion in which the surplus working time stands to the necessary working time, or the unpaid labour to the paid, and serves Marx, therefore, as the exact expression for the extent to which labour is worked for another's benefit (exploité) (i. 207 seq.). If, for instance, the working time necessary for the worker to produce the value of his day's wages of three shillings amounts to six hours, while the actual number of hours he works in the day amounts to twelve, so that during the second six hours, which is surplus working time, he produces another value of three shillings, which is surplus value, then the surplus value is exactly equal to the amount of variable capital paid in wages, and the rate of the surplus value is reckoned at 100%.
Totally different from this is the rate of profit. The capitalist calculates the surplus value, which he appropriates, not only upon the variable capital but upon the total amount of capital employed. For instance, if the constant capital be £410, the variable capital £90, and the surplus value also £90, the rate of surplus value will be, as in the case just given, 100%, but the rate of profit only 18%, that is, £90 profit on an invested capital of £500.
It is evident, further, that one and the same rate of surplus value can and must present itself in very different rates of profit according to the composition of the capital concerned: the greater the variable and the less the constant capital employed (which latter does not contribute to the formation of surplus value, but increases the fund, in relation to which the surplus value, determined only by the variable part of capital, is reckoned as profit) the higher will be the rate of profit. For example, if (which is indeed almost a practical impossibility) the constant capital is nothing and the variable capital is £50, and the surplus value, on the assumption just made, amounts to 100%, the surplus value acquired amounts also to £50; and as this is reckoned on a total capital of only £50, the rate of profit would in this case also be quite 100%. If, on the other hand, the total capital is composed of constant and variable capital in the proportion of 4 to 1; or, in other words, if to a variable capital of £50 is added a constant capital of £200, the surplus value of £50, formed by the surplus value rate of 100%, has to be distributed on a capital of £250, and on this it represents only a profit rate of 20%. Finally, if the capital were composed in the proportions of 9 to 1, that is, £450 of constant to £50 of variable capital, a surplus value of £50 would fall on a total capital of £500, and the rate of profit would be only 10%.
Now this leads to an extremely interesting and important result, in pursuing which we are led to an entirely new stage of the Marxian system, the most important new feature which the third volume contains.
 I quote from the second edition (1872) of the first volume of Das Kapital from the 1885 edition of the second volume, and from the 1894 edition of the third volume; and unless I otherwise indicate, I always mean by iii. the first section of the third volume.
 I. 15, 17, 49, 87, and often. Compare also Adler, Grundlagen der Karl Marxschen Kritik der bestehenden Volkswirtschaft, Tubingen, 1887, pp. 210 and 213.
 I gave at the time in another place (Geschichte una Kritik der Kapitalzinstheorieen, 1884, pp. 421 seq.; English translation by Prof. Smart: Macmillan, 1890, pp. 367 seq.) an exhaustive account of this part of his doctrine. I make use of this account now, with numerous abridgments, such as the present purpose demands.